Answer: 20 80
Step-by-step explanation:
So two 2-digit numbers
Find all the zeroes of the function
y=x^4-7x^2+12
show your work
x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex],-2,2
What is a quadratic equation ?
Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:
ax² + bx + c = 0
Given:
y=[tex]x^{4} -7x^{2} +12[/tex]
Let [tex]x^{2}[/tex] = k
So , y = [tex]k^{2}[/tex] -7k+12
On simplifying/factorising the given equation ,we get
y = [tex]k^{2}[/tex] - 4k - 3k +12
On taking common ,we get
y = k(k-4) -3(k-4)
y =(k-3)(k-4)
Thus , on factorising and equating it to zero we get
(k-3)=0 or (k-4)=0
k=3 or k=4
Now , replacing k by [tex]x^{2}[/tex] ,we get
[tex]x^{2}[/tex] = 3 or [tex]x^{2}[/tex] = 4
Further on solving ,we get
( [tex]x^{2}[/tex]-3)=0 or ( [tex]x^{2}[/tex]-4)=0
(x-[tex]\sqrt{3}[/tex])(x+ [tex]\sqrt{3}[/tex]) =0 or (x+2)(x-2)=0
x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex] or x= -2,2
Thus , x=-[tex]\sqrt{3}[/tex] ,[tex]\sqrt{3}[/tex],-2,2
Hence ,the obtained values of y are the zeros of x .
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what is 1 +1 x 30(200-125) + 999² ÷2000
what i got when i looked it up: 2750.0005
what i got when i did it 500.0005
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?
In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43 ) and matching the number on the gold ball (1 through 33). If one ticket is purchased, what is the probability of winning the jackpot?
Answer:
44
Step-by-step explanation:
given that the surface defined by top(x, y) satisfies and the surface defined by bottom(x, y) satisfies for all and , estimate the volume bounded by the two surfaces using monte carlo method. you can assume this volume lies within the box illustrated in the above figure, i.e., , and . store the volume of the object in a variable called volume. the setup code provides the following functions:
divide the volume by the total number of points to normalize it. The resulting value is the estimated volume of the bounded object.
def top(x, y):
return x+y
def bottom(x, y):
return x*2 + y*2
import numpy as np
xvals = np.random.uniform(-1, 1, size=10000)
yvals = np.random.uniform(-1, 1, size=10000)
# Initialize the volume
volume = 0
# Calculate the volume using Monte Carlo
for x, y in zip(xvals, yvals):
if top(x, y) > bottom(x, y):
volume += 1
# Normalize the volume by the total number of points
volume /= 10000
print(volume)
The Monte Carlo method is used to estimate the volume of a bounded object by randomly generating points within a known box. First, we generate a list of random (x, y) coordinates using numpy's uniform function. We then initialize the volume to 0 and loop through the list of coordinates and increment the volume by 1 if the point lies above the surface. Finally, we divide the volume by the total number of points to normalize it. The resulting value is the estimated volume of the bounded object.
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which of these is the quadratic parent function
The quadratic parent function is f(x) = x^2. (Option A)
In mathematics, family of functions refers to a group of functions that have the same degree or form. The examples of families of functions include linear functions, quadratic functions, square root functions, and absolute value functions. A parent function refers to the simplest function of a family of functions that preserves the definition of the entire family where the graph does not experience any transformations. The parent function of a quadratic equation is f(x) = x^2, whose graph has a vertex at the origin and experiences no vertical stretch or shrink. The other three options would be translated or transformed, hence are not the parent function of the quadratic equation.
Note: The question is incomplete. The complete question probably is: Which of these is the quadratic parent function? A. f(x) = x^2 B. f(x) = x^2 + 3 C. f(x) = x^2 – 5 D. f(x) = –4x^2
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Solve the following triangle for side a.
Solve for angle A in the following triangle.
Imagine you are building a triangular garden. Two sides of the garden measure 230 ft and 360 ft and the included angle between these two sides of the garden measures 38°. What is the measure of the third side?
Please help! will mark brainly. I appreciate it thans
Answer:
a = 5.2 unitsA = 53°, B = 44°, C = 83°b = 228 feetStep-by-step explanation:
You have triangles with two sides and the included angle given, or all three sides given. You want the measures of the missing sides or angles.
