In an isosceles triangle, the angle opposite the base is referred to as the vertex angle.
A triangle refers to a two-dimensional shape which comprises of three sides and three angles. The isosceles triangle is a type of triangle in which two sides are congruent i.e., they are the same length. The third side of an isosceles triangle is of different length and is referred to as the base. The three angles of any triangle add up to a sum of 180°. In isosceles triangles, the two angles located along the base are referred to as the base angles which are always congruent, or equal. The angle opposite the base is referred to as the vertex angle and is different value from the two base angles. The value for the vertex angle can always be calculated by subtracting the base angles from 180° using the general formula: 180° - 2B = A, where B refers to the base angle and A is the vertex angle.
Note: The question is incomplete. The complete question probably is: Which is the vertex angle of an isosceles triangle.
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Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line
with a slope of 5.9. See the figure below.
With 48 gallons of fuel in its tank, the airplane has a weight of 2383.2 pounds. What is the weight of the plane with 77 gallons of fuel in its tank?
Airplane
weight
(in pounds)
2383.2
48
Amount of fuel
(in gallons)
pounds
48
Answer:
To find the weight of the plane with 77 gallons of fuel in its tank, we can use the linear equation for the weight of the plane in terms of the amount of fuel in its tank. The equation has the form:Weight = m * Fuel + bWhere m is the slope of the line, which is 5.9, and b is the y-intercept, which is the weight of the plane when the amount of fuel is 0. We know that the weight of the plane with 48 gallons of fuel is 2383.2 pounds, so we can use this information to solve for b:2383.2 = 5.9 * 48 + b
b = 2383.2 - 5.9 * 48
b = 2383.2 - 280.8
b = 2102.4Now that we have the value of b, we can plug it back into the equation to find the weight of the plane with 77 gallons of fuel:Weight = 5.9 * 77 + 2102.4
Weight = 456.3 + 2102.4
Weight = 2558.7 poundsSo the weight of the plane with 77 gallons of fuel in its tank is 2558.7 pounds.
Step-by-step explanation:
How to graph:
y= 2x - 5
Answer:
see attached
Step-by-step explanation:
You want to graph y = 2x -5.
GraphOften, the easiest way to graph a linear equation in slope-intercept form is to graph the y-intercept point, then use the slope to identify one or more additional points on the line. The graph is the line through the plotted points.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b
where m is the slope, and b is the y-intercept.
The y-intercept is the point on the y-axis where the line crosses it. The coordinates there are (0, b).
Here, we have y = 2x -5, so m=2 and b=-5. The y-intercept point is (0, -5).
The slope is the ratio of "rise" to "run" for the line. A slope of 2 means the line rises 2 units for each 1 unit it goes to the right. That means (0 +1, b+2) will be another point on the line: (1, -3).
A bullet train travels in 3 and half hours for 320 km. And ordinary train travels 212 km in 8 and half hours. Work out their average speed. I need it now pls be quick
The average speed of the trains are Bullet train = 91.4 km/hr and Ordinary train = 24.9 km/hr
How to determine the average speed of the trains?From the question, we have the following parameters that can be used in our computation:
Bullet train
Distance = 320 km
Time = 3 and half hours = 3.5
Ordinary train
Distance = 212 km
Time = 8 and half hours = 8.5
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
So, we have
Bullet train = 320/3.5 = 91.4
Ordinary train = 212/8.5 = 24.9
Hence, the speed of the ordinary train is 24.9 km per hour
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find the length of the hypotenuse of the triangle pictured below. give your answer accurate to at least 2 decimal places.
The length of the hypotenuse of the triangle is √181 cm
Pythagoras theorem states that in the right -angled triangle , the square of the hypotenuse side is equal to the sum of the square of other two sides.
Hypotenuse it the longest side , as it is opposite to the angle 90°
Pythagoras theorem formula :
Let a be the base
b be the perpendicular and c is hypotenuse
So, according to the Pythagoras
c² = a² + b²
According to the question,
We have to find the length of hypotenuse
Given that base = 10
Perpendicular = 9
Let Hypotenuse = x
Using above theorem
=> x² = (10)² + (9)²
=> 100 + 81 = x²
=> c = √181
The length of hypotenuse is √181
I've answered the question in general as the question is incomplete
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question 1.
