Answer:
$26.25
Step-by-step explanation:
25% of 35 can be found by multiplying .25 x 35 to get 8.75
the coupon will reduce the regular price of $35 by 8.75 to produce the new price of $26.25
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in
mm, after d days:
f(d) = 9(1.04)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 12.81 mm. What is a reasonable domain to plot
the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 3 to d = 9, and what does it represent? (4 points)
A: The reasonable domain to plot the growth function would be all positive integers for the number of days, d, since the growth occurs over time.
B: The y-intercept of the graph of the function f(d) represents the initial radius of the algae when d = 0. In this case, the y-intercept is 9 mm.
C: To find the average rate of change of the function from d = 3 to d = 9, we need to find the difference in the radius of the algae at d = 9 and d = 3 and divide by the difference in the number of days.
f(9) = 9(1.04)^9 = 12.81 mm
f(3) = 9(1.04)^3 = 10.46 mm
Average rate of change = (12.81 - 10.46) / (9 - 3) = 0.71 mm/day
The average rate of change represents the average amount by which the radius of the algae increases each day from d = 3 to d = 9.
Hi HELLPPPPPPPP PLEASE HELP I WILL MARK BRAINLEST IF YOU HELP ME!!! Find the volume of each solid and round to the nearest tenth if necessary..
ANSWER BOTH!!!!!
The volume of a sphere of radius 5 yd is 523.33 yd³.
What is the volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
We have given,
the radius of a sphere is 5 yd,
To Find: the volume of the sphere solid
So,
Sphere volume = 4/3 πr³
= 4/3 * 3.14 * (5)³
= 4/3 * 3.14 * 125
= 523.33 yd³
Hence, the volume of a sphere of radius 5 yd is 523.33 yd³.
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Find the volume of a sphere with radius 13. Use 3.14 for pi, round your answer to the nearest hundredth if necessary, and do not include units.
the volume of a sphere:
V=[tex]\frac{4\pi r^3}{3} =\frac{4*3.14*13^3}{3}[/tex]≈9198.106
In a trial examination session a candidate at a school has to take of these In the chemistry paper and the biology paper. No two including the physics paper, three papers may be taken consecutively. There is no restriction other examination papers may be taken.
Find the number of different orders in which these 18 examination papers may be taken.
Answer:
What I did was:
Number of possible outcomes when three science papers are together: 3!×16!
Number of possible outcomes when two science papers are together: 2!×17!
Therefore, the answer is 18!−3!×16!−2×17!
I feel like there's some faulty logic in the second line. Correct answer is 4.39×10 15th
.
The deck of a bridge is suspended 205 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 205 − 16t2.
(a)
Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time.
(i)
0.1 seconds
ft/s
(ii)
0.05 seconds
ft/s
(iii)
0.01 seconds
ft/s
(b)
Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.
ft/s
The required answers are
i) -65.6
ii) -64.8
iii) -64
iv) -64
VelocityThe pace at which an object's position changes in relation to a frame of reference and time is known as its velocity.
Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.
Its SI equivalent is the metre per second (ms-1). A body is considered to be accelerating if its velocity changes, either in magnitude or direction.
Now in the given question,
1. Average velocity
When t=2
i. [2, 2.1]
= y(2.1) - y(2) / 2.1 - 2
= 205 - 16(2.1)^2 - 205 + 16(2)^2 / 0.1
= 205 - 16*4.41 - 205 +16(4) / 0.1
= -70.56 +64 / 0.1
= -6.56 /0.1
= -65.6
ii. [2, 2.05]
= y(2.05) - y(4) / 4.05 - 4
= 205 - 16(2.05)^2 - 205 +16(2)^2 / 0.05
= 205 - 16*4.2025 - 205 + 16(4) / 0.05
= -3.24 / 0.05
= -64.8
iii. [2, 2.01]
= y(2.01) - y(2) / 2.01 - 2
= 205 - 16(2.01)^2 - 205 + 16(2)^2 / 0.01
= 205 - 16*4.0401 - 205 + 16(4) / 0.01
= -64.64 + 64 / 0.01
= -0.64 / 0.01
= -64
iv. Instantaneous velocity
y = 205 - 16t^2
dy/dx = -32t
Considering t = 2
Instantaneous velocity after 2 seconds = -32(2)
Instantaneous velocity after 2 seconds = -64
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Evaluate the definite integral of: ∫_0^π (sin(x))^3 dx
Step-by-step explanation:
The definite integral of (sin(x))^3 from 0 to π can be evaluated using a trigonometric identity.
∫_0^π (sin(x))^3 dx = -cos(x)(sin(x))^2 |_0^π
Using the fact that sin(0) = 0 and sin(π) = 0, we have:
-cos(x)(sin(x))^2 |_0^π = -cos(π)(sin(π))^2 + cos(0)(sin(0))^2
= 0 - (-1)(0)^2 = 0
Therefore, the definite integral of (sin(x))^3 from 0 to π is equal to 0.
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm.
Round the probabilities to four decimal places.
It is possible with rounding for a probability to be 0.0000..
c) Find the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less.
this my homework problem
The probability that a randomly selected Atlantic cod has a length of 53.68 cm or less is given by the equation P ( x < 53.68 ) = 0.8439
What is a z-score?The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.
The Z-score is calculated using the formula:
z = (x - μ)/σ
where z: standard score
x: observed value
μ: mean of the sample
σ: standard deviation of the sample
Given data ,
Let the probability that a randomly selected Atlantic cod has a length of 53.68 cm or less be represented as P
Now , the equation will be
The observed value of x = 53.68 cm
The mean of the sample μ = 49.9 cm
The standard deviation of the sample σ = 3.74 cm
Now , z-score is calculated using the formula:
z = (x - μ)/σ
Substituting the values in the equation , we get
z = ( 53.68 - 49.9 ) / 3.74
z = 1.0107
Now ,the p value from the z table is
P ( x < 53.68 ) = 0.84392
And , the probability is P ( x < 53.68 ) = 84.392 %
Hence , the probability is 84.392 %
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The expression of f(x)=10,000(1.15)^x represents the population of Nashville each year. If x% represents the growth rate for each year, what is the value of x?
So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
The expression f(x)=10,000(1.15)^x represents the population of Nashville each year, where x is the number of years after a certain reference point. The growth rate for each year can be found by taking the natural logarithm of the factor (1.15) in the expression:
ln(1.15^x) = ln(f(x) / 10,000)
x ln(1.15) = ln(f(x) / 10,000)
x = ln(f(x) / 10,000) / ln(1.15)
The value of x represents the growth rate as a percentage, so we need to multiply it by 100 to get the percentage:
x = (ln(f(x) / 10,000) / ln(1.15)) * 100
So, the growth rate for each year, x%, can be calculated using the above formula if the population of Nashville for a specific year, f(x)= (ln(f(x) / 10,000) / ln(1.15)) * 100, is known.
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Find the exact lengths of the sides of quadrilateral ABCD with vertices A(4, 5), B(-3, 3), C(-6,-13) and D(6,-2).
As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.
what is quadrilateral ?In terms of the geometry, a quadrilateral is really a four-sided polygon with four corners and four corners. Its origins originate from the Latin terms tetra and latus (meaning "side"). A rectangle is a this double form with four sides, 4 vertices, with four corners. Two main types of convex and convex exist. Convex bedbugs or bed bug also have a number of subclasses, such as trapezoids, parallelograms, quarters, rhombuses, and squares. Corresponding points come in many irregular configurations, such as quadrilaterals, trapezoids, rectangles, kites, square, and rhombuses.
given
The vertices of the quadrilateral ABCD are A(-4, -5), B(-3, 0), C(0, 2), and D. (5, 1).
We need to determine whether ABCD is a trapezoidal shape or not.
We are known that a trapezoid has one set of parallel opposed sides, making it a quadrilateral. Moreover, the slopes of two parallel lines are equal.
To start, the slopes of sides AB, BC, CD, and DA will be calculated.
