tangential acceleration a in the form without finding t and n is |a|= T+ t N
The tangential acceleration is a measure of the rate of change in the magnitude of the velocity vector, i.e. speed, and the normal acceleration are a measure of the rate of change of the direction of the velocity vector.
r(t)=(cost+ t sin t )i +( sin t−t cost)j
first find the particle's velocity.
[tex]v=dr/dt\\=(−sint+sint+tcost)i^+(cost−cost+tsint)j^\\\\ \\=(tcost)i^+(tsint)j^[/tex]
find the speed.
|v|=[tex]\sqrt{t^{2} cos^{2}t+ t^{2} sin^{2}t }[/tex]
= √t^2
=t
When t>0 , |t| simply becomes t .
We know that a T= [tex]\frac{d}{dt}[/tex]|v|
, which we can use to find that [tex]\frac{d}{dt}[/tex](t)=1
Now that we know a T , we can use it to find a N
a=(cost−t sin t ) i+(sin t +t cos t)j
|a|^2=t^2+1
a N=√(t^2+1) -1
= t
By substituting this back into the original definition, we find that
|a|=(1)T+(t)N=T+ t N
a in the form without finding t and n is |a|= T+ t N
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the sum of three consecutive integers is 15. how many distinct prime factors does the product of these numbers have
Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors
Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
As we know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.
The numbers must be 4,5 , and 6 .
4+5+6=15 and
4*5*6=120
=2^3*3*5
Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors.
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Distinct prime factors do the product of these numbers have 2,3, and 5 are the three distinct prime factors
Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
As we know, a composite number has more than two factors, therefore, this method is applicable only to composite numbers and not to prime numbers.
The numbers must be 4,5, and 6.
4+5+6=15 and
4*5*6=120
=2^3*3*5
Distinct prime factors the product of these numbers have 2,3, and 5 are the three distinct prime factors.
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Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S'. Which rule describes this transformation?
Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S' using the rule is (x, y) ⇒ (x + 8, y + 7)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Transformation can either be rigid like translation, rotation, reflection or it can be non rigid like dilation.
Translation is a rigid transformation because it preserves the shape and size. Translation is the movement of a point either up, left, right or down in the coordinate plane.
Quadrilateral PQRS was translated 8 units to the right and 7 units up to create quadrilateral P'Q'R'S'.
The rule is (x, y) ⇒ (x + 8, y + 7)
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if the p value is less than alpha in a two-tailed test
If the p-value is less than α in a two-tailed test then the null hypothesis should be rejected.
Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution.
A method for drawing statistical conclusions from population data is hypothesis testing. It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an experiment are reliable.
Before doing the hypothesis testing, a null hypothesis and an alternative hypothesis are established.
Thus, If the p-value is less than α in a two-tailed test then the null hypothesis should be rejected.
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assume that t is a linear transformation. find the standard matrix of t.
If T is a linear transformation then the standard matrix of T is [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].
What is a matrix?
A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.
The transformation is given as - T : IR² → IR²
Take the (x,y) values as x(1,0) and y(0,1)
(x,y) = x(1,0) + y(0,1)
Apply the transformation -
T(x,y) = T[x(1,0) + y(0,1)]
Since T is a linear map then -
T(x,y) = x T((1,0)) + y T((0,1))
Now, substitute the values -
T(x,y) = x Te1 + y Te2
T(x,y) = x [e1 - 19e2] + y [e2]
T(x,y) = x e1 + e2(-19x + y)
Resubstitute the values back -
T(x,y) = x (1,0) + (0,1)(-19x + y)
T(x,y) = (x , -19x+y)
For T : IR² → IR²
T(x,y) = (ax+by , cx+dy)
Then A = [tex]\left[\begin{array}{ccc}a&b\\c&d\end{array}\right][/tex]
So, now the matrix A is -
A = [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex]
Therefore, the matrix is [tex]\left[\begin{array}{ccc}1&-19\\0&1\end{array}\right][/tex].
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PLEASE HELP ASAP
choose the method that would be BEST to represent the information.
——————————————————
scatter plot
stem-and-leaf plot
histogram
box-and-whisker plot
——————————————————
Best data tools to represent each information with the options from the image;
Scatter plot - 7th, 9th, 10th and 12th
stem-and-leaf plot - 1st, 3rd, 5th
histogram - 4th, 8th
box-and-whisker plot - 2nd, 6th, 11th
What are data representations?The form in which data is stored, processed, and transmitted is referred to as data representation. Scatter plot are graphs that show the relationship between two variables in a data set eg. to plot heights and weights of a group of people.
