Answers
The value of 'a' can be 20. The correct option is C, 20.
What is triangle inequality theorem?As per the triangle inequality theorem, the sum of any two sides of the triangle should be greater than the third side.
As per triangle inequality theorem, the sum of the two sides of the triangle should be greater than the third side of the triangle.
As per the triangle inequality theorem, if 'a' is the longest side of the triangle then,
21 + 6 > a
27 > a
If a is not the longest side of the triangle,
21 + a > 6
a > -21 + 6
a > -15
6 + a > 21
a > 21 - 6
a > 15
Therefore, the value of a should be greater than 15 and less than 27. Since the only option under this condition is 20.
Hence, The correct option is C, 20.
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Related Questions
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Answers
Answer:
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• Calculate the volume of 3 different spheres and cylinders; choose different radii for each sphere and cylinder.
• The height of the cylinders is equal to the diameter of the corresponding sphere.
Here’s the sheet:
Please help me with this question
Answers
To derive the formula that goes through these two points, we use the general equation for an exponential equation.
Y = a(b)^x
There we will substitute the two points into this equation to get two equations
45 = a(b)^2
5/9= a(b)^-1
By dividing the first equation by the second, we obtain:
27 = b^3
Therefore b= 3
We plug b=3 into the first equation using the second point:
45 = a(3)^2
We get a = 5
Therefore the equation is y = 5(9)^x
We can verify this equation by plugging in the two points given to see if it works.
5/9 = 5(9)^-1
5/9 = 5/9
And:
45 =5(9)^2
45 = 45
It does, so the equation is correct.
The answer is y =5(9)^x
What is exponential equation?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.Exponential equations are equations in which variables occur as exponents.For example, exponential equations are in the form a x = b y .To solve exponential equations with same base, use the property of equality of exponential functions .To learn more about exponential equation refer to:
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Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . The graph represents the situation . How many dogs was Becca walking by the end of the third month?
Answers
The graph shows that Becca walks five dogs at the end of the third month.
How many dogs are there in the third month?
We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.
We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month . We would now read off the graph to know the number of dogs that he walks after three months.
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according to wine-searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. wine scores range from to , with a score of indicating a great wine, indicating an outstanding wine, indicating a very good wine, indicating a good wine, indicating a mediocre wine, and below indicating that the wine is not recommended. random ratings of a pinot noir recently produced by a newly established vineyard in follow: excel file: data07-11.xlsx 87 91 86 82 72 91 60 77 80 79 83 96 a. develop a point estimate of mean wine score for this pinot noir (to decimals). 82.00 b. develop a point estimate of the standard deviation for wine scores received by this pinot noir (to decimals). 9.6389
Answers
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.
Below table showing calculation of Point Estimate of Mean and Standard Deviation:
Score X-X’ (X-X’)^2
87 5 25
91 9 81
86 4 16
82 0 0
72 -10 100
91 9 81
60 -22 484
77 -5 25
80 -2 4
79 -3 9
83 1 1
96 14 196
984 1022
Mean(X’) = Total Score/n
n = Total number = 12
X’ = 984/12 = 82
Standard Deviation (σ) = √∑(X-X’)^2/(n-1)
σ = √1022/(12-1)
σ = √1022/ 11
σ = 9.6389
(a) The point estimate of mean wine score for this pinot noir is 82.
(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389
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LMNO is a parallelogram. If NM\ =\ x+32\ and\ OL=2x+22,\NM = x+32 and OL=2x+22, find the value of x and then find NM and OL
Answers
Answer:
the value of x is 10
Step-by-step explanation:
Since LMNO is a parallelogram, the opposite sides are parallel and have the same length. This means that NO and LM have the same length, which we can call y. We can write the following equations to represent the given information:
NM = x + 32
OL = 2x + 22
NO = y
LM = y
Since NO and LM have the same length, we can set their lengths equal to each other to find the value of y:
x + 32 = y
2x + 22 = y
We can solve this system of equations by setting the two equations equal to each other and solving for x:
x + 32 = 2x + 22
-x = -10
x = 10
Substituting the value of x back into the equations for NM and OL, we find that:
NM = 10 + 32 = 42
OL = 2(10) + 22 = 32
Therefore, the value of x is 10, and the lengths of NM and OL are 42 and 32.