It has
The incline for
AB =0+5/ -3+4
5. In the first step.
Step 2: The slope in BC is
=> 2-0 / 0+3
=> 2/3.
Step 3: The CD's gradient is
1-2/5-0 is equivalent to -1/5.
The gradient of DA is equal to in step four.
=>-5.1/-4.4/2.3
=>2/3.
As a result, the answers to the above quadrilateral issue are A.5, B.2, 3, C.-1/5, and D.2/3.
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A particle that moves along a straight line has velocity
v(t)=t^2e^(-5t)
meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
NO LINKS!! URGENT HELP PLEASE!!!
1. Make a table showing the length, width, and area for every rectangle with a perimeter of 20 meters and whole-number side lengths. Describe some patterns that you observe in the table.
2. Make a graph of the data(length, area). Describe the shape of the graph.
3. How does the pattern in the table appear in the graph?
Answer:
1. See below.
2. See attachment.
3. See below.
Step-by-step explanation:
Question 1Definition of variables:
Let w be the width of the rectangle.Let l be the length of the rectangle.A rectangle has two pairs of parallel sides of equal length.
Therefore, the equation for the perimeter of a rectangle is:
[tex]P=2(w+l)[/tex]
If the perimeter is 20 meters then:
[tex]\implies 2(w+l)=20[/tex]
[tex]\implies w+l=10[/tex]
If the side lengths are whole numbers, then the length and width are restricted to whole numbers from 1 to 9 (inclusive).
The equation for the area of a rectangle is:
[tex]A =w\cdot l[/tex]
Table
[tex]\begin{array}{|c|c|c|}\cline{1-3}\vphantom{\dfrac12}\textsf{width, m}&\textsf{length, m}&\textsf{Area, m$^2$}\\\cline{1-3}\vphantom{\dfrac12}1&9&9\\\cline{1-3}\vphantom{\dfrac12}2&8&16\\\cline{1-3}\vphantom{\dfrac12}3&7&21\\\cline{1-3}\vphantom{\dfrac12}4&6&24\\\cline{1-3}\vphantom{\dfrac12}5&5&25\\\cline{1-3}\vphantom{\dfrac12}6&4&24\\\cline{1-3}\vphantom{\dfrac12}7&3&21\\\cline{1-3}\vphantom{\dfrac12}8&2&16\\\cline{1-3}\vphantom{\dfrac12}9&1&9\\\cline{1-3}\end{array}[/tex]
As the width increases by 1 m, the length decreases by 1 m.The values for area are symmetric about the point when width and length are the same.The step pattern of the values of area in the table are 7, 5, 3, 1, ...To create a graph of the data, plot the length along the x-axis and the area along the y-axis. Plot the following points:
(9, 9), (8, 16), (7, 21), (6, 24), (5, 25), (4, 24), (3, 21), (2, 16) and (1, 9).The shape of the graph is a parabola that opens downwards.
Its vertex is (5, 25) and its axis of symmetry is x = 5.
Question 3This step pattern of 7, 5, 3, 1, ... is apparent in the graph; as you move away from the vertex in the x-direction, the graph goes down by 7, then 5, then 3, etc. This is the step pattern of a parabola that opens downwards.
There is an axis of symmetry on the graph at the side length value when the width and length are the same (x = 5).
Find a unit vector with positive first component that is orthogonal to the plane passing through the pointsP=(4,5,−7),Q=(13,14,2), andR=(13,14,8)
The unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.
What is a unit vector?
A measurement that combines magnitude and direction is called a vector. A vector having magnitude 1 is referred to as a unit vector.
We are given three points P, Q and R.
The two vectors PQ and PR will lie on the plane through the three given points P(3, 0, 1), Q(4, -2, 1) & R(5, 3,-1).
The vector PQ = (9, 9, 9) and PR = (9, 9, 16) .
Therefore, the required vector is
N = PQ × PR
N = 63i - 63j + 0k
Hence, the unit vector with positive first component that is orthogonal to the plane passing through the points is 63i - 63j + 0k.
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24. Louise the Lion says that if a preimage has parallel lines, then the image will have
corresponding parallel lines after a rotation, translation, and reflection. Is the lion
right or wrong?
The lion is right. When a preimage has parallel lines, these lines will remain parallel under a rotation, translation, and reflection transformation.
This property is known as parallelism preservation. A rotation preserves parallelism because it does not change the orientation of the lines. A translation preserves parallelism because it moves all the points on the lines by the same distance and in the same direction. A reflection preserves parallelism because it flips the preimage across a line, which does not change the relative distances between points on the parallel lines.
Therefore, the image of a preimage with parallel lines under a combination of rotation, translation, and reflection transformations will also have corresponding parallel lines.
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CAN SOMEONE HELP WITH THIS?✨
In the polynomial f(x) = 3x² - 2x + 5, f(0) is solved to get -2
From the equation of the tangent line
m= -2
b = 5
How to find the derivativeThe derivative of the polynomial f(x) = 3x² - 2x + 5 is solved to be
f'(x) = 2(3)x - 1(2)
f'(x) = 6x - 2
f(0) = -2
Equation of the tangent to the parabola f(x) = 3x² - 2x + 5
f'(x) = 6x - 2 at x = 0, f'(x) = -2 hence the slope, m is -2
Using the point slope formula for (0, 5)
(y - 5) = m (x - 0)
y - 5 = -2x - 0
y = -2x + 5
comparing with y = mx + b
m = -2 and b = 5
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How many fifths are there in 6 and 4/5?
Answer:
Step-by-step explanation:
0
the general formula for the number of decibels corresponding to a change in sound intensity to i2 relative to the former intensity i1 is
Part A: β₂ = β₁ + 10 log₁₀ (f)
Part B: Δβ = 20 log10 (d₁/d₂)
This can be solved using the concept of sound intensity.
What is sound intensity?While amplitude is the distance between a wave's resting position and its crest, sound intensity is defined as the sound power per unit area. The power carried by sound waves per unit area in a direction perpendicular to that region is known as sound intensity or acoustic intensity. The watt per square metre is the SI measure of intensity that includes sound intensity.
Part A:
β₂ - β₁ = 10 log₁₀ (I₂/I₁)
given that : I₂ = f × I₁
hence, I₂/I₁ = f
so the equation becomes:
β₂ - β₁ = 10 log₁₀ (f)
β₂ = β₁ + 10 log₁₀ (f)
Part B:
P = Power by the source
I₁= intensity at distance d1 = P/(4πd₁²)
I₂ = intensity at distance d2 = P/(4πd₂²)
Δβ = β₂ - β₁ = 10 log₁₀ (I₂/I₁)
β₂ - β₁ = 10 log₁₀ ((P/(4πd₂²))/(P/(4πd₁²)))
Δβ = 10log₁₀ ((d₁/d₂)²)
Δβ = 20log₁₀ (d₁/d₂)
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Express f squared - 6f + 7 in completed square form.
Can somebody help me please
Answer:
330
Step-by-step explanation:
the actual answer is 328.77. 15% was 42.88
Answer:
330$
Step-by-step explanation:
the actual answer is 330$ it is true if you not believe then go
Point M is the midpoint of AB. The coordinates of point A are (−6, 1) and the coordinates of M are (−4, 1). What are the coordinates of point B?
Let the point of A be (x,y)Then, (2x−4,2y+19)=(2,8)2x−4=2,2y+19=8x=8,y=−3So, the point A is (8,−3)(b) Let the point B be (x,y)Then, (2x−1,2y+2)=(−2,4)2x−1=−2,2y+2=4x=−3,y=6So, point B is (−3,6)
I hope it helps mate
Have a nice day
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A plumber had two pipes. The ratio of the legth of the longer pipe to the shorter pipe was 9:2. When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe. Find the length of the shorter pipe in meters
The length of the shorter pipe will be 1.065 meters.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a plumber had two pipes. The ratio of the length of the longer pipe to the shorter pipe was 9:2.
When he cut 1.65m from the longer pipe, the remaining length was 3 times that of the shorter pipe.
L / S = 9 / 2
L - 1.65 = 3S
4.5S - 1.65 = 3S
1.5S = 1.65
S = 1.065 meters
Hence, the measure of the short pipe will be 1.065 meters.
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The perimeter of a square must be greater than 138
inches but less than 186
inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The perimeter of a square is given by P=4s
, where s represents the length of a side).
Express your answer in interval notation. Use decimal form for numerical values.
The range of possible side lengths that satisfy the these conditions is given as follows:
34.5 < s < 46.5.
How to obtain the perimeter of a square?The perimeter of a square of side length s is given by the multiplication of 4 by s, as follows:
P = 4s.
Hence, for a square with perimeter of 138 inches, the side length is given as follows:
4s = 138
s = 138/4
s = 34.5 inches.
For a square with perimeter of 186 inches, the side length is given as follows:
4s = 186
s = 186/4
s = 46.5.
Hence the interval is given as follows:
34.5 < s < 46.5.
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HOME LIFE In a survey, 837 people were asked about their living arrangements. Of the people surveyed, 329 of them lived in apartments. Of the 629 people who live with at least one other person, 218 live in an apartment.
Using this data, if a person is chosen at random, what is the probability that he or she is living with another person, given that they live in an apartment?
The probability that a person lives with another person, given that they live in an apartment, is approximately 0.664.
We need to utilise conditional probability to determine the likelihood that a person lives with another person given that they reside in an apartment.
Let's define the subsequent occasions:
A: at least one other person lives with the individual.
B: The resident is an apartment dweller.
The probability that a person shares a home with at most one other person, assuming that they reside in an apartment, is P(A|B).
We are aware of:
The probability that someone resides in an apartment is P(B) = 329/837.
The probability that a person shares a home with at most one other person, given that they reside in an apartment, is given by P(A|B) = 218/329.
P(A|B) can be calculated using Bayes' theorem as follows:
P(A|B) equals P(B|A)*P(A)/P (B)
We may calculate P(B|A), the probability that an individual resides in an apartments given that they share a residence with at most one other person, using the following formula:
P(A and B) = P(B|A) (A)
We are aware of:
The probability that someone lives in an apartment with at most one other person is P(A and B) = 218/837.
The probability that someone lives with at most one other person is P(A) = 629/837.
By entering these values, we obtain:
P(B|A) = (218/837) / (629/837) = 218/629
Now that all the numbers have been entered, we can calculate P(A|B):
P(A|B) = (218/629) * (629/837) / (329/837) = 0.664
Given that they reside in an apartment, the probability that a person lives with another individual is roughly 0.664.
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Find the area of the shaded region. Round your answer to the nearest hundredth.
The area of the shaded region is 13.76 square meters.
How to find the area of the shaded region?Basically, we have the area of a square minus 4 times the area of the quarter of a circle of radius of 4m.
Remember that for a square of side length S the area is:
A = S^2
And the area of a quarter of a circle of radius R is:
A' = pi*R^2/4
Then the area of the shaded region is:
area = (8m)^2 - 4*(3.14*(4in)^2/4)
area = 64 m^2 - 50.24 m^2
area = 13.76 m^2
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The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.
Which MEASURE OF VARIATION would be best to describe this distribution
A. median
B. interquartile range
C. range
D. mean
The correct measure of variation for best to describe this distribution is,
⇒ interquartile range
Option B is true.
What is interquartile range?For a data set has outliers and variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.
Given that;
The dot plot shows the ages of the 20 people currently in Ms. Jens classroom.
Hence, To describe this distribution we can use the interquartile range.
Thus, The correct measure of variation for best to describe this distribution is,
⇒ interquartile range
Option B is true.
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2 Two points located on JK are J(-1,-9) and K(5,3). What is the slope of JK
A. -2
B. -1/2
c. 1/2
D. 2
Answer:
2
Step-by-step explanation:
To find the slope when given two points, we can use the formula
m = ( y2-y1)/ (x2-x1)
= ( 3- -9)/( 5 - -1)
= ( 3+9) / ( 5+1)
= 12/6
= 2
The slope is 2.
A light bulb consumes 1800 watt-hours per day. How long does it take to consume 5850 watt-hours?
days hours
X
S
Answer:
it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.
Step-by-step explanation:
To solve for the time, we can set up a proportion:
1800 watt-hours / day = X / 5850 watt-hours
Cross-multiplying, we get:
1800 watt-hours * 1 day = X * 5850 watt-hours
Simplifying, we get:
X = (1800 watt-hours * 1 day) / 5850 watt-hours
X = 0.30769 days
To convert to hours, we can multiply by 24:
X = 0.30769 days * 24 hours/day
X = 7.3846 hours
Therefore, it takes 0.30769 days or 7.3846 hours for the light bulb to consume 5850 watt-hours.
algebra please help evaluate the function
The required individual functions are given as g(x) = x⁴- 6 and f(x) = [tex]\sqrt[7]{x}[/tex].
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,
Given funciton
h(x) = (f o g) (x)
Where g(x) = x⁴- 6 and h(x) = [tex]\sqrt[7]{x^4-6}[/tex]
Since, put h(x) ⇒ f(x) and g(x) = x⁴- 6
f(x) = [tex]\sqrt[7]{g(x)}[/tex]
Again put g(x) ⇒ x
f(x) = [tex]\sqrt[7]{x}[/tex]
Thus, the required individual functions are given as f(x) = x⁴- 6 and g(x) = [tex]\sqrt[7]{x}[/tex].
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30
A home theatre system listed at $1136 has a net price of $760.
What is the rate of discount?
the rate of discount will be 33.0986%.
What is Rate?
A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.
When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.
listed price = $1136,
net Price = $760
discount = 1136-760 = $ 376
rate of discount = discount / listed Price*100
= 376/1136 *100
33.0986%
Hence the rate of discount will be 33.0986%.
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Use synthetic division to find the result when 4x³ + 7x² - 4x - 4 is divided by
x + 1. If there is a remainder, express the result in the form q(x) + r(x)
b(x)
Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).
what is expression ?It is permissible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, term, and mathematical operator Three components of a numerical method include numbers, variable, and processes (such as addition, subtraction, multiplication or division etc.) It is possible to oppose expressions and words. An expression, often known as an analytical form, is any mathematics statement that contains variables, values, and an arithmetic procedure between them. For instance, the word m in the balanced formula is separated from the terms 4m and 5 by that of the arithmetic symbol +, as is the term m in the expression 4m + 5.
given
Given expression is (4x⁴-7x³+7x²-12x+15)/(x-1)
then dividing this
=4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
=4x³-3x²+4x-8+7/x-1 in form of q(x)+r(x)/b(x)
= 4x⁴/x-1-7x³/x-1+7x²/x-1-12x/x-1+15/x-1
= -7x² + 4 + 19/(x-1)
Solving the following expression (4x4-7x3+7x2-12x+15)/(x-1) yields the result -7x2 + 4 + 19/ in the form q(x)+r(x)/b(x) (x-1).
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst states we can therefore assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 76 stocks traded on the NYSE that day showed that 36 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of .
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The test static value for the stocks is obtained as 3.482.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
It is given that -
The number of stocks n = 76
X = Number of stocks that got increased in price = 36
p = Proportion of stocks that got increased in price.
The formula for p is p = X/n.
Substitute the values in the equation -
p = 76/36 = 2.11111
Now find the value for q -
q = 1 - p
= 1 - 2.11111
= -1.11111
P=0.3
Q = 1 - P
= 1 - 0.3
= 0.7
Now, the values for H0 and H1 are -
H0 : P = 0.3
H1 : P > 0.3
Under H0, the test statistic is given by -
Z = (p - P)/√(PQ/n)
Substitute the values in the equation -
Z = (2.11111 - 0.3)/√(0.3 × 0.7/76)
Z = 1.81111 /√0.002763
Z = 1.81111 /0.052
Z = 3.482
Therefore, test statistic is 3.482.
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