Answer:
Step-by-step explanation:
The original price of the hat is $35. Paolo paid $28 for the hat.
So discount for the hat is $(35-28) = $7
$7 is discounted from $35. We have to find the percentage of the discount.
To find the percentage we have to divide the discount amount by the original price and then have to multiply it by 100.
So the discount percentage =
((7/35)×100) %
We can simplify 7/35 by dividing 7 and 35 both by 7. So we will get 1/5 after simplifying.
((1/5) ×100) %
(100/5)% = 20%
So the hat was discounted by 20%.
A toy rocket is launched from a 5.6 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= - 4.97t^2+ 38.5t + 5.6. How long will it take for the rocket to hit the ground?
The toy rocket will hit the ground after approximately 3.86 seconds.
Calculating time for toy rocket to reach groundThe rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:
0 = -4.97t^2 + 38.5t + 5.6
-5.6 = -4.97t^2 + 38.5t
4.97t^2 - 38.5t - 5.6 = 0
This is a quadratic equation and can be solved using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 4.97, b = -38.5, and c = -5.6.
Plugging in these values, we get:
t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)
t = (38.5 ± √(1466.25 + 113.92)) / 9.94
t = (38.5 ± √1580.17) / 9.94
The square root of 1580.17 is 39.67, so:
t = (38.5 ± 39.67) / 9.94
t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94
The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.
The toy rocket will hit the ground after approximately 3.86 seconds.
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Find the equation of the line that passes through (1,3) and is perpendicular to
y=2x-1.
Leave your answer in the form ax+by=c
Where a, b and c are integers.
Answer:
Equation of perpendicular line:
[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]
Step-by-step explanation:
Generalized lope-intercept form of a line is y = mx + b [1]
where
m = slope
b = y-intercept
Equation of the given line is y = 2x - 1 [2]
We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)
If f(x)=-2x+4 and g(x)=x^2-5x, find all values of x for which f(x)=g(x)
The values of x for which f(x) = g(x) are -1 and 4
How to determine the values of xFrom the question, we have the following parameters that can be used in our computation:
f(x) = -2x + 4
g(x) = x^2 - 5x
Using the above as a guide, we have the following:
Plot the graphs of f(x) and g(x) on the same planeWrite out the x coordinate of the intersectionUsing the above as a guide, we have the following:
x = -1 and x = 4
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The figure shown has two parallel lines cut by a transversal:
A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Which angle is an alternate interior angle to ∠3?
∠5 is the alternate interior angle of ∠3.
What is transversal?
A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.
Line m and line n are parallel and line l is transversal.
The alternate pairs of that transversal are ∠3 and ∠5.
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A geolo
gistis going to ship two granite specimen weighs 22 pounds and the crate weighs 20pounds the shipping crate weighs 8pounds the shipping crate is what percentage of the total weight of the shipment
The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%
How to calculate the percentage of shipping crate?The weight of two granite specimen = 22 pounds
The weight of the crate = 20 pounds
The weight of shipping crate = 8 pounds
The total weight of the whole shipment = 22+20+8 = 50 pounds.
Therefore the percentage of shipping crate as compared to the total weight;
= 8/50 × 100/1
= 800/50
= 16%
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The area of the floor is (x2-169) sq units. Find the width of the floor if the length is (x - 13) units.
The width of the floor if the length is (x - 13) units is (x+13) units.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that area of the floor is (x²-169) sq units.
We have to find the width of the floor when length is (x - 13) units.
Area=Length×Width
x²-169=(x-13)width
We know that (a²-b²)=(a+b)(a-b)
(x-13)(x+13)=x-13width
Divide both sides by (x-13)
x+13=width
Hence, the width of the floor if the length is (x - 13) units is (x+13) units.
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OnOff
Question
A composite figure is shown.
What is the total area of this figure?
164 sq. cm.
136 sq. cm.
216 sq. cm.
160 sq. cm.
Answer:
164 cm^2
Step-by-step explanation:
lets find square of triangle first
corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90
(sum of all angles of a quadrilateral is 360,
B = 360 - C - F - E
360 - 90 - 90 - 90 = 90)
BD = CF - DE
BD = 16 - 8 = 8 cm
S ABD = AB * BD / 2 (coz corner B is 90 degrees)
S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2
lets find square of BEFC next
S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)
S BEFC = 16 * 7 = 70 + 42 = 112 cm^2
finally lets find total area
S = S ABD + S BEFC = 52 + 112 = 164 cm^2
SOMEONE HELLPPPP IM SCAREDDDDD
Answer: AE
Step-by-step explanation:
if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"
Triangle ABC is a right triangle.
