The p-value is the chance of finding a t-value with an absolute value at least as great as the one we actually observed in the sample data assuming the null hypothesis is actually true. The t-value is a way to measure the difference between the population means.
We reject the null hypothesis of the test if the p-value is less than a predetermined threshold (for example, 0.05). We are primarily concerned with the p-value for each form of t-test, and we merely employ the t-value as a first step in that process.
You'll see that we merely used the t-value as a first step before determining the p-value. The genuine value in which we were most interested was the p-value, but first, we had to determine the t-value.
Therefore the p-value is the likelihood that, if the null hypothesis is correct, each test will result in a t-value with an absolute value at least as great as the one we actually observed in the sample data. The t-value is a way to measure the difference between population means.
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The initial bacterium count in a culture is 500. A biologist later makes a sample count ofbacteria in the culture and finds that the relative rate of growth is 40% per hour.(a)Find a function that models the number of bacteria after t hours.(b)What is the estimated count after 10 hours?(c)When will the bacteria count reach 80,000?(d)Sketch the graph of the function . n(t)
a) The function is P = 500e^0.4t
b) The count after 10 hours is 27299
c) it would reach 80000 in 13 hours
What is the function?We know that at this time we are dealing with the population of the bacteria and we have to invoke the exponential growth ideology and we would have;
P = Poe^rt
P = population at time t
Po = Initial population
r = Population growth rate
t = Time taken
Then we have;
P = 500e^0.4t
After ten hours;
P= 500e^0.4 * 10
P = 27299
The count would reach 80000 when;
80000 = 500e^0.4 t
80000/500 = e^0.4 t
160 = e^0.4 t
ln160 = e^0.4 t
ln160 = 0.4t
t = ln160/0.4
t = 13 hours
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In a garden 5/6 of the area is filled with native plants. The native plants take up to 107/4 m2 . Let g represent the total area of the garden. chooses 2 answers. pleas help me :(
The total area of the garden is given as follows:
32.1 m².
How to obtain the total area of the garden?The total area of the garden is obtained applying the proportions in the context of this problem.
The area of native plants is given as follows:
107/4 = 26.75 m².
This area of 26.75 m² represents a fraction of 5/6 of the total area g of the garden, hence the total area of the garden is obtained applying the proportion as follows:
5g/6 = 26.75.
g = 26.75 x 6/5
g = 32.1 m².
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Abdi and Bashir run in an ultra marathon. After 5 hours Abdi is 4 miles behind Bashir If at this point in the race, Abdi begins to run at a constant speed of 8 mph and Bashir runs at a speed of 6 mph. How long will it take for Adbi to catch up with Bashir?
Using the Time-Distance Formula, it will take Adbi 2 hours.
How to Use Time-Distance Formula to Calculate Time?We can use the time-distance formula to find how long it will take for Abdi to catch up with Bashir. The time-distance formula is distance = speed x time.
Let t be the time in hours that it takes for Abdi to catch up with Bashir.
We know that the distance Abdi has covered is 4 miles more than Bashir, and the relative speed between the two runners is 8mph - 6mph = 2mph.
So we can write the equation:
4 = (8 - 6) * t
Solving for t, we get t = 4/2 = 2 hours.
So it will take Abdi 2 hours to catch up with Bashir.
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Find the missing parts of each quadrilateral and name the type of quadrilateral that best describes the figure.
I already know the missing angles, but I'm not sure how to classify these shapes.
The quadrilaterals in a and b have the missing values of x as 85° and 57° respectively and can be best described as a scalene quadrilateral.