Law of CosinesFor triangle ABC, the law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
Solving for the third side, we get ...
c = √(a² +b² -2ab·cos(C))
Solving for the angle, we get ...
C = arccos((a² +b² -c²)/(2ab))
The names of the sides and vertices can be permuted, as long as the angle is between the given sides.
1. A=35°, b=7, c=9a = √((7² +9² -2·7·9·cos(35°)) ≈ 5.176
The measure of side 'a' is about 5.2 units.
2. a=8, b=7, c=10C = arccos((8² +7² -10²)/(2·8·7)) = arccos(13/112) ≈ 83.33°
A = arcsin((8/10)·sin(83.33°)) ≈ 52.62°
B = arcsin((7/10)·sin(83.33°)) ≈ 44.05°
The last two angles are found using the law of sines:
sin(A)/a = sin(B)/b = sin(C)/c
3. a=230 ft, B=38°, c=360 ftb = √(230² +360² -2·230·360·cos(38°)) ≈ 228 . . . . feet
The third side measures 228 feet.
__
Additional comment
A calculator or spreadsheet can be programmed with the necessary formulas so that you can avoid a lot of repetitive work when you have several of these to solve. You need to make sure angles are treated appropriately, as the default is often radians, rather than degrees.
When solving for angles from three given sides, we like to solve for the largest angle first. That avoids any ambiguity when using the Law of Sines to find the other angles.
When using the Law of Sines to find a second angle after using the Law of Cosines, it can work well to find the smallest remaining angle. (In the first problem, that would be the angle opposite the side of length 7; in the last problem, that would be the angle opposite the side of length 230.)
Next (1 point) A quiz consists of 20 multiple-choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. P(pass)
The probability of passing if the minimum passing grade is 50 %. P(pass) is 0.000035 .
Given :
A quiz consists of 20 multiple - choice questions, each with 6 possible answers. For someone who makes random guesses for all of the answers .
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
Binomial problem with n = 20 and p = 1/6 , q = 5/6
50 % of 20 = 10
P ( x = 10 ) = C ( 20 , 10 ) ( 1/6 )^10 ( 5/6 )^10
= 184756 * ( 1/6 )^10 ( 5/6 )^10
= 0.000035
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If x = 7 units and h = 6 units, then what is the area of the rhombus pictured above? A 8 square units b 7 square units c 42 square units d 28 square units
The area of the rhombus is 42 square units, and the correct answer is C.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
We have given that side of the rhombus is 7 units and height is 6 units.
To find the area of rhombus:
Remember that a rhombus is any quadrilateral that has four equal sides.
As a rhombus is also a parallelogram.
Formula to calculate area of rhombus using base and height;
Area of the rhombus = base x height
We have base = 7 units
And height = 6 units.
Substituting the values to the formula,
Area of the rhombus = 7 x 6
Area of the rhombus = 42 unit squared.
Therefore, the area is 42 square units.
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test the series for convergence or divergence. if the series is convergent, use the alternating series estimation theorem to determine how many terms we need to add in order to find the sum with an error less than 0.0001?
By using the alternating series estimation theorem we found that the number of terms we need to add in order to find the sum with an error less than 0.0001 is 7.
We must employ one of the convergence tests to determine whether the provided series is convergent or divergent. The alternating series test, which states that a series converges if it takes the form ∑ [tex](-1)^{n}[/tex] x an, where 'an' is a decreasing sequence of positive terms, is the most applicable test for this series.
∑ [tex](-1)^{n}[/tex] x an
a n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex]
by taking the derivative of the expression for a n, this sequence is decreasing and showing that it is always negative. given by a'n = [tex]\frac{(n + 1)}{(n^2 + 2n + 3)}[/tex] [tex]- \frac{(n + 1) X 2)}{(n^2 + 2n + 3)^2}[/tex]
= [tex]\frac{(-2n - 2)}{(n^2 + 2n + 3)^2}[/tex]
for all values of n it is negative, therefore the sequence a n is decreasing. Thus, given series satisfies the conditions of the alternating series test. Therefore, the series is convergent.