B
(X-10)
(2X+40)
Which equations can be used to find the value of x? Check all that apply.
X+90+(x-10)- 180
OX+90+(2x+40)-180
Save and Exit
Next
The expression to measure {x} can be written as -
{x - 10} + {2x +40} + 90 = 180
What is Pythagoras theorem?We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.
Mathematically -
(hypotenuse)² = (base)² + (perpendicular)²
Given is a right triangle ABC
We an write the expression to measure {x} as -
{x - 10} + {2x +40} + 90 = 180
Therefore, the expression to measure {x} can be written as -
{x - 10} + {2x +40} + 90 = 180
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Multiply the polynomials. (2x+y)·(4x^2-2xy+y^2)
Answer:
Step-by-step explanation:
The answer is 4x^2y+8x^3+y^2-2xy
an airline would like to decide on an appropriate flight overbooking policy. since a certain percentage of ticketed passengers will cancel at the last minute, to avoid empty seats, they sell more tickets than there are seats, hoping that just about the right number of passengers will show up. we will assume that the rate of passages that cancel a flight at the last minute is equal to 5%. for a flight with 220 seats, the airline wants to find how sensitive various probabilities are to the number of tickets it issues. first, estimate the number of tickets to be sold such that, on average, all the seats in the flight will be occupied. second, using an appropriate probabilistic model, compute:
The probability of the flight being overbooked is 0.38742 or 38.7%.
To calculate the probability of the flight being overbooked, we need to use a probability formula. In this case, we can use the binomial probability formula. The formula is as follows:
[tex]P(x) = ^nC_x * p^x * q^{(n-x)}[/tex]
Where:
P(x) is the probability of x number of events occurring.
n is the total number of trials.
p is the probability of success.
q is the probability of failure.
nCx is the number of ways to choose x items from a set of n items.
Let's say a plane has 8 seats. The airline sells 10 tickets for this flight. The probability of all ten passengers showing up for the flight is quite low. Based on past experience, the airline knows that only 90% of ticketed passengers usually show up for a flight. This percentage is also known as the "show-up rate."
In our case:
n = 10 (total number of passengers)
p = 0.9 (probability of a passenger showing up)
q = 0.1 (probability of a passenger not showing up)
We want to find the probability of having more than 8 passengers show up, which would mean the flight is overbooked. To do that, we need to calculate the probability of having 9 or 10 passengers show up. We can use the formula to calculate this:
P(9 or 10) = P(9) + P(10)
P(9 or 10) = ¹⁰C₉ x 0.9⁹ x 0.1¹ + ¹⁰C₁₀ x 0.9¹⁰ x 0.1⁰
P(9 or 10) = 0.38742 or 38.7%
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Complete Question:
Airlines usually overbook for a flight (sell more tickets than the numbers of available seats). They do this because they know from past experience that only 90% of ticketed passengers actually show up for the flight.
A plane has 8 seats. If the airline sells 10 tickets for this flight, what is the probability that the flight will be overbooked?
The solution set of an equation of a circle is all of he points that lie on the circle.
A. True
B. False
you have a recipe that indicates to use 2 parts of milk for every 7 parts of flour. You use 8 cups of milk. How much flour do you need?
(Also complete the ratio table below pls)
Milk(cups) 2 , 4 _ , 8
Flour (cups) 7 , _ , 21 , _
Answer:
28 cups of Flower
Ratio Table:
2,4,6,8
7,14,21,28
Step-by-step explanation:
2x4/7x4=8/28
what is R30 into shillings?
Answer:
Step-by-step explanation:
The exchange rate between the South African Rand (ZAR) and the Kenyan Shilling (KES) fluctuates daily. As of my training data cut off in 2021, the exchange rate was approximately 1 ZAR = 10.87 KES.
So, 30 South African Rand would be equivalent to approximately 329.10 Kenyan Shillings. However, it is important to note that exchange rates can change over time, so it is always a good idea to check a reliable source for the most up-to-date conversion rate before making any currency exchanges.
it takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute. how many feet is this per second?
Answer:
170 feet per second
Step-by-step explanation:
To answer the question you need to find the unit rate. To find the unit rate divide the denominator with the numerator in a way that the denominator becomes 1.
