The diameter of circle is 20 inches. find the circumference in terms of pi
Answers
The below formula is used to find the circumference of a circle;
\(C=2\pi r\)But we know that the diameter of a circle is expressed as;
\(d=2r\)Let's replace 2r with d in the 1st equation, we'll then have;
\(C=\pi d\)We've been told that the diameter of the circle is 20inches, if we substitute this value into our equation, we'll have;
\(C=20\pi\)Related Questions
Consider the figure shown below. What is the volume of this figure? HELP PLEASEEE
Answers
Answer:
8
Step-by-step explanation:
Volume =
width x length x height.
2 x 2 x 2 = 8
There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Answers
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
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The city acquired more land next to the subdivision. If it decides to make each park 15.3 acres, how many additional acres would the parks occupy?
Answers
The additional acres that the parks occupy will be 33.75 acres.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
In this case, the additional acres that the parks occupy will be:
= (12.5 × 3) - 3.75
= 33.75 acres.
Note that the information is incomplete and the complete information is given below.
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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres
The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?
what is 5/8 6 times larger
Answers
Because smaller denominators result in larger fractional pieces, the denominators for the numbers 6 and 8 are 6 and 8, respectively. Therefore, 5/6 will be greater than 5/8.
Which fraction can be determined to be larger?As you saw, you may compare fractions with the same denominator by examining their numerators. As you can see below, 3/4 is larger than 1/4.
The fraction grows as the numerator gets bigger. Due to the fact that it represents a portion of a whole, the fraction 5/8 can never be a whole number. The fraction 5/8 represents 5 of the 8 parts that make up the whole.
Although the decimal 0.625 is equivalent to 5/8, it still does not make a whole. You may represent 5/8 as that. The complete response is provided below. Because smaller denominators result in larger fractional pieces, the denominators for the numbers 6 and 8 are 6 and 8, respectively. Therefore, 5/6 will be greater than 5/8.
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Write the equations of the lines with the following descriptions
8. m = 2/-3 and passes through the point (3,-5)
Answers
Explanation: The formula is y-y1=m(x+b).
Fill in what we know, which is,
y-(-5)=-2/3 (x-3) Then you distribute and get y+5=-2/3x+2. Then you subtract 5 from each side and get your final answer of y=-2/3x -3
Thirteen students entered the business program at Sante Fe College 2 years ago. The following table indicates what each student scored on the high school SAT math exam and their grade-point averages (GPAs) after students were in the Sante Fe program for 2 years.
Student A B C D E F G
SAT Score 421 375 585 693 608 392 418
GPA 2.93 2.87 3.03 3.42 3.66 2.91 2.12
Student H I J K L M
SAT Score 484 725 506 613 706 366
GPA 2.50 3.24 1.97 2.73 3.88 1.58
The least-squares regression equation that shows the best relationship between GPA and the SAT score is:_____.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
SAT SCORE :
421
375
585
693
608
392
418
484
725
506
613
706
366
GPA:
2.93
2.87
3.03
3.42
3.66
2.91
2.12
2.50
3.24
1.97
2.73
3.88
1.58
Using the online linear regression calculator ; the regression model obtained is :
ŷ = 0.00345X + 1.00301
0.00345 = slope or gradient
1.00301 = intercept ; where the regression line crosses the y axis
X = independent variable or predictor variable ; y = dependent variable or predicted variable
ill give brainiest if correct
Answers
It’s c( 250)
Trigonometry
Solve the entire triangle. Round sides to the nearest tenth.
A= 104 degrees, a=13, C = 27 degrees
A=
a=
B =
b=C=
c=
Answers
Answer: lowercase= sides Uppercase= angles
A=104 degrees
a=13
B=49 degrees
b=10.11
C=27degrees
c=6.08
Step-by-step explanation:
B=180.00∘−A−C=180.00∘−104.00∘−27.00∘=49.00∘b=sin(B)⋅asin(A)=sin(49.00∘)⋅13.00sin(104.00∘)=10.11c=sin(C)⋅asin(A)=sin(27.00∘)⋅13.00sin(104.00∘)=6.08
1. Show using the preimage theorem that the tangent space to the Stiefel manifold of orthonormal 2 -frames inRnat a point[v1,v2], is the vector space of vectors(u,w)∈Rn×Rnsatisfyingv1⋅uv2⋅wv1⋅w+v2⋅u=0=0=0.