Gerald purchased 55 paving stones to use in his garden. The graph shows points representing the number of stones left to place at several different times while Gerald is working.
Select from the drop-down menus to complete the equation, in standard form, that represents the relationship between the number of paving stones left to place, y, and the time, x, Gerald has spent working.
The linear equation representing the relationship between the number of paving stones left for Gerald to place, y, and the time, x, Gerald has spent working is 5x + y = 55.
What is the linear equation?A linear equation is always in the form of y = ax + b, where a is the slope and b is the y-intercept.
The slope, a, is given as (y2 - y1)/(x2 - x1).
Data Points:(0, 55), (3, 40), and (7, 20)
Taking (3, 40) and (7, 20), the slope is determined as follows:
7 - 3 = 4
20 - 40 = -20
-20/4
= -5
In standard form, the linear equation is 5x + y = 55.
Thus, based on the linear equation above, we can conclude that the more time Gerald spends playing with the paving stones, the fewer stones he has to place.
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Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $615. Otherwise, you have to pay your friend $37.
Step 2 of 2 :
If this same bet is made 621 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
If this same bet is made 621 times,then we expect to lose of $4514670
Probability
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The bet is done 621 times then expected value is that we may have a loss of $4514670.if the bet is that is heart comes we will get $615 and lose $37 if not comes.
$615 if hearts come and lose $37 when not comes and bet is made 621 times. Calculate the expected win after 621 times.
There are 578 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 578/52*577/51
=333,506/2652
=125.75
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-125.75
=124.75
When bet is made only 1 time expected value will be 125.75*615-124.75*37
=77,336.25 - 4,615.75
=-72720.5 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -72720*621= 4514670.
Then the expected value when bet is made 621 times is that we will lose $4514670 .
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What are the 5 properties of rhombus and rectangle?
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
Properties of rhombus:
1. All sides are equal in length.
2. Opposite angles are equal.
3. Diagonals bisect each other at 90°.
4. Diagonals are respective angle bisectors.
5. Any two adjacent angles add up to 180 degrees.
6. The area of the rhombus is a product of the lengths of the 2 diagonals divided by 2.
Properties of rectangle:
1. Opposite sides are equal in length.
2. All the angles are 90°.
3. Diagonals bisect each other.
4. Any two adjacent angles add up to 180 degrees.
Hence, the common properties are
1. Opposite angles are equal in measure.
and
2. Diagonals bisect each other.
3. Any two adjacent angles add up to 180 degrees.
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the cholesterol levethe cholesterol levels (in milligrams per deciliter) of 32 adults are listed below: 100 100 105 105 106 106 107 107 109 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134 find the interquartile range for the data.ls (in milligrams per deciliter) of 32 adults are listed below: 100 100 105 105 106 106 107 107 109 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 134 find the interquartile range for the data.
Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.
What is data ?A collection of information, whether numerical or not, can take any shape and is referred to as data in mathematics. Calculable information, such as student test scores, employee salaries, football team member heights, etc., is known as numerical data and is always gathered in numerical form.
here the explanation,
Five points in brief
Min=91, Q1=94, Q2=99, and Q3=104.75, with a maximum of 130 B] Outlier values are those that are either below or above Q1-1.5*IQR (IQR = Q3-Q1=104.75-91=13.75).
Reduced value: 94-1.5*13.75 = 73.37500
Since the upper value is 104.75 + 1.5 * 13.75 = 125.37500, the last observation, 130, is an outlier.
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Determine which integer in the solution set will make the equation true.