5,100/30 = 170
The skydiver falls at a rate of 170 feet per second before opening the parachute.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
It takes a skydiver 30 seconds to fall 5,100 feet before opening the parachute.
Hence, Height for this is,
⇒ 5100 / 30
⇒ 170 feet per second
Thus, the skydiver falls at a rate of 170 feet per second before opening the parachute.
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1. a certain type of tomato seed germinates 43% of the time. a backyard farmer planted 10 seeds. what is the probability that 2 or fewer germinate?
The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.
To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:
n is the total number of trials (plantings)p is the probability of success (a seed germinating)x is the number of successes we want to calculate the probability forIn this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
where X is the random variable representing the number of seeds that germinate.
Using the binomial distribution formula, we can calculate the probability of each outcome:
P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]
where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].
Plugging in the values, we get:
P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057
P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205
P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324
Therefore,
[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586
So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.
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An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
The graph below is a discrete function:
8
246
0 2
A True
B) False
f(x)
6
8 10
12
14
Answer: A.
Step-by-step explanation:
34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. a simple random sample of size 100 is chosen from the population to study this disease. let be the total number of people in our sample that have diabetes. what is the distribution of ?
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.
The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:
μ = np
where n is the sample size and p is the probability of success.
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:
X ~ B(100, 0.105)
Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.
In our case, the mean number of people with diabetes in our sample is:
μ = 100 x 0.105 = 10.5
This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.
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Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)
Answer:
So the simplified expression is:
2x - 4 / (x^2 + 9x + 20)
Step-by-step explanation:
To simplify the expression, we need to simplify the numerator and denominator separately, and then simplify the entire expression.
Starting with the numerator:
4x^2 + 12x - 16
For the denominator:
The first fraction: 2x + 10 can be simplified as follows: 2x + 10 = (2)(x) + (2)(5) = 2x + 10
The second fraction: 6x + 24 over x^2 + 9x + 20
We can simplify the denominator by using partial fraction decomposition. To do that, we need to write the denominator as a sum of simpler fractions, each with a numerator that is a constant. In other words, we write:
6x + 24 / (x^2 + 9x + 20) = (A x + B) / (x^2 + 9x + 20) + (C x + D) / (x^2 + 9x + 20)
Multiplying both sides by the denominator, we get:
6x + 24 = (A x + B)(x^2 + 9x + 20) + (C x + D)(x^2 + 9x + 20)
Expanding the right-hand side, we obtain:
6x + 24 = Ax^3 + (A 9 + B) x^2 + (A 20 + B 9 + C) x + (B 20 + D)
Comparing the coefficients of the polynomials on both sides, we get the following system of linear equations:
A = 0
B = 6
C = 0
D = -24
Therefore, the partial fraction decomposition of the denominator is:
6x + 24 / (x^2 + 9x + 20) = (6x + 24) / (x^2 + 9x + 20)
Putting it all together, we have:
4x^2 + 12x - 16 / (2x + 10) / (6x + 24) / (x^2 + 9x + 20) = (4x^2 + 12x - 16) / (2x)(6x + 24) / (x^2 + 9x + 20) = 2x - 4 / (x^2 + 9x + 20)
So the simplified expression is:
2x - 4 / (x^2 + 9x + 20)
A square and a rectangle have the same perimeter. The square has an area of 81 sq. inches and the rectangle has a width of 5 in. What is the area of the rectangle?
Answer:
Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]
Step-by-step explanation:
Let square side = [tex]a[/tex]
Area of square [tex]A = a^2[/tex]
Given [tex]A = 81[/tex] and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]
[tex]a = \sqrt{81} = 9\;in[/tex]
Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]
If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width
Perimeter P of rectangle = [tex]2(l + w)\\[/tex]
Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]
Given
[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]
[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]
- f(x) = 4x, g(x) = 9x¹/2; x = 9
The value of the functions at 9m is
3627What is the value of the functions at x=9?Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.
Functions can take many forms and be expressed in different ways, including:
Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Therefore, this function
- f(x) = 4x
g(x) = 9x¹/2
for
F(x)=4x
F(9)=4*9
f(9)=36
for
g(x) = 9x¹/2
g(9)=9√9
=27
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What is the r-value of the following data to three decimal places?
X. Y
4. 23
5. 12
8. 10
9. 9
13. 2
Note that the r-value of the above data is : -0.903 (Option A)
What is R-value?In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.
With regard to the above data:
A) Find the Sum of the X values: 4 +5+8+9+13 = 39
B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56
C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355
D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858
E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339
N = number of sets = 5
Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8
Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =
SQRT(355-39^2/5) x SQRT(858-56^2/5) =
SQRT(50.8) x SQRT(230.8) =
7.1274 x 15.1921 =
108.2803
r = -97.8 / 108.2803
r = -0.903
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Miss carol spendmore is not good at budgeting her money. She initially haf $500 in the bank. She lent her friend $65 this month and she notices that her bank account is declining by $15 dollard per day. Determine the rate of cHange
Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.
Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.
The information that her account is losing $15 every day can then be put to use. We can write this as:
Rate of change = -$15 per day
The negative symbol signifies a declining amount on her account.
Therefore, Miss Carol's bank account is losing money at a daily rate of
$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
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consider the function graphed below. What is the average rate of change of the function over the interval (2,3)?
The average rate of change of the function over the interval [2,3] will be around 3.
What is a function?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.
The rate of change is given by dy/dx
The average rate of change can be given as:
= (difference in y coordinate)/(difference in x coordinate)
= Δy/Δx
Average rate of change = ( 11 - 8 )/(3 - 2 )
= 3
Hence, the average rate of change is 3
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George needs a string that is 4 feet long. So far history is 44 inches. Is it long enough or does he need to make it longer
If so far the George's string is 44 inches long , then his string is not long enough , so he need to make it longer .
To find whether George's string is long enough, we first convert both measurements to same unit of measurement.
that means we convert length of the string in inches to feet by dividing it by 12 ; because there are 12 inches in a feet ;
⇒ (44 inches)/(12 inches/feet)
⇒ 3.67 feet ;
The George's string is currently 3.67 feet long and he needs a string that is 4 feet long .
So , his current string is not long enough and he needs to make it longer. He needs to add another 0.33 feet to his string .
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The given question is incomplete , the complete question i
George needs a string that is 4 feet long. So far his string is 44 inches. Is it long enough or does he need to make it longer ?
The sum of two numbers is 14. Four less than twice the smaller number is equal to the larger number x. Find the larger number.
The Larger number is 8
What is a linear equation in one variable?
The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.
Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number
let the larger number be 'a' and the smaller be 'b'
from the question,
a + b = 14 .....eq 1
a = 2b - 4 .....eq 2
By substituting eq 2 in eq 1:
2b - 4 + b = 14
3b - 4 = 14
3b = 14 + 4 = 18
b = 6
a = 2b - 4 = 2*6 - 4 = 8
Therefore, The two numbers are 8, 4
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Need help on these questions. What are the values of x? Need step by step.
8x²=6x²+5x²
-7x²+6=x²-7x²
7x²+9x²=-6x²-7x
The values of x for the given equations are:
1. The value of x = 0
2. The values of x are ±1
3. The values of x are 0 and -7/16
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
To find the values of x in each of the equations, we need to simplify them using algebraic operations:
1. 8x² = 6x² + 5x²
Combining like terms on the right-hand side:
8x² = 11x²
Subtracting 6x² from both sides:
2x² = 0
Dividing both sides by 2:
x² = 0
Taking the square root of both sides:
x = 0
Therefore, the only solution to this equation is x = 0.
2.Similarly, we can calculate values of x for this equation:
-7x² + 6 = x² - 7x²
x² = 1
Taking the square root of both sides:
x = ±1
Therefore, the solutions to this equation are x = 1 and x = -1.
3. 7x² + 9x² = -6x² - 7x
x(16x + 7) = 0
Using the zero product property:
x = 0 or 16x + 7 = 0
Solving for x in the second equation:
16x = -7
Dividing both sides by 16:
x = -7/16
Therefore, the solutions to this equation are x = 0 and x = -7/16.
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peter sets up a neurological study in which he wants to investigate three pre-defined groups of patients. each group of patients is already diagnosed with the same neurological syndrome. peter not only examines the average score for each group of patients, but also the scores for each individual patient. peter's study is an example of...
Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.
Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.
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Which one of the following best defines the notion of the significance level of a hypothesis test?
The probability of committing type 1 error best describes notion of significance level of hypothesis test.
What is probability?
Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.
Complete Question:
Which one of the following best describes the notion of the significance level of a hypothesis test?
i) the probability of committing a type 1 error
ii) the probability of committing a type 2 error
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