Answers
As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2] by using preimage theorem.
Let F be the Stiefel manifold of orthonormal 2-frames in Rn to apply the preimage theorem. The collection of all tangent vectors to curves passing through [v1, v2] in F is what is known as the tangent space T[F] at a location [v1, v2]. Let (t) be a straight line in F such that (v1, v2) is a smooth curve. The tangent vector to t at time t = 0 is then given by
γ′(0) = [u, w] ∈ T[F].
We must now determine the requirements that [u, w] must meet in order to be in T[F]. Assume that V is a matrix with columns named v1 and v2. If Q is an orthogonal matrix, then any orthonormal 2-frame [v1′, v2′] in Rn can be represented as VQ. The category to which [v1′, v2′] belong Q is a 2 by 2 matrix with determinant 1, and F is equivalent to Q. Given that Q(0) = I, let Q(t) be a smooth curve in SO(2). Then, there is
γ(t) = VQ(t) (t),
and
γ′(0) = VQ′(0) (0).
We have Q since Q(t) is orthogonal (t)
TQ(t) = I, indicating
Q′(0)T + Q′(0) = 0.
Let [u, w] T[F] now. Once this is the case, a smooth curve Q(t) in SO(2) exists with Q(0) = I and
[u, w] = VQ′(0) (0).
Applying the equation above, we obtain
v1uv2w plus v1wv2u equals 0.
As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2].
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Markes recipe for 24 cookies calls for 2½ cups of flour.How much flour will markes need to make 60 cookies?
Answers
Answer:
6 1/4 cups of flour
Step-by-step explanation:
24/2 = 12
2.5/2 = 1.25
12 x 5 = 60
1.25 x 5 = 6.25 cups
For every 24 cookies Markes needs 2.5 cups of flour. So, for 12 cookies he needs half of that which is 1.25 cups. 12 is a fifth of 60, so we multiply 1.25 by 5 which gives us 6.25 cups of flour. :D
Drag each tile to the correct box.Arrange the angles in increasing order of their cosines.
Answers
Given:
\(\begin{gathered} \frac{3\pi}{4} \\ \pi \\ \frac{7\pi}{6} \\ \frac{5\pi}{3} \\ \frac{7\pi}{4} \\ \frac{4\pi}{3} \\ \frac{3\pi}{2} \\ 2\pi \end{gathered}\)To arrange the angles in increasing order, we first get the value of their cosines as shown below:
\(cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}\)\(cos\pi=-1\)\(cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2}\)\(cos\frac{5\pi}{3}=\frac{1}{2}\)\(cos\frac{7\pi}{4}=\frac{\sqrt{2}}{2}\)\(cos\frac{4\pi}{3}=-\frac{1}{2}\)\(cos\frac{3\pi}{2}=0\)\(cos2\pi=1\)Therefore, the angles in increasing order of their cosines are:
\(\pi<\frac{7\pi}{6}<\frac{3\pi}{4}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi\)Select the correct answer.
Function bis nonlinear, and b(9) = 4. Which equation could represent function b?
Answers
The nonlinear- function which represents b(9)=4 is given by b(x)=72/x - 4 .
In mathematics and physics, a nonlinear system is one in which the change in the output is not proportional to the change in the input. Engineers, biologists, physicists, mathematicians, and many other scientists are interested in nonlinear problems since the majority of systems are inherently nonlinear.
Nonlinear function graphs don't resemble lines at all. It contains the formula f(x) = ax + b. Its equation can take any form, with the exception of f(x) = ax + b. The slope of the curve is the same between any two points. The point pairs on the graph do not all have equal slopes.
Of all the given options: the only equations which imply that b(9)=4 are :
i) b(x)=72/x - 4 and (iv) b(x)=4
Of this two options only the first option is non-linear.
Hence the required option is b(x)=72/x - 4 .
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Disclaimer:
The missing options are:
i) b(x) = 72/x - 4
ii) b(x) = √x + 7
iii)b(x) = 2x+1
iv) b(x) = 4
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Select the correct answer.
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
ОА,
f(x) = (x-6)(x-4)
OB.
fx) = (x-6)(x + 4)
fx) = (x + 6)(x + 4)
OD.