3p + 13 = 22
S: {−1, 1, 3, 4}
−1
1
3
4
The integer in the solution set that will make the equation true is (c) 3
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
3p + 13 = 22
Subtract 13 from both sides of the expression
So, we have the following representation
3p = 9
Divide both sides of the equation by 3
p = 3
Hence, the solution is p = 3
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Customers arrive at a checkout counter in a department store according to a Poisson distribution at an average of seven per hour. If it takes approximately ten minutes to serve each customer, find the mean use at least four digits after the decimal if rounding...)
and variance of the total service time for customers arriving during a 1-hour period. (Assume that a sufficient number of servers are available so that no customer must wait for service.) (use at least four digits after the decimal if rounding...) What is the probability that the total service time will exceed 2.5 hours? (use at least four digits after the decimal if rounding...)
The answer of this question is found to be 0.0012.
The mean total service time is 10 minutes times lambda (the average number to turn up during the hour)
Lambda is 7, since the average rate is 7 per hour and your time window is 1 hour.
mean service time = 7 × 10 = 70 minutes.
For a poisson process, lambda is both the mean and variance of the arrivals.
So the variance = 10² × lambda = 700, since we want the variance of the service time, rather than the variance of the arrival rate.
This is because:
σ(aX) = a × σ(X).
and σ = sqrt(variance)
σ(service time) = 10 σ(arrival time)
variance(service time) = (10 × σ(arrival time))²
variance(service time) = 100 × variance(arrival time) = 100 × lambda = 100 × 7
mean(servicetime) = 70
variance(servicetime) = 700
2.5 hour = 150 min
Z = [tex]\frac{(S - 70)}{\sqrt{700} }[/tex] follow N(0,1)
P(S > 150) = P( [tex]\frac{(S - 70)}{\sqrt{700} }[/tex]> [tex]\frac{(150 - 70)}{\sqrt{700} }[/tex])
=P(Z > -2.5512)
=0.0012
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Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
Answer:
her sales would be 56.9
Step-by-step explanation:
Answer:
56.9
Step-by-step explanation:
In the accompanying diagram, the slope of the ascent of an aircraft is 7/50. Find m
Answer:
∠ x ≈ 8°
Step-by-step explanation:
the tangent of the angle x is equal to the slope m , that is
tanx = m = [tex]\frac{7}{50}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{50}[/tex] ) ≈ 8° ( to the nearest degree )
Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 96(1.03)
Answer:
Growth; 3%-------------------------------------------
According to the function the change is 1.03.
It can be shown as:
1.03 = 103% = 100% + 3%As we see it is a 3% growth.
After calculating, the percentage increase will be equal to 3%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the data mentioned in the question,
In the form of the exponential equation.
y = [tex]ab^x[/tex]
The initial value is a, b is the growing (or decay) factor, and (b - 1) × 100% is the growth (or decay) rate,
A further point is that the equation depicts growth if b > 1 and decay if b < 1.
Taking into consideration the aforementioned, we discover that for exponential function,
y = 96(1.03)
a. Since 1.03 > 1, this show the growth in relationship.
b. the value of b = 1.03, so the growth factor is 1.03
c. The rate of growth
= ( 1.03 -1 ) × 100%
= 0.03 × 100% = 3%
d. Since 'a' has a value of 96, the starting value is also 96.
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Maya said farewell to her favorite uncle as he boarded a plane for Paris. That night she dreamed about an airplane that ran into a thunderstorm and crashed into a mountain, killing everyone onboard. When she woke up, she learned that her uncle’s plane had encountered violent turbulence on the way to Paris and that several passengers had been injured on the flight. She concluded that this series of events (E) is very strong evidence that she has the ability to see distant things using only her mind (H).
Maya thinks that E is strong evidence for H. Assuming she has updated properly given her probability assignments, what does this mean about her assignments to P( E | ~H ) and P( E | H )? For each of these values, how might you challenge her assignment? (Don’t focus on P( H ) and P( ~H ).)
The likelihood of this question will be determined as P( E | ~H)=1 - P(E|H).
For independent events the probability P( E | H ) is calculated as:
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
Since the event E has already happened and is obvious, if P(E | H)>P(E | H) then the event E is dependent on the mind of maya, but if P(E | H)>P(E | H) then the event E is not dependent on the mind of maya.
In our situation, P(E | H), which means that the plane crushing is independent of Maya's thoughts, is the probability that will suit this argument.