Stem-and-leaf plot is a table in which each data value is divided into a "stem" (the first digit or digits) and a "leaf" (usually the last digit) like; To show how many A's, B's, C's, D's and F's there were on a test.
Histogram are graphs that uses rectangles to show the frequency of numerical data such as to plot how many students brought lunch at school each month
Box-and-whisker plot is a graphical method of representing variation in a set of data such as to show the medians of quartiles of the grades on the chapter 5 test for 3rd periods and to show the median score of the basket ball games.
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How many years is 1 billion seconds?
for an approximate result, divide the time value by 3.154e+7
so the answer is 31.71 calendar years
There are approximately 31.71 years in 1 billion seconds. The solution has been obtained by using the unit conversion.
What is unit conversion?
A unit conversion is used to express the same attribute in a different unit of measurement. Instead of using hours to represent time, you could use minutes, and instead of using miles to express distance, you could use feet. Measurements are frequently requested in one set of units, such as chains, but are given in another set, such as feet.
We are given 1 billion seconds which are to be converted into years.
We know that 1 second = 3.171e-8 years
So,
⇒1,000,000,000 seconds = 1,000,000,000 * 3.171e-8
⇒1,000,000,000 seconds = 31.71 years
Hence, there are approximately 31.71 years in 1 billion seconds.
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Let v be the volume of the solid obtained by rotating about the y-axis the region bounded y = 9x and y = x2 9. Find v by slicing.
the titanic sunk more than 100 years ago. below is a summary of the class and fate of each passenger. show the use of an appropriate conditional probability formula to calculate the following: class survived died total first 201 123 324 second 118 166 284 third 181 528 709 total 500 817 1317 (a) if the passenger died, what is the probability they were in third class? (b) find the probability that a passenger survived given that they were in first class.
(a) The probability that a passenger who died was in the third class is 528 / 817.
we can find the probability by using the formula:
P(Third Class | Died) = P(Third Class and Died) / P(Died)
Where,
P(Third Class and Died) = the joint probability of a passenger being in third class and dying
P(Died) = the probability of a passenger dying regardless of class.
We can find P(Third Class and Died) by adding the no. of passengers in third class who died (528) and then dividing by the total no. of passengers (1317)
P(Third Class and Died) = 528 / 1317
Now we can find P(Died) by adding the no. of passengers who died (817) and dividing by the total no. of passengers (1317)
P(Died) = 817 / 1317
By using the values we got, we can find P(Third Class | Died):
P(Third Class | Died) = P(Third Class and Died) / P(Died) = 528 / 817
So, the probability that a passenger who died was in the third class is 528 / 817.
(b) The probability that a passenger survived given they were in first class is 201 / 324
we can find the probability by using the formula:
P(Survived | First Class) = P(Survived and First Class) / P(First Class)
Where,
P(Survived and First Class) = joint probability of a passenger surviving and being in first class.
P(First Class) = probability of a passenger being in first class regardless of survival.
We can find P(Survived and First Class) by adding the no. of passengers in first class who survived (201) and dividing by the total no. of passengers (1317)
P(Survived and First Class) = 201 / 1317
Now we can find P(First Class) by adding the no. of passengers in first class (324) and dividing by the total no.of passengers (1317):
P(First Class) = 324 / 1317
By using the values we got, we can find P(Survived | First Class):
P(Survived | First Class) = P(Survived and First Class) / P(First Class) = 201 / 324
So, the probability that a passenger survived given they were in first class is 201 / 324.
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The numbers of hours worked (per week) by 400 statistics students are shown below.Number of hours Frequency 0 - 9 20 10 - 19 80 20 - 29 200 30 - 39 100. The cumulative percent frequency for students working less than 20 hours per week is a.20% b.25% c.80% d.100%
The cumulative percent frequency for students working less than 20 hours per week is 25%.
In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on then, frequencies that are obtained this way are known as cumulative frequency (c.f.). A table that displays the cumulative frequencies that are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table. There are two types of cumulative frequency - lesser than type and greater than type. Cumulative frequency is used to know the number of observations that lie above (or below) a particular frequency in a given data set. Cumulative frequency is the total frequencies showcased in the form of a table distributed in class intervals. There are two types of cumulative frequency i.e. lesser than and greater than, let us learn more about both types.