What is the quotient of
102 and 5?
Answers
The leftover after dividing 102 by 5 is the quotient, which is:
Quotient 20
Remainder 2
102 5: Quotient and Remainder
The quotient and remainder method is one way to determine the quotient and remainder of a division. The dividend (102) and the divisor are already known to us (5). Now, we need to determine the residual and the quotient:
The Quotient and Remainder procedure is as follows:
20 quotient, 5 | 102 dividend, -10 2, and a reminder
As can be seen:
The remainder is 2, while the quotient is 20.
Sometimes, the remaining part is referred to as the "modulo," or simply "mod." This notation is used to say that:
102 mod 5 = 2
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Haylee selects 10 small businesses at random from her state's directory. Let BBBB be the number of businesses she selects that have websites What type of variable is B? Binomial Geometric Neither
Answers
From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
What is binomial variable ?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).
This distribution is used in probability theory and statistics.
A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.
The popular binomial test of statistical significance is based on the binomial distribution.
A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.
Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.
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explain the difference between arithmetic growth and exponential (geometric growth). would you recognize them if they were described in writing and/or by picture?
Answers
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
When one of the parent cell keeps dividing while the other matures, this is known as arithmetic growth. An illustration of arithmetic growth is the ongoing elongation of roots. The early stages of geometric growth are characterized by slow expansion, whereas the latter stages are characterized by rapid expansion.
The amounts added grow by a fixed rate of growth, expressed in percentages. Due to the fact that these remain constant while the amounts added rise, growth is then typically measured in doubling times.
Due to the fact that all populations of organisms have the potential to experience exponential growth, the concept of exponential growth is particularly intriguing in the field of population biology.
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Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long. Each wreath requires 5 yards of uncut ribbon. How many wreaths can Ms. Brooks make?
Answers
The number wreaths that Ms. Brooks make will be 7 wreaths.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that an expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. 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. People make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects
Here, Ms. Brooks has 2 pieces of ribbon to make wreaths. One piece is 18 yards long and the other is 17 yards long.
Since each wreath requires 5 yards of uncut ribbon, the number of wreaths that Ms. Brooks make will be:
= (18 + 17) / 5
= 35 / 5
= 7 wreaths.
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ecall that one of the ten parts of the definition of a vector space says that if is a vector space, then there exists a vector in such that for all in hceggg
Answers
This means that for any vector v in the vector space V, there is a vector 0 in V such that v + 0 = v.
This is known as the identity property, and it states that adding 0 to any vector in V does not change the original vector. The identity property is an essential part of the definition of a vector space.
In general, a vector space is a set of objects called vectors that can be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.
A vector space is a set V together with two operations that satisfy the eight axioms listed below.
Closure under addition. For all vectors u and v in V, the vector u + v is also in V.Closure under scalar multiplication. For all vectors u in V and all scalars c, the vector cu is also in V.Associativity of addition. For all vectors u, v, and w in V, (u + v) + w = u + (v + w).Commutativity of addition. For all vectors u and v in V, u + v = v + u.Existence of an additive identity. There exists a vector 0 in V such that for all vectors u in V, 0 + u = u + 0 = u.Existence of additive inverses. For every vector u in V, there exists a vector -u in V such that u + (-u) = (-u) + u = 0.Compatibility of scalar multiplication with field multiplication. For all vectors u and v in V and all scalars c and d, (c + d)u = cu + du and c(dv) = (cd)v.Compatibility of scalar multiplication with field addition. For all vectors u and v in V and all scalars c and d, c(u + v) = cu + cv.To learn more about vectors, visit:
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Marco has $16.72. He spends $9.21 on a movie ticket. How much money does Marco have left?
