In an acute triangle, the circumcenter of the triangle lies on the line O.
Acute triangle.
In geomentry, acute triangle is the type of triangle in which all the three internal angles of the triangle are acute
Given,
Here we need to prove that in the acute triangle ABC, the circumcenter of the triangle MNH lies on the line OH.
Let us consider T be the intersection of σ1 and σ1 other than W.
Now, the Lemma 1: T is on XY.
Now, the Proof is written as We have ∠XTW} = ∠YTW = 90 degres because they intercept semicircles.
Therefore, ∠XTY = ∠XTW + ∠YTW = 180 degrees,
Then XTY is a straight line.
Here we know that NHLB is cyclic because ∠BNH and ∠BLH, opposite and right angles, sum to 180 degree. Furthermore, we are given that NTWB is cyclic.
Therefore, the triangle MNH lies on the line OH.
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Put 51, -59, -1, and -98 in order
from least to greatest.
-1
51 -59
Submit
-98
I don't know this yet >
Answer:
Step-by-step explanation:
x>y
-x<-y
98>59
-98<-59
59>1
-59<-1
any negative value <any positive value (including 0)
combining
-98<-59<-1<51
By observing that f(x) = 1/(1 - 2x) is the sum of a geometric series (of the form a/(1 - r)), find the power series expansion of this function. Observation of Series: We'll observe the value of the first term or numerator aa and the common ratio r (it is the quotient of the second term to the first term) in the denominator of the rational function a1−ra1−r, plug these values in the formula of expansion. a1−r=a+ar+ar2+ar3+…a1−r=a+ar+ar2+ar3+… Where |r||r| is less than one.
The power series of the given function is 1 + (2x) + (2x)² + (2x)³+ --------------------- + (2x)ⁿ
We know very well that sum of n terms who are in geometric progression their sum of expression is given by a/1-r where a is first term and r is common ratio between the terms.
Now, we have function f(x)=[1 / (1-2x)]
On comparing with a/1-r with f(x),we get
=>a=1 and r=2x
Now, we know that first term of geometric progression is given by =1
second term of geometric progression is given by=a × r= 1 ×2x
third term of geometric progression is given by =a×r² =1×(2x)²
fourth term of geometric progression is given by=a×r³ =1 × (2x)³
nth term of geometric progression is given by =a×(r)ⁿ = 1 × (2x)ⁿ
Therefore, according to the given formula progression series of given function is=a+ ar +ar² + ar³ + -----------arⁿ
=>progression series = 1+ 2x + (2x)² + (2x)³ + --------- + (2x)ⁿ.
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f(x) = 2x – 3x and g(x) = 1 – 2x find (f+g)(x)
The value of the composite function is (f + g)(x) = -3x + 1
How to evaluate the composite functions?From the question, we have the following parameters that can be used in our computation:
f(x) = 2x - 3x
g(x) = 1 - 2x
The composite function is given as
(f + g)(x)
Mathematically, this can be represented as
(f + g)(x) = f(x) + g(x)
Substitute the known values in the above equation, so, we have the following representation
(f + g)(x) = 2x- 3x + 1 - 2x
Evaluate the like terms
(f + g)(x) = -3x + 1
Hence, the composite function is (f + g)(x) = -3x + 1
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An element with a mass of 520 grams decays by 25.1% per minute. To the nearest tenth of a minute, how long will it be until there are 60 grams of the element remaining?
The total time for the mass of the element to be 60 grams is 7.5 minutes
What is exponential growth factor?
The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ for growth rate
x ( t ) = x₀ × ( 1 - r )ⁿ for decay rate
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units = n
Given data ,
Let the total mass of element be = 520 grams
So , the value of x₀ = 520 grams
Now , the decay rate of element is given by r = 25.1 %
To calculate the time at which the amount of element left is 60 grams = n
where n is the total time = t
So , x ( t ) = 60
The decay rate formula is given by the equation ,
x ( t ) = x₀ × ( 1 - r )ⁿ
Substituting the values in the equation , we get
60 = 520 ( 1 - 25.1/100 )ⁿ
On simplifying the equation , we get
60 = 520 ( 1 - 0.251 )ⁿ
Divide by 520 on both sides of the equation , we get
( 0.749 )ⁿ = 6/52
Taking logarithm on both sides , we get
n × log ( 0.749 ) = log ( 6/52 )
Divide by log ( 0.749 ) on both sides , we get
n = log ( 6/52 ) / log ( 0.749 )
n = -0.9378 / -0.1255
n = 7.47 minutes
Therefore , the value of n time t = 7.5 minutes
Hence ,
The total time for the mass of the element to be 60 grams is 7.5 minutes
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the sale price of any item in a store is 85 percent off it's usual price what is a 18 dallor sweaters sale price
The sale price of the sweater is $2.7
How to determine the sales price of the sweater?From the question, we have the following parameters that can be used in our computation:
Markdown rate = 85% off
Original price of the sweater = $18
The retail price of the coat can be calculated using the following equation
Retail price = original price * (1 - Markdown rate)
Substitute the known values in the above equation, so, we have the following representation
Retail price = 18 * (1 - 85%)
Evaluate the products
Retail price = 2.7
Hence, the sales price is $2.7
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An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the
bearing 200° at 80 mph.
a. Find the component form of the velocity of the airplane.
b. Find the actual ground speed and direction of the airplane
(a) The component form of the velocity of the airplane is (-453.01 i + 79.88 j) mph.
(b) The actual ground speed and direction of the airplane is 392.76 mph and 30 degrees respectively.
What is the component form of the velocity of the airplane?
The component form of the velocity of the airplane is calculated as follows;
Vy = V sinθ
Vx = V cosθ
where;
Vy is the vertical component of the velocity of the airplaneVx is the horizontal component of the velocity of the airplaneV is the speed of the airplaneθ is the angle of the speedVy = 460 mph x sin (170 - 90) = 79.88 mph
Vx = 460 mph x cos (170) = -453.01 mph
The bearing of the two speeds forms a triangle and the angle of the triangle is calculated as follows;
θ = θ₁ + θ₂
θ = (180⁰ - 170⁰) + (200⁰ - 180⁰)
θ = 30⁰
The resultant speed of the airplane is calculated as follows;
Vr² = V₁² + V₂² - 2(V₁)(V₂) cos(θ)
Vr² = (460²) + (80²) - 2(460 x 80) x cos(30)
Vr² = 154,260.53
Vr = √(154,260.53)
Vr = 392.76 mph
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How many points are 4 units from the origin and 2 units from the linbe x=-1?
There are two points, 4 units from the origin and 2 units from the line x = -1.
What are coordinates?Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.
Given point is at a distance of 4 units from origin,
that is √x² + y² = 4
x² + y²= 16 is the equation of the locus of the point.
The given point is also 2 units from the line x =-1
that is √(x+1)² + y² = 2
(x+1)² + y²= 4 is the equation of the locus of the point.
Subtracting the second given equation from the first one,
we get x² - (x+1)² = 12
simplifying, x = 11/2
So the common coordinate point for these 2 points which is 11/2.
Substituting this value to the first equation,
(11/2)²+ y² = 16
Simplifying, y = ±(i√57)/2.
There are 2 points whose coordinates are;
( i√57/2 , 11/2 ) and ( -i√57/2 , 11/2 ).
Therefore there are two points, 4 units from the origin and 2 units from the line x = -1.
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Find Round your answer to the nearest tenth of a degree.
Answer:
55.5°
Step-by-step explanation:
You want the angle in a right triangle that has opposite side 16 and adjacent side 11.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
In this geometry, that means ...
tan(x) = 16/11
Taking the inverse tangent, we have ...
x = arctan(16/11) ≈ 55.49° ≈ 55.5°
The angle x is about 55.5°.