The alternating series estimation theorem can be used to determine how many terms are required to be added in order to find the total with an error of less than 0.0001. This asserts that the first disregarded term in an alternating series is smaller than the error in the series' sum. The error in the sum of the series with N + 1 terms is therefore smaller than the value of the (N + 1)th term in the series if we add N terms to the series and the error is less than E.
Find the first term in the series that is less than 0.0001 in order to calculate the number of terms we must add to the series in order to find the total with an error smaller than 0.0001.
given series that a 1 = [tex]\frac{2}{4}[/tex] = 0.5, a 2 = [tex]\frac{3}{9}[/tex] = 0.333, a 3 = [tex]\frac{4}{16}[/tex] = 0.25, and a 4 = [tex]\frac{5}{25}[/tex] = 0.2. Since the first term that is less than 0.0001 is a 7 = [tex]\frac{8}{64}[/tex] = 0.125, Adding, 7 terms to the series in order to find the sum with an error less than 0.0001.
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Solve 0=5y2-60 , round your answer to the nearest hundredth
Answer: y=-3.46,3.46
Step-by-step explanation:
isolate y
5y^2=60
y^2=12
y=-3.46,3.46
Find the matrix A representing the reflection about the line L in R^2 which consists of all scalar multiples of the vector [6 3]. A = []
the matrix A, which is composed of all scalar multiples of the vector [6 3], and represents the reflection about the line L in R2.A = [[-6/7, 9/7],[9/7, 6/7]]
Let L be the line in R^2 which consists of all scalar multiples of the vector [6 3], then the equation of the line is y= (3/6)x.
We need to find the matrix A which represents the reflection about the line L.
Let (x1, y1) be any point on the line L and let (x2, y2) be its reflection about the line L.
Now, we know that the slope of the line L is 3/6, hence the slope of the normal to the line L is -6/3.
So, the equation of the normal to the line L is y = -(6/3)x. Now, we can use the point-slope form of the line equation to calculate the equation of the line passing through (x1, y1) and its reflection (x2, y2).
The line that connects (x1, y1) and (x2, y2) has the following equation:
y-y1 = (y2-y1)/(x2-x1) (x-x1)
=> y-y
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Complete the fraction to make a true inequality, and explain your reasoning
4 × < 4
3
I know this because the fraction I made
Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine. (cos^4 (x) sin^4 (x))
The Trigonometric Expression can be written as :
cos⁴ x = 18(3 + 4cos2x + cos4x)
Power:
In mathematics, a power defines a base number raised to an exponent. The base is the factor multiplied by itself, and the exponent is the number of times the same base is multiplied.
Reducing / Lowering Power:
Power identities are trigonometric identities, allowing us to rewrite trigonometric expressions raised to powers in terms of simpler trigonometric expressions.
According to the question:
cos2x = 2cos²x -1
⇒ cos²x = 1/2 (1 + cos2x)
⇒ cos²2x = 1/2 (1 + cos4x)
⇒ cos⁴ x = (cos²x)²
= 1/4(1 + 2cos2x+cos²2x)
⇒ cos⁴ x = 1/4( 1 + 2cos2x + 1/2(1+cos4x))
⇒ cos4x = 1/8(3 + 4cos2x+cos4x)
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A parallelogram is a quadrilateral with two pairs of parallel sides.
A quadrilateral is a parallelogram _[blank]_.
Which answer correctly fills in the blank in the previous sentence?
if it has only two pairs of parallel sides
if and only if it has two pairs of parallel sides
because it has only four sides and two of them are parallel
if it has two pairs of parallel sides and is a polygon
The quadrilateral is a parallelogram if and only if it has two pairs of parallel sides
What is parallelogram?
In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.
It is given that:
A parallelogram is a quadrilateral with two pairs of parallel sides.
As we know,
The quadrilateral can be defined as the four-sided polygon in geometry having four edges and four corners.
The quadrilateral, has:
Two pairs of congruent sides.
It has one pair of opposite congruent angles.
The diagonals of a kite are perpendicular.
One diagonal is bisected.
The top and bottom angles are bisected but does not have congruent diagonals.
A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.
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What is volume of the rectangular prism?; What is the formula to rectangular prism?; How do you find the length of a rectangular prism?; What is the surface area of a box with a length of 6 ft a width of 3 ft and a height of 2ยฝ ft?
The formula of the volume of the rectangular prism is,
V = l * w * h
The formula of the surface area of the rectangular prism is,
A = 2(lw + wh + lh)
the surface area of a box is 72 sq.ft.
For a rectangular prism with length(l), width(w) and height(h),
The formula of the volume of the rectangular prism is,
V = l * w * h
The formula of the surface area of the rectangular prism is,
A = 2(lw + wh + lh)
For a rectangular box with a length of 6 ft a width of 3 ft and a height of 2 ft,
here, l = 6 ft, w = 3 ft and h = 2 ft
using the formula for the surface area of a rectangular prism, the surface area of box would be,
A = 2(lw + wh + lh)
A = 2(6 * 3 + 3 * 2 + 6 * 2)
A = 2(18 + 6 + 12)
A = 2(36)
A = 72 sq.ft.
Therefore, the surface area of a box is 72 sq.ft.
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f(x) = 3x² + 4x - 6
g(x) = 6x³5x² - 2
Find (f - g)(x).
O A. (f-g)(x) = 6x³ - 2x² + 4x - 8
O B. (f-g)(x) = -6x³ - 2x² + 4x - 8
O c. (f - g)(x) = 6x³ - 8x² - 4x + 4
O D. (f - g)(x) = -6x³ + 8x² + 4x - 4
The difference of the functions, f(x) = 3x² + 4x - 6 and g(x) = 6x³ - 5x² - 2, is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4.
How to Find the Difference of Two Functions?Finding the difference of two functions involves combining like terms together and then simplify.
Given the functions:
f(x) = 3x² + 4x - 6
g(x) = 6x³ - 5x² - 2
To find (f - g)(x), it implies that we find the difference between f(x) and g(x).
(f - g)(x) = f(x) - g(x)
Substitute
f(x) - g(x) = (3x² + 4x - 6) - (6x³ - 5x² - 2)
Open the parentheses:
f(x) - g(x) = 3x² + 4x - 6 - 6x³ + 5x² + 2
Combine like terms
f(x) - g(x) = - 6x³ + 8x² + 4x - 4
Therefore, the answer is: D. (f - g)(x) = -6x³ + 8x² + 4x - 4
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Usain Bolt masses 94 kg and runs at 10 m/s. How much kinetic energy does he have?
Usain’s brother, Insane Bolt, runs twice as fast and has the same mass. How much kinetic energy does he have?
If you double the mass of an object, how does this affect its kinetic energy?
You serve a volleyball with a mass of 2.1 kg. The ball leaves your hand with a speed of 30 m/s.
A car is traveling with a velocity of 40 m/s and has a mass of 1120 kg.
Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.
Kinetic energy of Usain is 4700kg-m²/s².
Kinetic energy of Usain's brother is 18800kg-m²/s².
If we double the mass kinetic energy get doubled.
What is kinetic energy ?
Kinetic energy of an object is the energy that it possess due to its motion.
It is calculated as [tex]\frac{1}{2}mv^{2}[/tex] where m is mass and v is velocity.
In Usain's case m = 94kg and v = 10m/s.
So, kinetic energy = 4700kg-m²/s².
In Usain's brother case mass is same but velocity is doubled.
So, kinetic energy = 18800kg-m²/s².
From the formula we can see ,
if mass is doubled then kinetic energy get doubled.
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Which statement correctly compares -9 and 2?
A. 92 because 9 is to the left of 2 on a number line.
B. 9 is to the left of 2 on a number line. -9> 2 because 92 because
C. 9 is to the right of 2 on a number line. D. 9 > 2 because 9 is to the right of 2 on a number line.
The statement that correctly compares -9 and 2 is A. -9 < 2 because 9 is to the left of 2 on a number line.
What is a number line?In arithmetic, a number line is a depiction of a graduated straight line which functions as a graphic representation of real numbers. It is presumed that every number line point and every real number correspond to one another.
Horizontal straight lines termed number lines have integers along them spaced equally apart. All of the numbers in a series can be shown on a number line. This line extends indefinitely at both ends.
In this case, -9 is on the left of a number line since it's negative. In conclusion, the correct option is A
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Which statement describes the end behavior of the function f (x) = 1/7 | x - 4 | + 3?
Using limits, it is found that the statement which describes the end behavior of the function f(x) is: As x approaches negative infinity, f(x) approaches positive infinity.
How we find the end behavior of a function f(x)?
It is given by the limit of f(x) as x approaches both positive infinity and negative infinity.
In this problem, the function is:
f (x) = 1/7 | x - 4 | + 3
Hence, the limits are:
[tex]\lim_{n \to -\infty} f(x) = \lim_{n \to -\infty} [1/7 | x - 4 | + 3] = \frac{1}{7} |-\infty - 4| + 3 = \infty\\\\ \lim_{n \to \infty} f(x) = \lim_{n \to -\infty} [1/7 | x - 4 | + 3] = \frac{1}{7} |\infty - 4| + 3 = \infty\\[/tex]
Approaches positive infinity in both cases, hence as x approaches negative infinity, f(x) approaches positive infinity.
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I have tried many times and I just can't get it
Answer:
1) 60
2) 15
3) 45
4) 105
5) 75
Step-by-step explanation:
7y + 5y = 180 A straight angle is 180 Combine like terms
12y = 180 Divide both sides by 12
y = 15
The sum of the interior angles is 180
y = 15
180 - (5y + 3y) = x
180 -(5(15) + 3(15)) = x
180 - (75 + 45) = x
180 - 120 = x
60 = x
Angle c
3y
3(15)
45
Angle DBC
7y
7(15)
105
Angle CBA
5y
5(15)
75
sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 8 tablespoons of raspberries. What is the ratio of tablespoons of raspberries to tablespoons of sugar?
8 to 14
8 to 6
6 to 14
6 to 8
The ratio of tablespoons of raspberries to tablespoons of sugar should be considered as the 8 to 6.
What is ratio?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Calculation of the ratio:
Since Macy's aunt makes raspberry jam using 6 tablespoons of sugar and 8 tablespoons of raspberries.
So here the ration be like
= 8 raspberries tablespoons to 6 tablespoons of sugar
= 8 to 6
hence, the second option is correct.
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Which of the following represents a one to one function?A.Students to thier height B.Students to their weight C.Students to their LRN D.Students to their age
(Option C. Students to their LRN) In this case, each student has a unique LRN, meaning that it can be used in a one-to-one function where each student is mapped to their LRN.
Which of the following represents a one-to-one function?Option C. Students to their LRNA one-to-one function is a type of function where each element in the domain has one and only one image in the range. In this case, each student can be mapped to their LRN (Learning Reference Number) in a one-to-one function. This means that for every student, there is a unique LRN, and for every LRN, there is a unique student. This type of function is useful for keeping track of individual student information, as each student has a unique LRN associated with them.
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what is the volume of the rectangular pyramid shown? a square pyramid. the square base has side lengths 15 yards and the height is 12 yards.
The volume of the rectangular pyramid is 900 cubic yards.
The standard formula of the volume of the rectangular pyramid is written as
V = 1/3s²h
where s refers the base edge and h refers the height.
Here we have given that the square base has side lengths 15 yards and the height is 12 yards.
Now, we have to find the volume of the rectangular pyramid
As we know the the value of base edge is 15 yard and the height is 12 yards.
Now, we have to apply the values on the formula then we get,
=> V = 1/3 x 15² x 12
It can be simplified as,
=> V = 4 x 225
When we do the appropriate arithmetic operation, then we get,
=> V = 900 cubic yard.
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Simplify the expression.
fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 as the denominator
ten fourths
negative ten fourths
8
−8
The simplified form of the given expression as required in the task content is; 8.
What is the simplified form of the expression as described?It follows from the task content that the simplified form of the given expression; -4 ( 2 - (³√8 × 6) ) / 5 is to be determined.
Therefore, By solving the innermost parentheses; we have;
-4 ( 2 - (2 × 6) ) / 5
= -4 ( 2 - 12 ) / 5
= -4 ( -10 ) / 5
= 40 / 5
= 8.
Therefore, the simplified form of the expression is; 8.
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What is the solution to the system of equations y 2 3x 3 x?
The system of equations y 2 3x 3 x= -2 has a solution.
What is Equation?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, etc.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" symbol in it.
According to our question-
y = -2*2/3+3
y= -4/3+3
now simplifying,
5/3
Hence, The system of equations y 2 3x 3 x= -2 has a solution.
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Complete question-
What is the solution to the system of equations y 2 3x 3 x?
the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of pennsylvania showed a mean annual premium of $1,430 with a standard deviation of s s = $165.
(a)
Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
H0: ???? > 1,503
Ha: ???? ≤ 1,503
H0: ???? < 1,503
Ha: ???? ≥ 1,503
H0: ???? ≤ 1,503
Ha: ???? > 1,503
H0: ???? = 1,503
Ha: ???? ≠ 1,503
H0: ???? ≥ 1,503
Ha: ???? < 1,503
(b)
What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)
$
(c)
At
???? = 0.05,
test for a significant difference.
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
The hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium is between -2.064 and 2.064.
Hypothesis testing
The standard formula to calculate the hypothesis testing is given by the z test is
Z = (X – U) / (SD / √n)
Where:
X – Sample Mean
U – Population Mean
SD – Standard Deviation
n – Sample size
Given,
Here we have the the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,430 with a standard deviation of is $165.
Here we need to develop the a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
While we looking into the given question we have identified the values of
Sample mean = 1430
Sample size = 25
Population mean = 1503
Standard deviation = 164
Then the hypothesis testing is calculated as,
=> Z = (1430 – 1503) / (164 / √25)
Therefore, if we reject the null hypothesis and accept the alternative hypothesis. The z score of -2.23 is within the rejection area.
And the 2 critical values (cutoff points) are -2.064 and 2.064. Since the z score, -2.23, is outside this interval, we reject the null hypothesis. We accept the alternative hypothesis.
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Find the area of this triangle. 30ft and 8ft.
Answer: 120 square feet
Step-by-step explanation:
Area formula of triangle:
(height of triangle x length) divided by 2
[tex]\frac{30*8}{2} =\frac{240}{2} =120[/tex]
Answer:
120 ft²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
From inspection of the given triangle:
b = 30 fth = 8 ftSubstitute the given base and height into the formula to find the area of the triangle:
[tex]\implies A=\dfrac{1}{2} \cdot 30 \cdot 8[/tex]
[tex]\implies A=15 \cdot 8[/tex]
[tex]\implies A=120\; \sf ft^2[/tex]
Therefore, the area of the given triangle is 120 ft².
at a certain university, students who live in the dormitories eat at a common dining hall. recently, some students have been complaining about the quality of the food served there. the dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. one evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the dining hall needs improvement Do you think that the quality of food served here needs improvement; even though that would increase the cost of the meal plan? Yes No No opinion a) What is the population of interest? What is the population parameter of interest (that is, what number are you trying to estimate)? b) What sampling plan did the manager use to collect his data? c) In this setting; explain how bias may have been introduced based on the way this sample was selected. That is, explain how those chosen for the sample may be different from those who were not chosen with respect to their answers to the question being asked in the survey: d) How might the sample be selected differently to avoid the bias discussed in part c)? Use one of the methods from the Random Rectangle Activity: In this setting, explain how bias may have been introduced based on the way the question was worded_ That is, explain how the wording of the question might lead toward a specific answer 0 Give an alternative wording to the research question that will avoid the bias discussed in part e)?
To avoid bias - increase the sample size and take reviews randomly
The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. one evening, the manager asked the first 100 students entering the dining hall
There is a bias if taken data contain only the first 100 students, primary reasons students come in a friend circle to the dining hall, possibly that whole friend circle did/ didn't like food. Chances are the first hundred students like the food and the remaining students don't like, vice - versa.
To avoid bias - increase the sample size and take reviews randomly
Therefore, the manager should increase the sample size and take reviews randomly to avoid sampling bias.
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