Responses
A $7.68$7.68
B $7.51$7.51
C $7.48$7.48
D $7.61
Answers
Answer:
7.51
Step-by-step explanation:
16.72 - 9.21
Nadine's Nursery sells St. Augustine grass seeds for $10 per lbs. and Zoysia grass seeds for $15 per lbs. Nancy wants to buy 20 ;bs. of grass seeds and wants to pay an average of $12 per lbs. How much of each type should she get?
Answers
The quantity of each type that Nadine should get would be= 96 of St. Augustine grass seeds and 144 of Zoysia grass seeds.
What is an average cost ?An average cost is defined as the total cost of production divided by the total number of units produced.
The cost of St. Augustine grass seeds per lbs = $10
The cost of Zoysia grass seeds per Ibs = $15
The quantity of seed Nadine wants to buy = 20
The average amount the Nadine want to pay per Ibs = $12
That is the total money available for the grass seeds = 20 × 12 = 240
To find the number of each grass seed she can buy the following is carried out;
10 + 15 = 25 ( Total cost for both grass seed)
The number of St. Augustine grass seeds she can buy ;
= 10/25 × 240
= 2400/25
= 96
The number of Zoysia grass seeds she can buy;
= 15/25 × 240
= 3600/25
= 144.
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what is the circumference
Answers
The circumference is 12.56
PLEASE ANSWE NOW
In △XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ.
AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ?
Enter your answer in the box.
Answers
The perimeter of triangle XYZ is calculated as: 48 units.
What is the Perimeter of a Triangle?The perimeter of a triangle is found by summing all the lengths of the three sides of the triangle.
Given the following measures as shown in the image below as:
AC = 7
AB = 5
XY = 24
The perimeter of triangle XYZ = XY + YZ + XZ
Based on the triangle midsegment theorem, we have:
YZ = 2(AC) = 2(7)
YZ = 14
XZ = 2(AB) = 2(5)
XZ = 10
Therefore:
The perimeter of triangle XYZ = 24 + 14 + 10
The perimeter of triangle XYZ = 48 units.
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Question 3
Evaluate g(x)=-3x+1, when x=10
Give a numerical answer.
Answers
Multiply
-30+1
Calculate
Solution
-29
15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be
a. 1.96.
b. 3.
c. 1.67.
d. 2.5.
Answers
The investment multiplier must be 2.5 i.e.Option (d).
What is an Investment multiplier?
The amount by which the growth in output or income exceeds the increase in investment is referred to as the investment multiplier. It is represented by the letter "k" and is calculated as the ratio of changes in investment and income.
Multiplier(k) = Change in income / change in investment = 1/ {1-MPC}
where MPC is the marginal propensity to consume
Given, MPC = 0.6
Then, the multiplier(k) = 1/( 1 - 0.6) = 1/ 0.4 = 10/4 = 2.5 times
Hence, the investment multiplier is 2.5 i.e.Option (d).
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please help meeeeeeee
Answers
Answer: B & A
Step-by-step explanation: I think?
One way to measure the amount of energy that a moving object (such as a car) possesses is by finding its Kinetic Energy. The Kinetic Energy (Ex, measured in Joules) of an object depends on the object's mass (m, 2Ek measured in kg) and velocity (v, measured in meters per second), and can be written as v = . m What is the kinetic Energy of an object with a mass of 1,700 kilograms that is traveling at 50 meters per second? Ek Joules The volume of a cone of sand moved by harvester ants given it's radius can be found with the following 3V formular = A mound of gravel is in the shape of a cone with the height equal to twice the radius. 2л Calculate the volume of such a mound of gravel whose radius is 4.92 ft. Use = 3.14. V = (round to the nearest whole number)
Answers
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
Given that,
The Kinetic Energy of an object depends on the object's and velocity , and can be written as v = m
Kinetic Energy of an object with a mass = 1,700 kilograms
Traveling = 50 meters per second
Radius = 4.92 ft
Kinetic energy, which may be seen in the movement of an item or subatomic particle, is the energy of motion. Kinetic energy is present in every particle and moving object. Examples of kinetic energy in action include a person walking, a baseball soaring through the air, a piece of food falling from a table, and a charged particle in an electric field.
Kinetic Energy of a body is given by ,
1/2 mv²
Where m = mass = 1700 kg
v = velocity = 50m/s
Therefore ,
KE = 1/2 * 1700kg * 50m/s
KE = 2125000 J.
Now to calculate the volume
Let's assume that the solution to the problem will be found using your formula. If so, let's carry out the following operations when solving for v in the equation:
On multiplying the equation by 2, the outcome is
2[tex]r^{2}[/tex]
=3[tex]\sqrt{3V}[/tex]
To find volume
enter (v=(2[tex]r^{2}[/tex])/33)
rationalize the right side of the equation's numerator.
v=(2π[tex]r^{2}[/tex] )
A simplified version of 3/333 is
v=(2[tex]r^{2}[/tex])3/9.
Substitute
v=(23.143.1523)/9
v=11.9.
Therefore,
The body has a kinetic energy of 2125000 joules, and the gravel mold has a volume of 11.9 cubic units.
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|x+9|=|-x-9|
How do I solve this equation and graph it?
Answers
The value of x is :
x≤ -9 or x > -9
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
|x+9|=|-x-9|
Both the sides have absolute symbols, consider as below:
x+9 = -x-9
=> 2x = -9 - 9 = -18
=> 2x = -18
=> x= -9
This means, x≤ -9 or x > -9
For graph:
consider as below:
y = |x+9|
y = |-x-9|
graph them without absolute symbols
consider upper v shaped graph. ignore downward v shaped graph
By taking some random values for x and finding the corresponding y values, we get the ordered pairs in the form of (x,y).
By plotting and joining those points, we get the graph as shown in the attachment.
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Cone W has a radius of 6 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.
Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?
Answers
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
Define cone and square pyramid
A thick or empty device with an approximately round or elliptical base that tapers to a notch is known as a cone.
on the other hand ,
A three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.
CalculationCone W has a radius of 6 cm and a height of 5 cm.
The base area of the cone will be
A = πr²
A = π (6)²
A = 113.04 square cm
Then the volume of the cone will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm
Square pyramid X has the same base area and height as cone W.
Then the volume of the square pyramid will be
V = (1/3) x base area x height
V = (1/3) x 113.04 x 5
V = 188.4 cubic cm.
Manuel's argument is correct on why the volume of cone W and square pyramid are related . Paul used the incorrect base area to find the volume of square pyramid X. Then the correct option is C.
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1. A tire has the specification 225/60R14. What is the sidewall of the tire in inches (1 inch = 25.4 mm)?
a. 9.3in b. 60in
c. 8.9 in
d. 5.3in
2. If the diameter of a tire is 25 inches, approximate what distance does the tire cover in 8 rotations?
a. 628in
b. 392in
c. 60 in
d. 225in
Answers
The distance that tire covered in 8 rotations with diameter 25 inches is 628in using circle circumference's formula .
What is circumference of circle ?
The circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line, then the length of that line will be the circle's circumference.
The formula is :
2πr where r is the radius of the circle.
We know that diameter = 2*radius.
Given diameter = 25 inches
So, the radius = 25/2 inches.
So, the circumference = 2*(22/7)*(25/2)
Circumference of circle = distance covered by tire in one rotation.
So, the distance covered in 8 rotations = 8 * circumference
= 8* 2*(22/7)*(25/2)
= 628.5 inches
≈ 628 in
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 9200(1.018)²
Answers
Answer:
growth
1.8%
Step-by-step explanation:
If the number raised to the power x is between 0 and 1, it is decay since as the exponent increases, the value of the power expression decreases.
For example, think of 0.1, a number between 0 and 1.
0.1^x
x = 1, 0.1^1 = 0.1
x = 2, 0.1^2 = 0.01
x = 3, 0.1^3 = 0.001
As you see, as x increases, the value of the expression decreases from 0.1 to 0.01 to 0.001
Now look at a power in which the base is greater than 1.
If the number raised to the power x is greater than 1, it is growth since as the exponent increases, the value of the power expression increases.
For example, look at 1.5^x
1.5^x
x = 1, 1.5^1 = 1.5
x = 2, 1.5^2 = 2.25
x = 3, 1.5^3 = 3.375
As you see, as x increases, the value of the expression increases from 1.5 to 2.25 to 3.375.
Now our problem:
y = 9200(1.018)^x
What base is raised to x?
Answer: 1.018
Since 1.018 is greater than 1, as the exponent, x, increases, the value of 1.018^x increases. Therefore, this is exponential growth.
1.018 = 1 + 0.018 = 1 + 1.8%
The percentage is 1.8%
The function f(x)=9.25x + 3 represents the amount radda earns dog walking for X hours
Answers
Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.
How to write a linear function for the total amount of money Radda earns?In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;
T = mx + b
Where:
T represents the total amount of money earned.m represents the rate of change (slope) per hour.x represents the number of hours or time.b represents the y-intercept or initial amount.Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;
f(x) = T = 9.25x + 3
When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;
f(1) = T = 9.25(1) + 3
f(1) = T = 9.25 + 3
f(1) = T = $12.25.
In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.
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Complete Question:
The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?
The function below has at least one rational zero. Use this fact to find all zeros of the function. f(x)=7x^4 +27x^3 -40x^2 +x +5
Answers
The rational zeros of the function can be found using the Rational Zero Theorem. The possible rational zeros of the function are ±1, ±5, ±1/7, ±5/7.
Zeros:
x=-5, -1/7, 0, 1, 5
The Rational Zero Theorem states that if a polynomial function of degree n has integer coefficients, then the possible rational zeros of the function will be of the form ±p/q, where q is a factor of the leading coefficient and p is a factor of the constant term.
In this case, the degree of the polynomial is 4, which means that the leading coefficient is 7 and the constant term is 5. Thus, the possible rational zeros of the function will be of the form ±p/q, where p is a factor of 5 and q is a factor of 7. The factors of 5 are ±1 and ±5, and the factors of 7 are ±1 and ±7. This means that the possible rational zeros of the function are ±1, ±5, ±1/7, and ±5/7.
To find the zeros of the function, we can use the rational zeros we found and plug them into the original equation. We can then solve for the zeros and find that the zeros of the function are x=-5, -1/7, 0, 1, 5.
x=-5: 7(-5)^4 +27(-5)^3 -40(-5)^2 +(-5) +5= 0
x=-1/7: 7(-1/7)^4 +27(-1/7)^3 -40(-1/7)^2 +(-1/7) +5= 0
x=0: 7(0)^4 +27(0)^3 -40(0)^2 +(0) +5= 0
x=1: 7(1)^4 +27(1)^3 -40(1)^2 +(1) +5= 0
x=5: 7(5)^4 +27(5)^3 -40(5)^2 +(5) +5= 0
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You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 7.
While it is an uncommon confidence level, find the critical value that corresponds to a confidence level of 95.9%.
(Report answer accurate to three decimal places with appropriate rounding.)
ta/2 = ±
Answers
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
The distribution of the sample mean will be roughly normally distributed, according to the Central Limit Theorem, if we have an unknown population with a mean and standard deviation and adequately small random samples (n < 30) are chosen from the population with replacement.
Then, the mean of the sample means is given by,
μ(x) = μ
And the standard deviation of the sample means is given by,
σ = σ / [tex]\sqrt{n}[/tex]
In this case the sample selected is of size, n = 7.
As the sample size n = 7 < 30, the sampling distribution of sample mean will be approximately normal.
So, a z-interval will be used to estimate the population mean.
The confidence level is, 95.9%.
The value of α is:
∝ = 1 - confidence level
∝ = 1 - 0.959
∝ = 0.041
The critical value is:
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{\frac{0.041}{2} }[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = [tex]z_{0.0205}[/tex]
[tex]z_{\frac{∝ }{2} }[/tex] = -1.99
[tex]z_{1-∝/2}[/tex] = 1.99
Use a z-table.
Therefore,
The critical value that corresponds to a confidence interval of 95.9% is 1.99.
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The angle formed between one side and another, always less than 180 degrees.
Answers
Answer:obtuse angle
Step-by-step explanation:
An obtuse angle is an angle of greater than 90° and less than 180°. It is bigger than an acute angle. It is smaller than a straight angle, which measures 180°. Angles are measured with a protractor obtuse angle is specifically present in hexagon and pentagon and others.
what number is 16 2/3% more than 240
Answers
280 is the number which is 16 2/3% more than 240
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.
(1/6) th of 240 = 240/6 = 40
40 more than 240 = 280
So, 280 is the number which is 16 2/3% more than 240
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Heights are generally normally distributed. Men have a mean of 69.5 inches and standard deviation 2.4 inches. Women have
a mean of 63.8 inches and standard deviation 2.6 inches. The US Air Force has a height requirement for their pilots to be
between 64 inches and 77 inches.
Make sure you are rounding z-scores properly to two places.
Part A: Find the two z-scores for women who meet this height requirement z =
and z=
I
(larger value)
For Blank 1
Part B: Using the z-scores from part A, find the proportion of women who meet the height requirement. Give this answer as a
decimal.
Z=
(smaller value)
Part C: Find the two z-scores for men who meet this height requirement z =
(larger value)
Part D: Using the z-scores from part C, find the proportion of men who meet the height requirement. Give this answer as a
decimal.
QUESTION 2
(smaller value) and
Part E: If the height requirement were changed to exclude only the shortest 1% of women and tallest 1% of men, what are the
new heights? The short value would be
in inches and the tall value would be
in inches. Please give these two values rounded properly to one decimal place.
Answers
Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.
What is meant by normal distribution curve?A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.
In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.
According to the normal distribution curve:
"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.
Area from a value (Use to compute p from Z)
Value from an area (Use to compute Z for confidence intervals)
Let the parameters be
Mean 64
Standard deviation 2.75
Above 1.96
Below 1.96
Between 64 and 69.5
Outside -1.96 and 1.96
Area (probability) 0.4772
And that value is 95 % of the whole data
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Kevin has an annual salary of $41,732, and he earned $33.52 interest from his savings account. He also paid $1050 in student loan interest and contributed $3900 to an IRA retirement account. Calculate Kevin’s adjusted gross income.
Answers
Kevin's adjusted gross income is $36, 815. 52
What is adjusted gross income?Adjusted gross income is simply described as gross income minus certain adjustments from the income.
These adjustments includes;
Educator expensesStudent loan interestAlimony paymentsContributions to an account, etcIt is calculated as;
Adjusted gross income = sum total of income - expenses
Now, let's substitute the values into the formula, we have;
Adjusted gross income = $(41,732 + 33.52) - $(1050 + 3900)
Add the values
Adjusted gross income = $(41, 765. 52 - 4950)
Subtract the values
Adjusted gross income = $36, 815. 52
Hence, the value is $36, 815. 52
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a 9 foot ladder is leaning against a wall. if the top of the ladder is sliding down the wall at a rate of
Answers
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]
Given that,
Length of the ladder is, [tex]l=9ft[/tex]
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
[tex]AB^{2} +BC^{2} =AC^{2}[/tex]
[tex]h^{2} +b^{2} =l^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]
[tex]h^{2} +b^{2}[/tex] = 81 (Equation-1)
Differentiating the above equation with respect to time, 't'.
So,
We can write,
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)
[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0
[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0
[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0 (Equation-2)
In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.
Let us assume,
h = 3 ft and db/dt = 3 ft/s
We can substitute values in equation-1,
[tex]3^{2} +b^{2}[/tex] = 81
9 + [tex]b^{2}[/tex] = 81
[tex]b^{2}[/tex] = 81-9
[tex]b^{2}[/tex] = 72
b = [tex]\sqrt{72}[/tex]
b = 8.48 ft
Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]
3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0
3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0
3*[tex]\frac{dh}{dt}[/tex] = - 25.44
[tex]\frac{dh}{dt}[/tex] = -25.44/3
[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s
Therefore,
The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
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