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Condense the expression to the logarithm of a single quantity
-4 ln(3x)
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)
1. ln (2x)
Condense the expression:
- 4 ln (3x) = ln (3x)⁻⁴Used property:
n logₐ b = logₐ bⁿPart 2Expand the expression:
ln (2x) = ln 2 + ln xUsed property:
log (ab) = log a + log bAnswer:
[tex]\ln(3x)^{-4}[/tex]
[tex]\ln2 + \ln x[/tex]
Step-by-step explanation:
Given expression:
[tex]-4\ln(3x)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]
[tex]\implies \ln(3x)^{-4}[/tex]
---------------------------------------------------------------------------------
Given expression:
[tex]\ln(2x)[/tex]
[tex]\textsf{Apply the product law}: \quad \ln xy=\ln x + \ln y[/tex]
[tex]\implies \ln2 + \ln x[/tex]
Which of the following statement is true ?
a) All the rhombuses are squares
b) each square is a parallelogram
c) each parallelogram is a square
d) each trapezium is a parallelogram
The following statement is true is a) All the rhombuses are squares .
Given :
In contrast to a square, the lengths of all four sides of a rhombus are equal, the diagonals of a rhombus bisect each other, and all four angles of a rhombus are not equal to 90 degrees.
Parallelograms are not all squares. Parallelograms have equal length opposite sides, hence squares with all sides equal are parallelograms. Rhombuses are the only kites that fly.
Because a parallelogram contains two pairs of parallel sides, a trapezium is not a parallelogram. A trapezium, on the other hand, has only one pair of parallel sides.
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I’ll give brainliest if correct.
Answer:
58 degrees
Step-by-step explanation:
a - 15 + a + 43 + 36 = 180
2a - 15 + 79 = 180
2a + 64 = 180
2a = 180 - 64
2a = 116
2/2 a = 116/2
a = 58 degrees
the ent weight in pounds of a packaged chemical herbicide in uniform for 49.62 < x < 50.12 pounds. what is the probability that the net weight is greater than 49.9 pounds?
The probability that the net weight is greater than 49.9 pounds is 0.44
What is probability?
The probability function expressing the density of a continuous random variable ranging between a particular range of values is defined by the probability density function. The probability density function, in other words, generates the likelihood of values for the continuous random variable. It may also go by the names probability function or plain probability function.Given f (x) = 2.0 for 49.62 < x < 50.12 pounds.
Our goal is:
a). We need to find the probability that a package weighs more than 50 pounds.
b). We need to find How much chemical is contained in 90% of all packages.
a). The probability of more than 49.9 pounds.
Given P(X>50).
P(X>49.9) = [tex]\int\limits^a_b {2} \, dx[/tex] (a=50.12, b= 49.9)
P(X>49.9) = [2x]₄₉.₉⁵⁰.¹²
P(X>49.9) = 2(50.12)-2(49.9)
P(X>49.9) = 100.24-99.8
P(X>49.9) = 0.44
Therefore, P(X>49.9) = 0.44
Hence, the probability that the net weight is greater than 49.9 pounds is 0.44
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Write 2^100 as a power with the following base.
4
Answer:4^50
Step-by-step explanation:
Since 4 is twice as much as 2, you would divide 100/2 which would equal 50. Therefore, you get 4^50.
Suppose f(x,y,z) = x^2 + y^2 + z^2 and W is the solid cylinder with height 5 and base radius 2 that is centered about the z-axis with its base at z = -1. Enter \theta as theta.
(a) As an iterated integral,
\displaystyle \iiint\limits_{W} f \, dV = \int_A^B \!\! \int_C^D \!\! \int_E^Fdz \, dr \, d\theta
with limits of integration
A =
B =
C =
D =
E =
F =
(b) Evaluate the integral.
If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.
They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt
Note that you need another r because you are integrating in cylindrical
coordinates.
conversion equations:
x = rcost
y = rsint
x² + y² = r²
(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt
W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.
Around the z-axis, cylinders take the forms of circles: x² + y² = r²
This cylinder will have the equation: x² + y² = 16
Its height is 3 so from z = -1 to z = 2
z bounds: -1 <= z <= 2
r bounds (based on the circle): 0 <= r <= 4
t bounds (based on the circle): 0 <= t <= 2pi
\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)
(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)
= 2r^3 + (8/3)r + r^3 + (1/3)r
= 3r^3 + 3r
dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216
dt integral gives: 216t --> 432pi
Hence we get the integral value as 432π
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calculate a 90% confidence interval for the positive difference between the mean annual income of all households for the following sectors of this community. round your answers to the nearest whole dollar, if necessary.
90% confidence interval for positive difference between means that there is a 90% probability that the confidence interval will contain the true population mean
The difference in sample means is used to calculate the difference in population means. A confidence interval reveals how accurate the estimate is.
We will make three assumptions in order to build a confidence interval:
1. The variance between the two populations is equal. The second assumption of homogeneity of variance is what this premise is known as.
3. The populations are evenly distributed.
4. Each value is sampled separately from every other value.
The following formula is used to construct a confidence range for the mean difference:
[tex]Lower Limit = M_1 - M_2 -(t_{CL})(S_{M1} - S{M2})\\Upper Limit = M_1 - M_2 +(t_{CL})(S_{M1} - S{M2})[/tex]
where [tex]S_{M1} - S{M2}[/tex] is the expected standard error of the difference between sample means, tCL is the desired level of confidence, and M1 - M2 is the difference between sample means.
The given question is incomplete So, I've answered in general according to my knowledge
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Exxon sells its bonds at 108.375. The amount of premium or discount the bond is selling for is:
Multiple Choice
$83.75
$13.75
$13.25
$8.38
The amount premium on bond selling is $83.75. Option A is correct.
Given that,
Exxon sells its bonds at 108.375%. The amount of premium or discount the bond is selling for is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Face value of bonds = $1000
The selling price of bond = 1000 × 108.375%
=$1083.75
Premium on bonds = difference in the selling price - value of a bond
= 1083.75-1000
= $83.75.
Thus, the amount of the premium on bond selling is $83.75. Option A is correct.
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Which of the following properties apply to all parallelograms?
The following are parallelograms' essential characteristics: The opposing sides are parallel. The opposing parties are in agreement (they have the same length).
What are the four characteristics of a parallelogram?The four most crucial characteristics of a parallelogram are: A parallelogram has two opposed sides that are parallel to one another and have equal measurements. A parallelogram has equal opposite angles. The interior angles of a parallelogram sum to 360°. A parallelogram's subsequent angles should be supplementary (180°).
What shape does a parallelogram take?A quadrilateral having opposite sides that are equal and parallel is called a parallelogram. A parallelogram's opposing angle is also equal. A parallelogram is essentially a twisted rectangle.
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Write a polynomial function f of least degree that has rational coefficients, a
leading coefficient of 1, and zeros 3 and 3 – i
Answer:
f(x) = x³ -9x² +28x -30
Step-by-step explanation:
You want a monic polynomial f of least degree with zeros 3 and 3-i.
FactorsFor zero x=a, the polynomial has a factor (x -a). Complex zeros come in conjugate pairs, so another one is 3+i. This means the factored form is ...
f(x) = (x -3)(x -3 +i)(x -3 -i)
f(x) = (x -3)(x² -6x +9 +1) . . . . . combine the two right factors
f(x) = x³ -9x² +28x -30
__
Additional comment
When multiplying polynomials mentally, it can be useful to consider the coefficients of the product terms in order of decreasing powers:
f(x) = (1)x³ +(-3 -6)x² +(10 +(-3)(-6))x +(-3)(10)
How do I solve this diagram map? Diagram shows the following:
1 - 3
2 - 5
3 - .....?
?..... - 17
10 - ......?
100 - ......?
The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201
Given that,
To complete the map diagram,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,
10th = 21
100th = 2001
For the value 17
17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,
Thus, The complete diagram map has been shown.
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Which of the following are the most likely factors of the function graphed above?
The factors of the function graphed in the given graph is option (C) (x-1)(x+5)
The function is the mathematical statement that shows the relationship between the dependent variable and independent variable
From the given graph
The given graph is a parabola and the equation of the graph will be a quadratic function
x intercepts of the lines are
x = -5 and x = 1
Then to find the factors of the function graphed
x = -5
x + 5 = 0
Similarly the second equation will become
x = 1
x-1 = 0
Then the factors function will be
(x+5)(x-1)
Therefore, the factors are option (C) (x-1)(x+5)
I have solved the question in general, as the given question is incomplete
The complete question is
Which of the following are the most likely factors of the function graphed above?
A. (x+1)(x-5)
B. (x)(x-5)
C. (x-1)(x+5)
D. (x)(x+5)
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The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.
Time of Day
10 AM
12 Noon
2 PM
4 PM
6 PM
8 PM
10 PM
Temperature ((Degrees Fahrenheit))
30
35
36
36
34
30
28
What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.
a.
6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.
b.
Negative 6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.
c.
Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
d.
1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
The average rate of change of the temperature from 6 to 10 pm is given as -1.5. Option C is correct
How to solve for the rate of changeFrom 6 pm to 10 pm we have a total of 4 hours that is in between this period of time.
From the table the temperature at 6 pm is 34, the temperature at 10 pm is 28 degrees
Such that we would have:
[tex]\frac{28-34}{4}[/tex]
= -6 / 4
= - 1.5
Hence we would have that Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
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water flows into a cylindrical tank at the rate of 2 ft/min. if the radius of the top of the tank is 4ft and the height is 6 ftdetermine how quickly the water level is rising when the water is 2 feet deep in the tank.
0.477 ft/min, the water level is rising when the water is 2 feet deep in the tank.
What is Derivative?The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value).
Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.
When it occurs, the slope of the tangent line to the function's graph at a given input value is the derivative of a function of a single variable.
The function closest to that input value is best approximated linearly by the tangent line. Because of this, the derivative is
According to our question-
The tank's water volume, V, is as follows:
V=πr2h
When the height, h, of the water rising from the tank's bottom increases with time, t, and the radius, r=4ft, is constant.
Using the volume's first derivative, we obtain:
dVdt=πr2dhdt
How to solve for the height change over time:
dhdt=1πr2dVdt
dhdt=1π(4ft)2(24ft3min)
dhdt≈0.477ftmin
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select all of the roots of x3 2x2 16x 32 1 2 4 1 4 5
Therefore the solution to the given problem is the roots of the given equation are -2,-4,+2
What is equation?A mathematical statement that shows the equality of two mathematical expressions is the definition of an equation in algebra. As an illustration, the two equations 3x + 5 and 14 are joined by the equal sign to get the equation 3x + 5 = 14. Algebraic mathematical equations frequently have one or more variables.
Given:
[tex]x^{3} +2x^{2} -16x-32[/tex]
We are given a cubic polynomial.
Thus find the roots of the polynomial. the roots can be find by solving the equation in terms of x
=> [tex]x^{3} +2x^{2} -16x-32[/tex]
[tex]x^{2}(x +2)-16(x+2)\\(x+2)(x^{2}-16)\\x+2=0\\x=-2\\x^{2}-16=0\\x^2=16\\x=+4,-4[/tex]
=so roots are -2,-4,+4
Therefore the solution to the given problem is the roots of the given equation are -2,-4,+2
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Answer:
-2,-4, 4
Step-by-step explanation:
Find the values of x and y.
I need help with this please help me
Find the sector area for the following:
(Use \large \pi=3.14 when necessary and round your final answer to the hundredths.)
Sector Area =
The Area of the given sector is 14.1 yd²
Define Sector of a Circle
A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.
Given,
radius = 6 yd
Angle θ = 45°
The formula for, Sector Area = (θ / 360°) * πr²
Now, plug in the values
Sector Area = (45 / 360) * 3.14 * 6²
= 14.1 yd²
Hence, the Area of the given sector is 14.1 yd²
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Answer: 4.5
Step-by-step explanation:
sector area = 4.5 on 14.143 yd ^2
△GHJ∼△MN E.) GH=MNPWhich statements are true? Select each correct answer. A.) m∠J=m∠P B.) GJMP=GHMN C.) ∠H≅∠N E.) GH=MN
The correct options are
B.) GJ / MP = GH / MN
C.) ∠H≅∠N
By using the property of similarity of triangles, We get
The corresponding sides of the similar triangles are proportional to each other and the corresponding angles are congruent to each other.
So, given △GHJ∼△MNP
⇒ GH/MN = HJ/NP = GJ/MP , and
∠G ≅ ∠M , ∠H ≅ ∠N , ∠J ≅ ∠P........(1)
The given options are :
A.) m∠J=m∠P
B.) GJ / MP = GH / MN
C.) ∠H≅∠N
D.) HJ ≅ NP
E.) GH=MN
Now, from equation (1)
The correct options are
B.) GJ / MP = GH / MN
C.) ∠H≅∠N
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3(4d + 4m+ a + 2c). help
Answer:
12d+12m+3a+6c
Step-by-step explanation:
distribute 3 by multiplying
I dont understand this ones. Please help
The distance between the line segment from P to RQ is 2.83 units
Distance Between Two PointsDistance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x₂ – x₁)² + (y₂ – y₁)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
In this case, we need to find the coordinate of P and RQ
From P to the line RQ, we will meet the midpoint of the line RQ which has a coordinate of (3, 3)
Let's use the formula of distance of a line segment and solve this
d = √((x₂ - x₁)² + (y₂ + y₁)²)
P = (1, 1)RQ = (3, 3)d = √(3 - 1)² + (3 - 1)²
d = √(2)² + (2)²
d = √8
d = 2√2
d = 2.83 units
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Test the claim that for the population of statistics final exams, the mean score is 71 using alternative hypothesis that the mean score is different from 71. Sample statistics include n = 26, ã = 72, and s = 18. Use a significance level of a = 0.05. (Assume x : normally distributed population.) = a a The test statistic is 0.283 The positive critical value is 1.645 The negative critical value is 1.645
Since the test statistic is not greater than the critical value, the null hypothesis cannot be rejected. Therefore, the claim that the mean score is 71 is not rejected.
1. We are given the population of statistics final exams and asked to test the claim that the mean score is 71 using an alternative hypothesis that the mean score is different from 71. We are also given the sample statistics including the sample size (n = 26), the sample mean (ã = 72), and the sample standard deviation (s = 18). We are asked to use a significance level of α = 0.05.
2. Since we are assuming that the population is normally distributed, we will use a two-tailed z-test to test the claim.
3. The null hypothesis is that the mean score is 71 and the alternative hypothesis is that the mean score is different from 71.
4. The test statistic is calculated as:
Test statistic = (sample mean - population mean) / (standard deviation/√n)
= (72 - 71) / (18/√26)
= 0.283
5. The critical values for a two-tailed z-test with a significance level of α = 0.05 are 1.645 for both the positive and negative critical values.
6. Since the test statistic (0.283) is not greater than the critical value
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What type of function is odd?
Rotational symmetry about the origin is present in odd functions. By substituting x with -x and computing f, we can determine algebraically if a function is even, odd, or neither (-x). The function is odd if f(-x) = f(x).
Which one of the following functions is odd?If -f(x) = f(-x), then the function f is said to be odd for all values of x. When studying additive inverses, the functions even and odd are those that satisfy particular symmetry relations.
Is odd function continuous?Evenness or oddness in a function does not imply continuity or differentiability. For instance, the Dirichlet function is even but in no way continuous.
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