Since it is illogical to claim that Maya can perceive far-off objects with her mind, the likelihood of this question will be determined as P( E | ~H ) = 1 - P( E | H ).
For independent events the probability P( E | H ) is calculated as
P( E | H ) = P( E ) * P( E and H)
P( E and H) = P(E) * P(H).
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Find the standard matrix of the given linear transformation from R2R2 to R2R2 Projection onto the line y=2xy=2x So basically, I got the standard matrix to be (1200),(1020), my question is: is this actually right? I have been looking online and it appears that maybe I am wrong?
The standard matrix of the linear transformation given in the question is
= 1/ 5 [ 1 2 ]
[ 2 4 ]
The direction vector of the given line is , v = ( 1 ,2 ).
So the projection of the line will be,
projection ( x ,x ) = ( (x , y ) . v / v^2 )v
= ( ( x + 2y)/5 ) v
Therefore, the required standard matrix will be ,
1/5 2/5
2/5 4/5
= 1/ 5 [ 1 2 ]
[ 2 4 ]
A matrix is also known as a rectangular array . The elements are arranged in the form of rows and tables forming a table . Arrays are an important part of both mathematical and computational applications.
The data in a conputer is stored in the form of an array . We can perform various operations on matrix like addition, subtraction , multiplication or division.
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If the average of 7 positive integers is 100, find the highest possible value of the largest number.
PLS ANSWER QUICKLY FOR THE SAKE OF THE GOD!!!1
Answer:
Step-by-step explanation:
a) ( combining like terms)
Simplify (7a + 10b) − (4a − 6b).
b) Simplify the expression. ( combining like terms)
−5x + 8y + 2x − 3y
c) Solve and graph the inequality x - 4 ≤ -1 (the name of the game is ...)
a) Combining like terms (7a + 10b) − (4a − 6b) = 3a + 16b
b) The Simplify expression −5x + 8y + 2x − 3y the answer is -3x + 5y
c) The inequality x - 4 ≤ -1 Graph is given below.
What do you mean by algebraic expression?
When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
An algebraic expression is composed of various parts.
a) Given expression:
(7a + 10b) - (4a - 6b)
= 7a + 10b - 4a + 6b
On combining like terms we get,
(7a - 4a) + (10b + 6b)
= 3a + 16b
Therefore, (7a + 10b) − (4a − 6b) = 3a + 16b
b) Given expression :
−5x + 8y + 2x − 3y
On combining like terms we get,
-5x + 2x + 8y - 3y
= (-5x + 2x) + (8y - 3y)
= -3x + 5y
therefore, −5x + 8y + 2x − 3y = -3x + 5y
c) Given expression:
x - 4 ≤ -1
⇒ x ≤ -1 + 4
⇒ x ≤ 3
Graph of the function is given below:
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Determine whether the following statement is sometimes, always, or
never true.
The range of an even function is (-∞o, max], where max is the
maximum of the function.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
what is range ?the range of variation that is conceivable or the boundaries between it: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.
here the explanation
We can say that our range is any real number value between -infinity and infinity, or (,), if our range is any real number value. The range is all real numbers, but we can express this more succinctly by using the symbol R.
a position where the value of a function is highest. It is an absolute maximum if the value is larger than or equal to all other function values.
It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.
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The ratio of moose to reindeer is 5 to 4. If
there are 60 moose, how many reindeer are
there?
Answer:
48 reindeer
Step-by-step explanation:
the 5 part of the ratio relates to 60 moose , then
60 ÷ 5 = 12 ← value of 1 part of the ratio
then
4 × 12 = 48 ← number of reindeer
Evaluate the expression 5(7 − 4)2 ÷ 3 + 11.
3
14
26
33
Answer:
26
Step-by-step explanation:
which option describes a situation in which reduction occurs
The option which describes a situation in which reduction occurs Cl2 becoming Cl–. (Option B)
Reduction refers to the type of chemical reactions in which the number of electrons in an atom, or a group of atoms increases. The electrons taken up by the substance reduced are supplied by another substance, which is thereby oxidized. Hence, oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state. In the given situation, Cl2 becoming Cl- represents reduction as the oxidation state is decreased from 0 to -1.