What is a scalene quadrilateralA scalene quadrilateral is a four-sided polygon in which all four sides have different lengths and all four angles have different measures. This is also known as an asymmetric quadrilateral.
we shall evaluate for the missing values of x as follows:
x + 109° + 96° + 70° = 360° {sum of interior angles of a quadrilateral}
x + 275° = 360°
x = 360° - 275° {subtract 275° from both sides}
x = 85°
x + 85° + 94° + (180° - 58°) = 360° {sum of interior angles of a quadrilateral}
x + 301 = 360°
x = 360° - 303° {subtract 303° from both sides}
x = 57°
Therefore, the missing values of x for quadrilaterals in a and b are 85° and 57° respectively, and can be best described as a scalene quadrilateral.
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In a right triangle, sin(7x+5)=cos(8x-5). Find the smaller of the triangles two acute angles
In a case whereby a right triangle, sin(7x+5)=cos(8x-5), the smaller of the triangles two acute angles is 43°.
How can the smaller of the triangles two acute angles be calculated?The concept that will be used is right triangle. An acute angle is one that is smaller than 90 degrees in length. The correct angle is larger than this angle (which is equal to 90 degrees).
We can see that sin(7x+5)=cos(8x-5)
An it implies that 7x+5 -8x-5 =90°
15x=90
x= 6
Then 7(6)+5= 47° 8(6)-5 = 43°
Hence the smaller of the triangles two acute angle is 43°
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In exercises 5–8 tell whether a correlation is likely in the situation. If so tell her there’s a casual relationship. Explain your reasoning. 6. favorite color and color of shoes 
ANSWER FAST PLEASE
WILL GIVE BRAINLIEST
There may be a correlation, but there is no direct link. This is because it is more likely that you will get shoes in the color you want.
It's likely that the preferred color and the color of the shoes are related. A person's favorite color may or may not match the color of their shoes, so there is no direct correlation. Particularly, the color of the shoes may have influenced the preferred color.
There may be a correlation, but there is no direct link.
How does correlation work?Correlation is a method for figuring out how two variables relate to each other. You learned that putting two variables on a "scatter plot" can help you figure out if they are usually connected. Despite the fact that there are other measures of association for variables measured at the ordinal or higher level of measurement, correlation is the strategy that is utilized the most frequently.
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56 parts were lost. 3% of the total parts were lost. How many total parts were there?
Answer:
3% = 56
100% = ?
Rule of three:
56 x 100
—————
3
Answer = 1,866.667 ≈ 1.867
Step-by-step explanation:
dont mind the answer below have a great day ______
\|/
Realiza el ejercicio utilizando las fórmulas para la curva normal.
Calcular la proporción de estudiantes que siguen una distribución normal, con media 78 y desviación estándar 36 y tienen puntuaciones que exceden por lo menos en cinco puntos de la puntuación que marca la frontera entre el Apto y No-Apto (es declarado No-Apto el 25 % de los estudiantes que obtuvieron las puntuaciones más bajas).
Datos:
Distribución normal
u = 78
O = 36
The proportion of students that had a grade at least 5 points greater than the 25th percentile is given as follows:
0.7054 = 70.54%.
How to obtain the z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 78, \sigma = 36[/tex]
The 25th percentile is X when Z = -0.675, hence:
-0.675 = (X - 78)/36
X - 78 = -0.675 x 36
X = 53.7
The proportion of students with a grade of at least 58.7 is one subtracted by the p-value of Z when X = 58.7, hence:
Z = (58.7 - 78)/36
Z = -0.54
Z = -0.54 has a p-value of 0.2946.
1 - 0.2946 = 0.7054 = 70.54%.
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Sine/Cosine of Complementary Angles Solve for x
In a right triangle,sin (8x-9) = cos (x+6) Round to the nearest tenth if nessecary
The value of the variable , x is 10. 33
How to determine the value of the variable
It is important to note that in mathematics, complementary angles are defined as angles that sum up to 90 degrees.
Some properties of complementary angles are;
If the addition of two angles add up to 90 degrees in a right angle, they are called complementary anglesC represents complement and also for the corner of a right angleComplementary angles can be adjacent or non-adjacent anglesFrom the information given, we have the angles as;
8x - 9x + 6Equate the angles to 90 degrees
8x - 9 + x + 6 = 90
collect like terms
8x + x = 90 +3
add the like terms, we get;
9x = 93
Make 'x' the subject of formula by dividing both sides by 9
x = 93/9
x = 10. 33
Hence, the value is 10.33
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How to solve -7=5x-2. 2 step equations using inverse operations
Answer:
-1
Step-by-step explanation:
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x.
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x.
So the solution to the equation is x = -1.
Alternatively, you can also use inverse operations to solve the equation by isolating x to one side.
Add 2 to both sides of the equation: -7 + 2 = 5x - 2 + 2. This gives you -5 = 5x
Divide both sides of the equation by 5: -5/5 = 5x/5. This gives you -1 = x
So the solution to the equation is x = -1.
Please answer this question for me
Hector has to put the fixed point of the compass on points A and C.
Option (C) is correct.
What is the angle bisector of an angle?
The angle bisector of an angle is a line, ray, or segment that divides an angle into two congruent angles. It is a line that bisects (divides into two equal parts) the angle.
For example, if you have a right angle of 90 degrees, the angle bisector would be a line that divides the angle into two 45-degree angles.
In the given figure, Hector is using a compass and straightedge to construct the bisector of angle CEB.
So he has to put the fixed point of the compass on points A and C.
Hence, Hector has to put the fixed point of the compass on points A and C.
Option (C) is correct.
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On the coordinate plane, the segment B(1-4) toC(7,4) forms, one side of triangle BCD. The triangle has an area of 15 square units select all points where D you could be
A coordinate plane is a two-dimensional graph that is used to locate points in a plane using an x-axis and a y-axis.
Explain about coordinate plane:Each point on the plane is defined by an x-coordinate (horizontal position) and a y-coordinate (vertical position). It is used in various branches of mathematics and sciences, such as geometry, algebra, and physics. It is a fundamental tool for graphing and analyzing mathematical equations and functions.To find the possible coordinates of point D, we first need to find the equation of the line that passes through points B(1, -4) and C(7, 4). We can use the slope-intercept form (y = mx + b) to find the equation of the line. Each point on the plane can be identified by its x and y coordinates, which are the distances from the point to the y-axis and x-axis, respectively. The x-coordinates are measured to the right of the y-axis, and the y-coordinates are measured upward from the x-axis. The coordinate plane is used to graph equations and inequalities, plot points, and identify patterns in data. It is a fundamental tool for understanding and manipulating mathematical concepts.The slope of the line is (4-(-4))/(7-1) = 8/6 = 4/3.
The y-intercept is -4.
So the equation of the line is y = (4/3)x - 4.
We know that the area of triangle BCD is 15 square units. To find the possible coordinates of point D, we can use the formula for the area of a triangle (A = (1/2)bh). Since we know the area and the base, we can find the height of the triangle and use that to find the possible coordinates of point D.
The equation of the line is y = (4/3)x - 4. We can use this equation to find the y-coordinate of point D.
y = (4/3)x - 4
15 = (1/2)(x)((4/3)x - 4)
By solving the equation above, we can find the possible x coordinate of point D, which are (-2, -4/3) and (12, 4). Therefore, the possible coordinates of point D are (-2, -4/3) and (12, 4).
Note: you can use the same formula to find the y coordinate if you were given the x coordinate of D, but it gives the same solution.
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the late fee for library books is $2.00 plus 15 each day for a book that is late. If Maria's fee for a late book was $3.20, wrote and solve a linear equation to find how many days late the book was
Answer:
8 days
Step-by-step explanation:
I assume you meant $0.15/day late fee (15 cents per day)? If so, the answer is:
x = # of days late
$2.00 + ($0.15/day)x = $3.20
($0.15/day)x = $3.20 - $2.00 = $1.20
x = $1.20/ ($0.15/day) = 8 days
When building a house, the number of days required to build is inversely
proportional to with the number of workers. One house was built in 85 days by 5
workers. How many days would it take to build a similar house with 25 workers?
It would take 17 days to build a similar house with 25 workers.
What is Inverse Proportion?Inverse proportion is a type of proportionality relationship. If two quantities are inversely proportional then as one quantity increases, the other decreases. In inverse proportion, the product of the given two quantities is equal to a constant value
One house was built in 85 days by 5 workers;
The relationship will be;
d ∝ 1/n
where
n = number of workers
d = number of days
d = k/n
when d = 5
k = 85
k = 5 x 85
k = 425
when n = 25
d = 425/25
d = 17
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Complete the following tables with values for the functions f _ and h given that: (a) f is an odd function: (b) g is an even function. (c) h = g(f(x)) h(x)
The result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
f(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
f(x) | 5 | -3 | 0 | -3 | 5
g(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
g(x) | 6 | 0 | 0 | 0 | 6
h(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
h(x) | 6 | 0 | 0 | 0 | 6
h(x) = g(f(x))
For x = -2, h(x) = g(f(-2)) = g(5) = 6
For x = -1, h(x) = g(f(-1)) = g(-3) = 0
For x = 0, h(x) = g(f(0)) = g(0) = 0
For x = 1, h(x) = g(f(1)) = g(-3) = 0
For x = 2, h(x) = g(f(2)) = g(5) = 6
Since f is an odd function and g is an even function, then h(x) = g(f(x)) will be an even function. This means that for any given x, h(x) will always equal 0 or a positive value. For the set of values provided above, the result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
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Hassan's history class is taking a field trip to the state capitol building. The capitol building is
50 miles from Hassan's school. The class plans to stop after 45 minutes, or 0.75 hours, to
view a local monument. The bus driver plans to drive at an average speed of 40 miles per
hour.
Which equation can you use to find how many hours, x, the second part of the trip will take?
The equation that can be used to find how many hours, x, the second part of the trip will take is:
distance = rate x time
Which equation can you use to find how many hours?Where distance is the remaining distance from the capitol building to the school, rate is the average speed of the bus, and time is the time it takes to travel that distance.So, if we know that the distance is 50 miles and the rate is 40 miles/hour, we can find the time it takes to travel the remaining distance by plugging these values into the equation and solving for x:50 miles = 40 miles/hour x xthen by dividing both sides by 40 miles/hourx = 50/40 = 1.25 hours The equation to use to find how many hours, x, the second part of the trip will take is:distance = rate x timeIn this case, the distance is the remaining distance from the capitol building to the school, which is 50 miles - (40 miles/hour x 0.75 hours) = 35 miles. The rate is the average speed of the bus, which is 40 miles/hour. Therefore, the equation to find the time, x, of the second part of the trip is:35 miles = 40 miles/hour x xTo solve for x, divide both sides of the equation by 40 miles/hour:x = 35 miles / 40 miles/hour = 0.875 hours, or 52.5 minutes.To learn more about capitol building refer to;
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Solve for the value of n.
(6n+5)°
(4n-5)°
Step-by-step explanation:
(6n+5)°(4n-5)°
use the method of expand
6n(4n-5)+5(4n-5)
24n²-30n+20n-25
24n²- 10n -25
use middle term/ quadratic formula
n=5/4 (1.25) or n= -5/6 (-0.833333)
4. A distributor of fasteners is opening a new plant and considering whether to use a mechanized process or a manual process to package the product. The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag. The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag. The company expects to sell each bag of fasteners for $2.75. a) What is the break-even point for the manual process (in units)?
166158 is the break-even point for the manual process
What is Expression?An expression is combination of variables, numbers and operators.
Given that The manual process will have a fixed cost of $36,234 and a variable cost of $2.14 per bag.
Let the number of bags will be x
36234+2.14x..(1)
The mechanized process would have a fixed cost of $84,420 and a variable cost of $1.85 per bag.
84420+1.85x..(2)
From equation 1 and 2
36234+2.14x=84420+1.85x
2.14x-1.85x=84420-36234
0.29x=48186
Divide both sides by 0.29
x=166158
Hence, 166158 is the break-even point for the manual process
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A survey was done 1/4 voted for a restaurant 4/7 voted a library the rest voted for a gym what fraction voted for the gym
The fraction that voted for the gym is calculated as: 5/28.
How to Use Fractions to Solve Word Problems?To find out what fraction voted for the gym, you have to subtract the fractions that voted for the restaurant and the library from 1, which represents the total number of people surveyed.
You can do this by adding the fractions that voted for the restaurant and the library and then subtracting the sum from 1.
(1/4) + (4/7) = (7/28) + (16/28) = (23/28)
so 1 - (23/28) = (5/28)
Therefore, 5/28 of the people surveyed voted for the gym.
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50% means___ parts of a total 200
Answer:
Step-by-step explanation:
50% of 200 is =100
Today 5 friends went out for lunch. Their total bill was $35.20 including tax and gratitude. They decide to split the bill equally and each paid with a $10 bill how much money will each person get back
??
Answer: The total bill including tax and gratitude is $35.20
And each one of the 5 friends paid $10 for the bill.
So the total amount paid is $10*5 = $50
If each person paid $10 and the total bill was $35.20
then the change will be $50-$35.20 = $14.80
And since they split the bill equally then each one of them will get back $14.80/5 = $2.96
So each person will get back $2.96
Step-by-step explanation:
If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is __________.
If a particular sample has 36 participants and the other sample has 40 participants, the total degrees of freedom for the study is
What is the degrees of freedom?In Mathematics, the degrees of freedom in a sample are typically used to correct a possible bias that exists between the alternative and null hypotheses.
Mathematically, total degrees of freedom for the study can be calculated by using this mathematical expression:
v = n - k
Where:
v represents the total degree of freedom.n represents the number of individuals in a samplek represents the number of parameters being estimated.Note: k is equal to 2 in this scenario.
Total degrees of freedom, v = n₁ + n₂ - k
Total degrees of freedom, v = 36 + 40 - 2
Total degrees of freedom, v = 74.
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suppose that a large influx of electric scooter rentals in a crowded downtown area results in a lot of new riders on the streets. for their safety, the mayor of the city decides to enact a law requiring helmets when renting scooters. these new helmets reportedly decrease the probability of injury by 29% in the event of a scooter crash. While the new helmets (increase/decrease) the probability of injury resulting from a scooter accident, they also incentivize individuals to ride (more/less) recklessly, which could (increase/decrease) the number of scooter collisions and therefore injuries to renters. Please choose one
While the new helmets decrease the probability of injury resulting from a scooter accident, but they also incentivize individuals to ride more recklessly, which could increase the number of scooter collisions and therefore injuries to renters.
The reason for the above statement is based on the concept of risk compensation. When the perceived risk of an activity is reduced, individuals may engage in more risky behavior. For example, if individuals believe that wearing a helmet makes them safer while riding a scooter, they may feel less concerned about the potential consequences of riding recklessly, leading to an increase in the number of accidents. On the other hand, the helmet does decrease the probability of injury in the event of a crash, but an increase in the number of crashes could lead to an overall increase in the number of injuries, offsetting the protective effect of the helmets. Therefore, the net impact of the new helmets on the number of scooter injuries is unclear, and further study is needed to determine their overall effect.
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Elizabeth practices the piano 504 minutes in 2 weeks. Assuming she practices the
same amount every week, how many minutes would she practice in 1 weeks?
Elizabeth will practice piano for 252 minutes in one week by solving function f(x)=504x where x = time in multiple of 2years.
What is a function?
A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).
There are several types of functions in math. Some important types are:
Injective function or One to one function: When there is mapping for a range for each domain between two sets.
Surjective functions or Onto function: When there is more than one element mapped from domain to range.
Polynomial function: The function which consists of polynomials.
Inverse Functions: The function which can invert another function.
Now,
As given
f(x)=504x where x = time in multiple of 2 years
For 1 year x=1/2
Hence,
y=504*1/2
y=252 minutes
Elizabeth will practice piano for 252 minutes in one week.
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in trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the [ select ] , the value of the hypotenuse is [ select ] , and is the angle adjacent to the [ select ] .
In trigonometry it is important that the right triangles (reference triangles) have a consistent orientation. the reference triangles always have a leg perpendicular to the y-axis , the value of the hypotenuse is positive , and is the angle adjacent to the y-axis and hypotenuse.
A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. They represent, successively, Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent.
So, when we graph a right angle triangle, we draw a side of triangle perpendicular to y-axis and another side will be on y-axis. The remaining side left would be hypotenuse that will always be positive and is adjacent to the side perpendicular to y-axis and the side on the y-axis.
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NO LINKS!!
58. You invest $200 in an annuity that earns 7% annual interest. After how many years will the value of the annuity double?
Answer:
The time taken for $200 invested at 7% annual interest compounded yearly:
[tex]\boxed{\mathrm{10.245 \; {years}}}[/tex]
which roughly works out to
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]
Step-by-step explanation:
The formula for the accrued value of an amount P deposited at i% interest for a time period of t years compounded annually is given by the formula
[tex]\boxed{A = P(1 + r)^t\;\cdots[1]}[/tex]
Here A is the accrued value, P the principal and r = i/100
If you are given A, P and r we can compute t by taking the logarithms on both sides
In Equation [1] we get
[tex]\dfrac{A}{P} = (1 + r)^t \;\cdots[2][/tex]
Taking logs on both sides,
[tex]\log A - \log P = \log((1+r)^t)\\\\\log x^a = a \log x\\\\\\[/tex]
Therefore the right side becomes
[tex]t \log (1+r)[/tex]
Replacing right side of equation [2] with this expression yields
[tex]\log A - \log P = t \log (1+r)\\\\\textrm{Or, }\\\\t =\dfrac{ \log A - \log P}{\log (1 + r)}\\\\[/tex]
This is the general equation for determining how long it will take for the principal P to reach the value A if compounded annually at rate r(in decimal)
Since we are interested in seeing our principal P=200 double to A = 400 at r = 7% = 7/100 = 0.07
and
1 + r = 1 + 0.07 = 1.07
[tex]t = \dfrac{\log 400 - \log 200}{\log 1.07}\\\\[/tex]
[tex]t = \boxed{10.245 \; \textrm{years}}[/tex]
or approximately
[tex]\boxed{\mathrm{10\;years\;and\;3\;months}}[/tex]
Answer:
10.24 years (approx. 10 years 3 months)
Step-by-step explanation:
Most fixed annuities pay annual compound interest.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ A=P\left(1+r\right)^{t}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
A = $400 (double the principal)P = $200r = 7% = 0.07To calculate after how many years the value of the annuity will double, substitute the given values into the formula and solve for t:
[tex]\implies 400=200(1+0.07)^t[/tex]
[tex]\implies 2=(1.07)^t[/tex]
[tex]\implies \ln 2=\ln (1.07)^t[/tex]
[tex]\implies \ln 2=t \ln 1.07[/tex]
[tex]\implies t=\dfrac{\ln 2}{\ln 1.07}[/tex]
[tex]\implies t=10.2447683...\rm years[/tex]
Therefore, the value of the annuity will double after 10.24 years (approximately 10 years 3 months).
Find the point on the curve y = -x^2 - 2 that is closest to the point (0, 1)
Answer:
[tex](0,-2)[/tex]
Step-by-step explanation:
Let the coordinates of the desired point be [tex](a, -a^2-2)[/tex]. Let the distance of this point from [tex](0,1)[/tex] be [tex]f(a)[/tex].
By the distance formula, [tex]f(a)=\sqrt{a^2+(a^2+3)^2}[/tex].
Clearly, [tex]f(a)[/tex] is minimized when the radicand is minimized.
Clearly, the radicand is always increasing, so the minimum is achieved at the left endpoint of the maximal domain of [tex]f(a)[/tex], which is [tex]a=0[/tex].
So, the coordinates are [tex](0,-2)[/tex].
The point on the curve y = -x^2 - 2 that is closest to the point (0, 1) will be (0, -2)
How to calculate the value?From the information, we want to know the point on the curve y = -x^2 - 2 that is closest to the point (0, 1).
Let the coordinates of the desired point be illustrated as (a - a² - 2).
The distance of the point from (0, 1) is depicted as f(a).
When the radicand is minimized, f(a) is minimized.
In this case, the minimum will be achieved at the left endpoint of the maximal domain of f(a) which is a = 0.
Therefore, the coordinates will be (0, -2).
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A ball is thrown straight down from the top of a 220-foot building with an initial velocity of - 22 feet per second. (Use the position function s(t)=−16t2+v0t+s0 for free-falling objects.)
(a) What is its velocity after 3 seconds?
(b) What is its velocity after falling 108 feet?
The velocity after 3 second is -118 ft/sec and the velocity after falling 108 feet is -87.6 ft/sec.
(a)
For the given position function
[tex]s(t)=-16t^2+v_0.t+s_0[/tex]
The ball is dropped from top of the building of height 220 ft, therefore
[tex]s_0=220ft[/tex]
Also, the initial velocity of the ball is −22 feet per second, thus.
[tex]v_0=22\frac{ft}{s}[/tex]
We will differentiate the position function to find the velocity function and then calculate velocity at (a) t=3sec and (b) after failing 108 ft.
Differentiate Position function to acquire the velocity function v(t).
[tex]s(t)=-16t^2+v_0.t+s_0\\\\s'(t)=-32t+v_0[/tex]
Now substitute t=3s,
v(3) = -32(3) + (-22)
v(3)= -118 ft/sec
b)
To find the velocity of ball after falling 108 ft, first we need to find the time at which ball is dropped 108 ft. and then find velocity at that time using velocity function.
let s(t)=108 ft, then using position function, we can write
[tex]s(t)=-16.t^2+v_0t+s_0\\\\108=-16t^2+(-22)t+220\\\\-16t^2-22t+112=0[/tex]
After solving the quadratic equation, we get
t= -3.42 and 2.05
Since time always positive,
therefore t=2.05 sec.
v (2.05) = -32(2.05)-22
v (2.05) = -87.6 ft/sec
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Use the Empirical The mean speed of a sample of vehicles along a stretch of highway is 70 miles per hour, with a standard deviation of 5 miles per hourEstimate the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour(Assume the data set has a bell-shaped distribution )
Using the empirical rule, 95% of vehicles travel between 60 miles per hour and 80 miles per hour.
What is the empirical rule?Generally, Given that
Mean = 66 and Standard deviation 4To find the percent of vehicles whose speeds are between 60 miles per hour and 80 miles per hour
60 = 70-(2*5) ,
this shows that the 58 value is 2 standard deviations below the mean
and
80 = 70 +( 2*5)
This shows that the 74 value is 2 standard deviations above the mean
Using the empirical rule, we know that 95% of data fall within 2 standard deviations from the mean.
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Please help me and give me all 3 of the answers i dont need an expalanation or anything just the answers this is due in 25 minutes.
Simplify all:
a) 2/5 : 3/4 = 2/5 × 4/3 = 8/15b) 9/4 : (- 3/4) = - 9/4 × 4/3 = - 9/3 = - 3c) - 5/7 : (- 1/3) = 5/7 × 3 = 15/7 or 2 1/7d) - 5/3 : 1/6 = - 5/3 × 6 = - 10