The number of hours frequency is given as follows:
Number of hours Frequency Cumulative frequency
0 - 9 20 20
10 - 19 80 100
20 - 29 200 300
30 - 39 100 400
So, the cumulative percent frequency for students working less than 20 hours per week is
= (No. of students working less than 20 hours/ total number of students)* 100
= (100/400)*100
= 25%
Thus, the cumulative percent frequency for students working less than 20 hours per week is 25%.
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One brick is 215 mm long. How many of these bricks, put end to end, WIll cover a 5.15 meter wall?
Answer:
24 bricks will cover a 5.15 meter wall
Step-by-step explanation:
1 meter = 1000 mm
5.15 meters = 5150 mm
5150/215 = 23.9534884
23 bricks will not be enough because 23 x 215 = 4945
24 will be the better option because 215 x 24 = 5160
So 24 bricks will cover a 5.15 meter wall
Molly uses 9.3 pints of blue paint and white paint to paint her bedroom walls.
2
5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
PLEASE HELP!!!
The pints of white paint molly used to paint her bedroom walls is 5.58 pints.
How many pints of white paint did molly use?Quantity of paint molly used for her bedroom walls= 9.3 pints
Fraction of blue paint= 2/5 of 9.3 pints
= 2/5 × 9.3
= 0.4 × 9.3
= 3.72 pints
Quantity of white paint = Quantity of paint molly used for her bedroom walls - Quantity of blue paint
= 9.3 pints - 3.72 pints
= 5.58 pints
Hence, Molly used 5.58 pints of white paint to paint her bedroom walls.
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A hore named northern dancer won the Kentucky derby with a time of exactly 2 minute. At thi contant rate, how long would it take Northern Dancer to run the Belmont take?
Northern Dancer will take 2 2/5 minutes to run the Belmont stakes
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
2 minutes / (1 1/4 miles) = x / (1 1/2 miles)
We transform the mixed fractions into improper fractions and we have:
1 1/4 =
[(4*1)+1])/ 4=
(4+1) / 4 =
5/4
1 1/2 =
[(2*1)+1] / 2 =
(2+1) / 2 =
3/2
Substituting and clearing the value we get:
2 minutes /5/4 miles = x / 3/2 miles
8/5 = 2x/3
2x = 8/5 * 3
2x = 24/5
x = 24/5 / 2
x = 24/10
x = 12/5 = 2 2/5 minutes
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Correctly written question:
A Horse named Northern dancer won the Kentucky derby with a time of exactly 2 minutes. At this rate, how long would it take Northern dancer to run the Belmont stakes? The Kentucky Derby is 1 1/4 miles in the Belmont stakes is 1 1/2 miles.
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
What is the domain of the relation?
{−3, −2, −1, 0, 1, 2, 4}
{−3, 0, 1, 4}
{−2, −1, 0, 1, 4}
{−3, −1, 0, 2, 4}
The domains of the relation are (-3, -2, -1, 2, 4)
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The independent variables are the domain of the relation.
Now,
The coordinates from the graph are:
(2, 0), (4, -1), (-1, 1), (-3, 4), and (-2, 0)
Now,
2, 4, -1, and -3 are the independent variables.
The domains are (-3, -2, -1, 2, 4)
Thus,
The domains are (-3, -2, -1, 2, 4)
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find the number of terms in an AP whose first term is 5 common difference is 3 and the sum is 55
On solving the provided question, we can say that Hence, there are 26 terms in given arithmetic progression.
What is arithmetic progression?A series of numbers known as an arithmetic progression is one in which the difference between each term and the term before it stays constant over the course of the sequence. In this mathematical progression, the constant difference is referred to as the tolerance. A series of numbers is arranged in an arithmetic progression (AP) if the difference between any two consecutive integers is a constant value. additionally known as mathematical order. The gap between succeeding terms in an arithmetic progression is always the same. Because the difference between succeeding phrases is always 2, episodes 3, 5, 7, and 9 are examples of arithmetic.
Clearly, the given sequence is an AP with first term a=5 and common difference d=3.
Let there are n terms in this AP. Therefore,
⇒5+(n−1)3=80
⇒(n−1)3=75
⇒n−1=25
⇒n=26
Hence, there are 26 terms in given AP
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
What is the least number of items Team A will need to sell to avoid losing money?
Team A will need to sell at least 256 bags of popcorn to avoid losing money.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given total amount to be raised by each team is $100,
Team A wants to sell popcorn,
rent of popcorn machine = $15
total cost to be earned for team B = $100 + $15 = $115
let the number of candies sold be x
cost used in popcorn bag = $0.05 per stick
cost used in x popcorn bag = $0.05x
the selling price of each popcorn bag = $0.50
the selling price of x popcorn bag = $0.50x
total gain = $0.50x - $0.05x
total gain = $0.45x
minimum number of popcorn bags to be sold for no loss
$0.45x = $115
x = 115/0.45
x = 255.55
x = 256
Hence for no loss, at least 256 popcorn bags are to be sold.
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Solve the following pair of equations for the vectors u and v. Assume i = (1,0) and j = (0;1).
the solution to the pair of equations is u = (1,1) and v = (1,0).
u + 3v = (2,1)
3u + v = (3,2)
u = (1,1) and v = (1,0)
The first equation can be written as:
u + 3v = (2,1)
We can rewrite this equation as:
u + 3(1,0) = (2,1)
By substituting the values of i and j, we can solve for u:
u + (3,0) = (2,1)
u = (2-3,1) = (-1,1)
Now, we can substitute the value of u in the second equation:
(1,1) + v = (3,2)
By subtracting (11) on both sides, we can solve for v:
v = (3-1,2-1) = (2,1)
Therefore, the solution to the pair of equations is u = (1,1) and v = (1,0).
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todd has 48 words to spell for a puzzle. as an incentive, his mother offers to pay him 20 cents for each word he spells correctly, if todd will pay her 5 cents for each word he spells incorrectly. he earned $7.35 how many words did he spell correctly
Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spell correctly 39 words and 9 words missed.
Given that,
Todd has 48 words to spell for a puzzle
His mother offers to pay him 20 cents for each word
If Todd will pay her 5 cents for each word he spells incorrectly,
Let x= number of words Todd spells correctly
48-x = number of words that he misses
In order to avoid the decimals, let's solve this in "cents". Does that make "cents" to you, It means that he gets 20 cents for correct words, he pays 5 cents for words missed, and there is a total income of 735 cents. Here is the equation:
[tex]20*x[/tex] -5(48-x) = 735
[tex]20x[/tex] - 240 + [tex]5x[/tex] = 735
[tex]25x[/tex] - 240 = 735
[tex]25x[/tex] = 735 + 240
[tex]25x[/tex] = 975
[tex]x[/tex] = 39 words correct
48-39 = 9 words missed
So,
39*$.20 -9*$.5 = $7.35
$780-$45 = $735
Therefore,
Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spell correctly 39 words and 9 words missed.
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Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spells correctly 39 words and 9 words missed.
Given that,
Todd has 48 words to spell for a puzzle
His mother offers to pay him 20 cents for each word
If Todd will pay her 5 cents for each word he spells incorrectly,
Let x= number of words Todd spells correctly
48-x = number of words that he misses
In order to avoid the decimals, let's solve this in "cents". Does that make "cents" to you, It means that he gets 20 cents for correct words, he pays 5 cents for words missed, and there is a total income of 735 cents. Here is the equation:
20x -5(48-x) = 735
20x - 240 + 5x = 735
25x - 240 = 735
25x = 735 + 240
25x = 975
x = 39 words correct
48-39 = 9 words missed
So,
39*$.20 -9*$.5 = $7.35
$780-$45 = $735
Therefore,
Todd has 48 words to spell for a puzzle, then he earned $7.35 and he spells correctly 39 words and 9 words missed.
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find a parametrization for the line in which the planes intersect:
3x-6y-2z=3 and 2x y-2z = 2
The parametrization of the line of intersection of the two planes is <12, -6, 12>
A parametrization is a way of representing a line or a curve using a set of parameters.
First, we can find the normal vectors of the two planes.
For the first plane, the normal vector is given by <3, -6, -2>, and for the second plane, the normal vector is given by <2, 1, -2>.
The line of intersection will be parallel to the cross product of these two normal vectors, which is <12, -6, 12>.
Plugging in the values from the first plane, we get:
3x - 6y - 2z = 3
3x = 6y + 2z + 3
x = 2y + z + 1
Now that we have a point on the line, we can use this to parametrize the line.
We can use the direction vector <12, -6, 12> and the point <1, 0, 0> to find the parametrization of the line:
x = 1 + t * 12
y = 0 - t * 6
z = 0 + t * 12
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hich of the following is a case in which the area bounded by two curves is most easily found by integrating with respect to y?
The parabola and line's intersection can be easily determined which the area bounded by two curves is most easily found by integrating with respect to y. So the option A is correct.
We can readily locate the area by looking at the following sketches; the first sketch, integrating with respect to x, is in figure one.
The curve in the first illustration is a parabola and a line, as you can see.
The parabola and line's intersection can be easily determined.
The area between the curves is then calculated using the formula
A = integration from a to b [(higher curve) - (lower curve)] dx,
which means that the first sketch represents the right response.
So, the first option A is correct one.
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The complete question is given below:
Drag each symbol to the correct location on the equation. Not all symbols will be used. A group of third-grade and fourth-grade students are taking a field trip. The group will fill a total of vans to take them on the field trip. Each van seats 8 students. There are 27 third-grade students in the group. The rest of the students in the group are fourth-graders. Complete the equation to show how to find , the number fourth-grade students in the group.
The equation that represents the number of fourth-grade students in the group will be 4 x 8 - 27 = f.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The capacity of four vans is given as,
⇒ 4 x 8
There are 27 third-grade students in the group. Then the number of fourth-grade students in the group will be given as,
4 x 8 - 27 = f
The equation that represents the number of fourth-grade students in the group will be 4 x 8 - 27 = f.
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15. In Houston, taxis charge $3 plus $.75 per mile for an airport pickup. How far from the airport can Courtney
travel for $12?
It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.M is 12.
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
3 + 0.75m = 12
(3/4)m = 9
m=12
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6.5 m far from the airport can Courtney travel for $12.
What is a linear equation?
It is referred to as the relationship between two variables, and a straight line is produced when the linear equation's graph is shown.
If there is just one variable in the equation, it is referred to as a linear equation in one variable.
A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
In Houston, taxis charge $3 plus $.75 per mile for an airport pickup.
3 + 75 m = 78
78 m / 12 = 9
m = 78 / 12 = 6.5 m
6.5 m far from the airport can Courtney travel for $12.
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a coral reef is 5 miles due north of its closest point along a straight shoreline. a visitor is staying in a cottage that is 6 miles east of that point. the visitor is planning to go from the cottage to the coral reef. suppose the visitor runs at a rate of 8 mph and swims at a rate of 1 mph. how far should the visitor run to minimize the time it takes to reach the coral reef? round to two decimal places.
Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.
How far should the visitor run to minimize the time it takes to reach the coral reef?
Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.
distance swimming = root of x^2+5^2= root of x^2+25.
Times: time= distance / speed time running =6-x/8
time swimming =x^2+25/8 Total time
time running + time swimming:
T=6-x/8+x^2+25/8
The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.
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Answer is 5.54 miles. The decimal digit generally refers to the representation of a number in the decimal number system, often referred to simply as a decimal, or less precisely as a decimal.
How far should the visitor run to minimize the time it takes to reach the coral reef?Assume she runs up to a point that is x miles to the east of the coral reef: distance running =6 -x miles.
distance swimming = root of x²+5²= root of x²+25.
Times: time= distance / speed time running =6-x/8
time swimming =x²+25/8 Total time
time running + time swimming:
T=6-x/8+x²+25/8
The accepted method of representing integers and non-integers is the decimal number system. It is an extension of the Indo-Arabic numeral system to non-integer values. Decimal notation is a term used to describe how numbers are represented in the decimal system.
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then use your function to find the two roots. display ""x1"" and ""x2""
the two roots of the equation are x1 = -2.5 and x2 = -1.5.
x1 = -2.5;
x2 = -1.5.
Step 1: Calculate the discriminant
b2 - 4ac = (-2)2 - 4(2)(-3) = 4 + 24 = 28
Step 2: Calculate the roots
x1 = (-b + √D) / 2a = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5
x2 = (-b - √D) / 2a = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5
We start by calculating the discriminant, which is b2 - 4ac. In this case we have b2 = (-2)2 = 4 and ac = 2(-3) = -6, so the discriminant is 4 + 24 = 28. Then we calculate the two roots, x1 and x2, using the formula x1 = (-b + √D) / 2a and x2 = (-b - √D) / 2a. Substituting in the values we have, x1 = (-(-2) + √28) / 4 = (-2 + 5.29) / 4 = -2.5 and x2 = (-(-2) - √28) / 4 = (-2 - 5.29) / 4 = -1.5. Therefore, the two roots of the equation are x1 = -2.5 and x2 = -1.5.
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Find the area of the composite figure. Use 3.14 for pi.
The area of the composite figure that consists of a half circle and a triangle is calculated as 86.24 cm^2.
How to Find the Area of a Composite Figure?The composite figure shown is composed of a half circle and a triangle. Therefore:
The area of the composite figure = area of semicircle + area of triangle = pi*r^2 + 1/2(base * height)
r = 4 cm
Base = 2(4) = 8 cm
Height = 9 cm
Area = 3.14 * 4^2 + 1/2(8 * 9)
= 50.24 + 36
Area of composite figure = 86.24 cm^2
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Ten less than twice a number is equal to at least 52. What are all the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter x as the variable, and write the inequality so that the x term comes first.(1 point)
Answer:
x [tex]\geq[/tex] 21
Step-by-step explanation:
2x - 10 [tex]\geq[/tex] 52
2x [tex]\geq[/tex] 42
x [tex]\geq[/tex] 21
HELPP THIS IS DUE AT 11:59
Answer: what grade u in?
Step-by-step explanation:
When testing a new treatment, what is the difference between statistical significance and practical significance? Can a treatment have statistical significance, but not practical significance? Choose the correct answer below. O A. Statistical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. Practical significance is achieved when the result is very unlikely to occur by chance. It is possible for a treatment to have statistical significance, but not practical significance. O B. Statistical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. Practical significance is achieved when the result is very unlikely to occur by chance. It is not possible for a treatment to have statistical significance, but not practical significance. O C. Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is not possible for a treatment to have statistical significance, but not practical significance. O D. Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance.
(D) Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance is correct.
Statistical significance is achieved when the result is very unlikely to occur by chance, and is usually determined by a p-value. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use, and is determined by the magnitude of the effect, such as the size of the difference between the treatment and control groups.
It is possible for a treatment to have statistical significance, but not practical significance. This means that the result is unlikely to occur by chance, but the magnitude of the effect may be small and not clinically meaningful. Conversely, a treatment can also have practical significance, but not be statistically significant, meaning that the magnitude of the effect is large enough to be considered important, but the result may not be statistically significant due to a large sample size, for example.
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You invest a certain amount of money at an interest rate of 6% for 4 years, and earn $168 in interest, how much did you originally invest?
Answer:
Amount originally invested = $700
Step-by-step explanation:
[This answer assumes that the interest is simple interest.]
We are told that upon investing a certain amount of money for 4 years at a rate of 6%, we get $168 in interest. We are then asked to calculate the amount originally invested.
To solve this problem, we have to use the formula for simple interest:
[tex]\boxed{I = PRT}[/tex],
where:
• I ⇒ interest = $168
• P ⇒ principal (original) amount = $?
• R ⇒ interest rate = 6% = 0.06
• T ⇒ time for which the money is invested = 4 years.
Using the above formula and rearranging it to make P the subject of the equation, we can calculate the principal amount:
[tex]I = PRT[/tex]
⇒ [tex]P = \frac {I}{RT}[/tex]
⇒ [tex]P = \frac{168}{0.06 \times 4}[/tex]
⇒ P = 700
Therefore, the amount originally invested was $700.
in 1980, the population of a city was 5.2 million. by 1992 the population had grown to 7.6 million. type the rate at which the population of the city was growing as an integer or reduced fraction. million per year
The rate at which the population of the city was growing was an average of 1.5 million people per year, which can be expressed as an integer or reduced fraction as 3/2.
To break this down further, this means that the city's population was increasing by an average of 416,666 people each month or 14,053 people each day.
This is an impressive rate of growth, especially when considering that the city was already quite large at 5.2 million people. This growth can be attributed to a number of factors, including high levels of immigration, a strong economy, and a booming job market.
Moreover, the growth in population can be seen as a testament to the city's quality of life and its ability to attract new residents.
The population of the city in 1980 was 5.2 million and by 1992 it had grown to 7.6 million. This shows that the rate at which the population of the city was growing was an average of 1.5 million people per year, which can be expressed as an integer or reduced fraction as 3/2.
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3 minus 1 over 3 to the power of 4 (I don’t know how to do this so can you please explain) please hurry
First, let's determine what (1/3) to the power of 4 is:
1/3 x 1/3 x 1/3 x 1/3 = 1/81
(1 x 1 x 1 x 1 = 1; 3 x 3 x 3 x 3 = 81)
1/81
Now what is 3 as a decimal?
We have to use the same denominator as 1/81 to be able to do a subtraction:
81 x 3 = 243
3 = 243/81
243/81 - 1/81 = 242/81
The answer is D.
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