Note: The question is incomplete. The complete question probably is: Which option describes a situation in which reduction occurs? A) S2– becoming S. B) Cl2 becoming Cl–. C) Al becoming Al3+. D) Xe2+ becoming Xe6+.
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On July 1, 2021, purchased $11,000 of IBM Corporation bonds at face value. The bonds pay interest twice a year on January 1 and July 1. The annual interest rate is 10%.
the interest will be $1000 IBM corporation bank.
What is simple interest?
A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
where P is the principal amount of money, R is the interest rate as a decimal, T is the time.
So simple interest will be = 10000*10*1 /100 = $1000
Hence, the interest will be $1000 IBM corporation bank.
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Jim Moore opens a new savings account. He deposits $12,000 at 12% compounded semiannually. At the start of the fourth year, Jim deposits an additional $50,000 that is also compounded semiannually at 12%. At the end of six years, the balance in Jim Moore's account is
Multiple Choice
$90,195.20
$93,932.28
$95,072.31
$88,555.42
After six years, Jim Moore's account will have a balance of $69,341 thanks to compound interest.
What is compound interest?Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.
As per the given information in the question,
The account in this issue is split up into two distinct investments. The first one is for $12,000 with a 12% compound interest rate over six years. Consequently, the criteria are as follows:
P = $12,000
r = 0.12
t = 6 years.
[tex]A_1(t)=P(1+\frac{r}{n} )^n^t[/tex]
[tex]A_1(6)=12000(1+\frac{0.12}{6} )^(^2^)^(^6^)[/tex]
A₁(6) = $15219.
The value of the second investment, which is $50,000 and is likewise compounded semi-annually at 12%, will be as follows at the conclusion of the fourth year:
[tex]A_2(t)=P(1+\frac{r}{n} )^n^t[/tex]
[tex]A_2(2)=50000(1+\frac{0.12}{6} )^(^2^)^(^2^)[/tex]
A₂(2) = 54122
Hence,
A(6) = A₁(6) + A₂(2)
A(6) = 15219 + 54122
A(6) = $69341
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A= 25 ft
B = 45 ft
A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25
ft and Garden B has a diameter of 45 ft.
a.
If the gardener wants to outline the gardens in edging, how many feet will be needed to
outline the smaller garden? (Express as an exact answer in terms of .)
Formula:
The perimeter of smaller circle is 78.5 ft
What is area?
Area is that the amount that expresses the extent of a vicinity on the plane or on a semicircular surface. space|the world|the realm} of a plane region or plane area refers to the world of a form or planate plate, whereas area refers to the world of associate degree open surface or the boundary of a three-dimensional object.
Main Body:
A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25 ft and Garden B has a diameter of 45 ft.
outline the smaller garden means circumference of the circle.
Perimeter of circle is 2πr.
diameter = 25 ft
radius = 25/2 = 12.5 ft
Radius = 2π *12.5
= 25 π
= 25*3.14
= 78.5 ft
Hence the perimeter of circle is 78.5 ft
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Need help answer please!
Answer:
The second option/ B
Step-by-step explanation:
6 coins plus 4 coins is 10 coins, and you can’t forget the x amount of pennies.
Please Answer with Explanation
Answer:
a.
Step-by-step explanation:
it is not clear what your teacher discussed and wants from you here.
formally, all triangles are similar, as the description says. and the sequence of the vertexes in the "name" does not make any difference in identifying the triangle. this would be only important when identifying a specific angle (the center letter). in other words : a triangle is identified by naming its three corners in any sequence. simply because for the similarity concern you can twist and turn the triangle until it has the same orientation as the other triangle to compare.
so, again, a very strange question from your teacher. many greetings from me.
as explained, formally all 4 statements are correct.
but in order to identify one, it has to be a.
because the sequence of the corners are the same.
in QTS the side QT (the shortest of the 3 sides) is named first. and TS (the longest of the 3 sides) is named last.
in PQT we have the same sequence. PQ is the shortest side first, and QT is the longest side last.
no other answer option has the same sequence on the left and the right side.
but again, this is actually irrelevant for the similarity relation.
e.g. triangle RQS = triangle SQR, they are just twisted and turned images of the same triangle.