AX) = (x + 6)(x-4)
Algebra
Answers
Suppose that the matrix A has repeated eigenvalue with the following eigenvector and generalized eigenvector: A = 1 with eigenvector = [] and generalized eigenvector - [1-3]. Write the solution to the linear system' = Ar in the following forms. A. In eigenvalue/eigenvector form: [x(t)] = C1 [8] 248-89 + e B. In fundamental matrix form: [x(t)] [y(t)] [188 C. As two equations: (write "c1" and "c2" for c₁ and c₂) x(t) = y(t) = Note: if you are feeling adventurous you could use other eigenvectors like 47 and other generalized eigenvectors like - 37. Just remember that if you change , you must also change for its fundamental solution!
Answers
The solution for the linear system will be , x(t) = 4 c₁e^t + 4 c₂e^t and
y(t) = -c₂e^t + c₂(1 - t)e^t .
The solution is given by ,
matrix | x y | = c₁ .v . e^λt + c₂( w + v.t ) e^λt
Given that the matrix has repeated eigenvalue with eigenvector generalized vectors ,
λ = 1 with eigenvector v = [ 4 , -1 ] and generalized vectors w =[ 0,1 ].
then the solution will be,
c₁ [ 4 , 1 ] e^t + c₂[ 0 , 1] + [ 4 , -1 ] )e^t
therefore,
x(t) = 4 c₁e^t + 4 c₂e^t
y(t) = -c₂e^t + c₂(1 - t)e^t
Matrixes represent linear maps and allow for explicit linear algebra operations. As a result, matrices play an important role in linear algebra, and most characteristics and operations in abstract linear algebra may be represented in terms of matrices.
Matrix multiplication, for example, depicts the combination of linear maps.
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A 98% confidence interval is found to be (32, 42). What is the margin of error?
A. 5
B. 4.9
C. 9.8.
D. 10
Answers
Answer:
A
Step-by-step explanation:
Just took the exam
Using confidence interval concepts, it is found that the margin of error is 5.
What is a confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval has the format (a,b).
The margin of error is half the difference between the two bounds, that is:
M = ( b - a ) / 2
In this problem, the interval is (32, 42), hence, and the margin of error is:
M = ( 42 - 32 ) / 2 = 10 / 2 = 5
Therefore the margin of error is 5.
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A gumball machine has 21 red gumballs, 24 yellow gumballs, and 15 blue gumballs. The gumballs are randomly mixed.
a. Calculate the probability that the gumball machine dispenses 2 red gumballs in a row?
Answers
Considering the definition of probability, the probability that the gumball machine dispenses 2 red gumballs in a row is 7/59.
Definition of probabilityProbability establishes a relationship between the number of favorable events and the total number of possible events.
The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
P(A)= number of favorable cases÷ number of posible cases
The conditional probability P(A|B) is the probability that event A occurs, given that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:
P(A|B) = P(A∩B)÷ P(B)
Expressed another way:
P(A∩B)= P(B)× P(A|B)
Probability that the gumball machine dispenses 2 red gumballs in a rowIn this case, you know a gumball machine has:
21 red gumballs.24 yellow gumballs.15 blue gumballs.Total number of gumballs= 21 +24 +15= 60Considering the definition of probability, since there are 21 red gumballs in a total of 60 gumballs, the probability of getting a red gumball on the first try is 21/60.
Now, the probability of getting a red gumball on the second try, given that you got a red gumball on the first try and now you have a 59 gumballs an 20 red gumballs on the machine, is 20/59.
So, the probability of getting 2 red gumballs in a row is calculated as:
P(A∩B)= P(B)× P(A|B)
P(A∩B)= 21/60× 20/59
P(A∩B)= 7/59
Finally, the probability that the gumball machine dispenses 2 red gumballs in a row is 7/59.
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What is the period of y= tan x?
O A
O c.
O D. 211
Answers
Answer:
B) π
Step-by-step explanation:
The distance between the repetition of any function is called the period of the function. In this case, the period of the parent function y = tan x will have a period of π. This means it takes a distance of π units to complete one cycle of a tangent function.
Determine the rational zeros for the function f(x)=8x^(3)-6x^(2)-23x+6.
a. -(1)/(2),(1)/(4),2
c. -1(1)/(2),(1)/(4),2
b. 1(1)/(2),(1)/(4),-2
d. -1(1)/(2),-(1)/(4),2
Answers
Answer:
Step-by-step explanation:
BOOMER GENERATION: At 84%, Boomers are the highest amongst all the generations that want to shop in-store. In a sample size of 75 people in the Boomer Generation, estimate how many of them prefer to shop in-store.
Answers
In a sample size of 75 people in the Boomer Generation, proportionately, the estimated number of people who prefer to shop in-store is 63.
What is proportion?Proportion shows the relative number of objects or people in the whole.
Proportions are ratios equated to each other.
They are expressed as fractional values, in decimals, percentages, and fractions.
The percentage of Boomers who want to shop in-store = 84%
The sample size of the Boomer Generation = 75
The estimated number of Boomers in the sample size who want to shop in-store = 63 (75 x 84%)
Thus, 63 Boomers representing 84 percent of 75 want to shop in-store.
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2. A cannon launches a ball across the battlefield. An arms engineer is calculating its
trajectory using a quadratic function. The point where the ball is first launched from the
cannon is best represented by which of the following key features? (1 pt)
a) Vertex
b) The zeros
c) y-intercept
d) Axis of symmetry
Answers
The answer is A Vertex
The amount of shore at a local beach changes an average of -3/4 foot each year. What is the change in the amount of shore after 7 years?
Answers
Answer:
Negative 5 and a Quarter.
Step-by-step explanation:
-3/4 × 7
= -21/4
= -5 1/4
The change in the amount of shore after 7 years is -21/7 foot or -4 1/4 foot.
What is rate of change?A rate of change is a rate that describes how one quantity changes in relation to other.
Now it is given that,
The amount of shore changes = -3/4 foor each year
To find the change in the amount of shore = 7 year
So. the change in the amount of shore after 7 years = amount of shore changes each year x 7
⇒ change in the amount = (-3/4)*7
⇒ change in the amount = -21/7foot or -4 1/4 foot
Hence,the change in the amount of shore after 7 years is -4 1/4 foot.
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A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel.
The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that
changes a 1 to a 0 with probability 0.1 and changes a 0 to a 1 with probability 0.2. Show your work below.
a. What is the probability a 1 is received?
b. If a 1 is received, what is the probability a 0 was sent?
Answers
Answer:
A: the probability that a 1 is received is 0.56.
B: the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
Step-by-step explanation:
To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.
a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.
Let's denote:
P(1 sent) = 0.6 (probability a 1 is sent)
P(0→1) = 0.2 (probability a 0 is flipped to 1)
P(1 received) = ?
P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)
= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)
= 0.6 * (1 - 0.2) + 0.4 * 0.2
= 0.6 * 0.8 + 0.4 * 0.2
= 0.48 + 0.08
= 0.56
Therefore, the probability that a 1 is received is 0.56.
b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.
Let's denote:
P(0 sent) = ?
P(1 received) = 0.56
We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).
Using Bayes' theorem:
P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)
P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08
P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56
Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):
P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56
Simplifying:
P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56
= 0.08 * (1 - P(0 sent)) * (1 / 0.56)
= 0.08 * (1 - P(0 sent)) * (25/14)
= (2/25) * (1 - P(0 sent))
Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).
A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?
The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to have changed -1 5/6 inches. What was the total change in the water level over the two years?
Answers
Answer:
The total change in water level over the past 2 years is \(\displaystyle -4 \frac{1}{6}\).
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightFractions
Proper and ImproperNumbers
Least Common Multiple (LCM)Step-by-step explanation:
Step 1: Define
Identify
Year 1 water change: \(\displaystyle -2 \frac{1}{3}\)
Year 2 water change: \(\displaystyle -1 \frac{5}{6}\)
Step 2: Find Total Water Change
[Set up] Add yearly water changes: \(\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}\)[Fractions] Convert to improper: \(\displaystyle \frac{-7}{3} - \frac{11}{6}\)[Fraction] Rewrite [LCM]: \(\displaystyle \frac{-14}{6} - \frac{11}{6}\)[Order of Operations] Subtract: \(\displaystyle \frac{-25}{6}\)[Fraction] Convert to proper: \(\displaystyle -4 \frac{1}{6}\)*not drown to scale
What is the distance between A and D? Enter the answer in the box. Round the answer to the nearest hundredth of an inch.
inches
Answers
Answer:
26.9 inches
Step-by-step explanation:
2x Pythagorean theorem
First we find the length of AC with ABC. AC is the hypotenuse of triangle ABC.
AC = sqrt(7^2+24^2) = sqrt625 = 25.
Now, AD is the hypotenuse of ACD. So AD = sqrt(25^2+10^2) = sqrt(725) = 26.925824 which is about 26.9 inches.
Answer:
26.93 inStep-by-step explanation:
Use Pythagorean:
\(AD^2 = AB^2+BC^2+CD^2\\AD = \sqrt{7^2+24^2+10^2} = \sqrt{725}\) ≈ 26.93 inPlease look at the photo for the question. Thank you!
Answers
The zeros with each multiplicity are given as follows:
Multiplicity one: x = 6.Multiplicity two: x = 11.Multiplicity three: x = -6 and x = -5.How to obtain the multiplicities?The factor theorem is used to define the functions, which states that the function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the linear factors of the function in this problem, the zeros are given as follows:
(x + 6)³ -> zero at x = -6 with multiplicity of 3.(x - 11)² -> zero at x = 11 with multiplicity of 2.x - 6 -> zero at x = 6 with multiplicity of 1.(x + 5)³ -> zero at x = -5 with multiplicity of 3.More can be learned about the Factor Theorem at brainly.com/question/24729294
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F(x)=|x|-7 describe the transformation of each function compared to its parent function
Answers
Compared to the parent function f(x)=|x|, the graph of F(x) is a translation 7 units down.
First, the negative on the top of the fraction indicates that there is a reflection. This means that you will be filling in quadrants II and IV rather than I and III prior to the other transformations.
Dilation is indicated by the 3 in the numerator of the fraction and will actually affect the main points marked on the graph. For the parent function y= 1/x, the coordinate (1,1) is the main point in the first quadrant and the coordinate (-1,-1) is the main point in the third quadrant. When a dilation occurs, it dilates the x value for one of the coordinates and the y-value in the other. Since a reflection has also occurred, our initial points are (-1,1) and (1,-1) so the points in the second quadrant will be (-1,3) and (-3,1) as compared to the asymptotes (multiple translations have also occurred) and the points in the fourth quadrant will be (1,-3) and (3,-1) as compared to the asymptotes.
Lastly, let's consider translations: a horizontal translation involves the addition or subtraction of a number from x in the denominator of the fraction whereas a vertical translation involves the addition or subtraction of a number from (1/x), completely separate from the fraction. Therefore, the -2 is part of a horizontal translation and the +4 is part of a vertical translation. I always tell my students that the direction of the vertical translation(up or down) will be what you would assume, but the direction of the horizontal translation (right or left) will be the exact opposite of your assumption. For this reason, the -2 would indicate a shift to the right 2 units and the +4 would indicate a shift upwards 4 units. This would result in a shift of the vertical asymptote to the right 2 units and a shift in the horizontal asymptote upwards 4 units. The horizontal asymptote is written as y = 4 and the vertical is written as x=2
The wholesale price for a shirt is $7.50. A certain department store marks up the wholesale price by 80%. Find the price of the shirt in the
department store.
Round your answer to the nearest cent, as necessary.
Answers
Answer:
$13.50.
Step-by-step explanation:
80% = 0.80 as a decimal fraction.
The marked up price
= 7.50 + 0.80 * 7.50
= $13.50.
so the new price will just be 7.5 plus 80% of 7.5
\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{80\% of 7.50}}{\left( \cfrac{80}{100} \right)7.50}\implies 6\hspace{5em}\underset{selling~price}{\stackrel{7.50~~ + ~~6}{13.50}}\)
Find the geometric means in the following sequence. –14, ? , ? , ? , ? , –235,298
Answers
Answer:
The answer is -98, -686, -4802, -33,614.
Step-by-step explanation:
Theprofit(indollars)earnedbysellingwappletreesisrepresentedby w2 − 4w + 14. The profit (in dollars) earned by selling w pear trees is
represented by 2w + 10. Write a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
Answers
\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
The profit earned by selling w pear trees is 2w + 10
To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:
\((w^2 - 4w + 14) - (2w + 10)\)
Simplifying the expression:
\(w^2 - 6w + 4\)
Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).
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a political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee. which of the following statements about this survey is true?
A) The survey results are invalid because it’s impossible to word questions about politics without creating bias.
B) The survey results are invalid because only surveys conducted by phone are free from bias.
C) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money.
D) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
E) Since the survey was sent to randomly-selected households, it should be free of bias.
Answers
Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.
Given,
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.
We have to find the correct statement about the survey from the given options;
Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.
The correct statement about the survey is option c;
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