The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50.
Part 1: The point of maxima is 21.212
Part 2: x = 21.212 is approximately equal to the year 2022
Part 3: The percentage at that time is 16.37%
Part 4: The rate of change of the percentage at that time is 0.294
Part 1:
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
where x is the number of years since 2000, data from 0<=x<=50
Differentiating the function with respect to x and equating it to 0
p'(x) = -0.00066x^2 + 0.028x - 0.0033
We will find the critical points of p'(x)
p''(x) = dp'(x)/dx = -0.00132x + 0.028
Critical points of p'(x) lies at x where p''(x) = 0
Thus, -0.00132x + 0.028 = 0
x = 0.028/0.00132 = 21.212
Now, p'''(x) = -0.00132<0
x = 21.212 is a point of maxima of p'(x)
Therefore, the maximum possible values of x could lie at x = 21.212 as well as the extreme points of the domain p'(x), i.e. at x = 0 and 50
p'(0) = -0.00066(0)^2 + 0.028(0) - 0.0033 = -0.0033
p'(21.212) = -0.00066(21.212)^2 + 0.028(21.212) - 0.0033 = 0.2936
p'(50) = -0.00066(50)^2 + 0.028(50) - 0.0033 = -0.2533
Hence p'(x) attains maxima at x = 21.212
Therefore, p(x) increases most rapidly at x = 21.212
Part 2:
From the given condition in the question, x = 0 corresponds to the year 2000
Thus x = 21.212 is approximately equal to year 2022
Part 3:
The percentage at that time:
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
p(21.212) = -0.00022(21.212)^3 + 0.014(21.212)^2 - 0.0033(21.212) + 12.236
= 16.365
= 16.37%
Part 4:
Rate of change of the percentage at that time
p(x) = −0.00022x^3 + 0.014x^2 − 0.0033x + 12.236
p'(21.212) = -0.00066(21.212)^3 + 0.028(21.212) - 0.0033
= 0.2936
=0.294
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3 5/2 in radical form
The simplest form of the exponent number of 3^(5/2) is √243.
What is exponential form of a number?
To express numbers that are either too large or too tiny, use exponential notation, which raises the number to the power of the appropriate exponent. The exponent's power might either take the positive or negative form.
For instance, we may express the exponential form of 5 × 5 × 5 × 5 as 5⁴, where 5 is the base and 4 is the power. The power here indicates how many times we are multiplying the base by itself.
Given number is 3^(5/2)
The base of the given number is 3 and exponent 5/2.
Apply the formula a^(m/2) = √a^m in the given number:
3^(5/2) = √3⁵
Putting 3⁵ = 243
3^(5/2) = √243.
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Adrian hopes that his new training methods have improved his batting average. Before starting his new regimen, he was batting 0.250 in a random sample of 52 at bats. For a random sample of 25 at bats since changing his training techniques, his batting average is 0.480. Determine if there is sufficient evidence to say that his batting average has improved at the 0.10 level of significance. Let the results before starting the new regimen be Population 1 and let the results after the training be Population 2.
Step 1 of 3 :
State the null and alternative hypotheses for the test. Fill in the blank below.
H0Ha: p1=p2: p1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯p2
According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic.
The value of the test statistic is z = 1.65.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
Average of 0.48 in 25 at bats,
Test if there was improvement:
At the null hypothesis :
[tex]H_0 : P_1 - P_2 = 0[/tex]
At the alternative hypothesis:
[tex]H_1 : P_1 - P_2 > 0[/tex]
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
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In 2018, the circulation of a local newspaper was 2,125. In 2019, its circulation was 2,250. In 2020, the circulation was 2,350.a. Find the percent of increase in the newspaper’s circulation from 2018 to 2019 and from 2019 to 2020.
b. Which period had a higher percent of increase, 2018 to 2019, or 2019 to 2020?
Answer:
circulation was 2,250. In 2020, the circulation was 2,350.
Step-by-step explanation:
