F(x) = sin x, F(x) = x2 + 3, F(x) = 1/x, F(x) = 2x + 3, etc. are a few further instances of functions.
Polynomial functions include functions like the identity function, linear function, quadratic function, and cubic function. Therefore, it is useful to define the type of function using the function equation y = f(x).
Algebraic, exponential, logarithmic, and trigonometric functions are available depending on the domain. Modulus, rational, signum, even and odd, periodic, biggest integer, smallest integer, inverse, and composite functions are the functions based on the range.
For instance: It is declared that the polynomial function with degree zero is a constant function. One-degree polynomial functions are referred to as linear functions. Quadratic function is the name given to the degree two polynomial function.
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Does his residual plot make sense based on the scatter plot? explain. the random residual plot makes sense because the scatter plot appears to have a linear relationship. the random residual plot makes sense because the scatter plot appears to have a negative relationship. the random residual plot does not make sense because it should have a linear relationship like the scatter plot. the random residual plot does not make sense because it should have a nonlinear curve, as the scatter plot is negative.
Random residual plots are not make sense because it should have a non linear curve, as the scatter plot is negative.
What is a scatter plotA chart that displays the values of two variables along two axes. Each correlation is indicated by the placement of the resulting points.
A series of points plotted on the horizontal and vertical axes is called a scatterplot. Statistical scatterplots (called variables) are very important because they can show the extent, if any, of relationships between the values of observed quantities or events. You can see that the scatterplot is a non-linear curve with negative points.
Therefore, since the scatterplot is negative, the residual plot is meaningless as it must have a non-linear curve.
your question is incomplete, but most probably your full question was
The relationship of miles per gallon of SUVs to weight is represented by the following scatter plot:
Brian created the following residual plot:
Does her residual plot make sense based on the scatter plot? Explain.
The random residual plot makes sense because the scatter plot appears to have a negative relationship.
The random residual plot does not make sense because it should have a linear relationship like the scatter plot.
The random residusl plot does not make sense because it should have a noninar curve, as the scatter plot is negative.
The random residual plot makes sense because the scatter plot appears to have a lines relationship.
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Python:
(Assign grades) Write a program that reads a list of scores and then assigns grades based on the following scheme:
The grade is A if score is 7= best – 10.
The grade is B if score is 7= best – 20.
The grade is C if score is 7= best – 30.
The grade is D if score is 7= best – 40.
The grade is F otherwise.
A program that reads a list of scores and then assigns grades based on the following scheme is listed below.
Python 2.6 version
def grade(score, best):
if score >= best -10:
return 'A'
if score >= best -20:
return 'B'
if score >= best -30:
return 'C'
if score >= best -40:
return 'D'
return 'F'
score = raw_input("Enter scores: ")
scores = [ int(s) for s in score.split()]
best = scores[0]
for i in range(len(scores)):
if scores[i] > best:
best = scores[i]
for i in range(len(scores)):
print "Student", i, "score is", scores[i], "and grade is", grade(scores[i], best)
# Copy pastable link: https://paste.ee/p/qA5RQ
def grade(score, best):
if score >= best -10:
return 'A'
if score >= best -20:
return 'B'
if score >= best -30:
return 'C'
if score >= best -40:
return 'D'
return 'F'
score = input("Enter scores: ")
scores = [ int(s) for s in score.split()]
best = scores[0]
for i in range(len(scores)):
if scores[i] > best:
best = scores[i]
for i in range(len(scores)):
print("Student", i, "score is", scores[i], "and grade is", grade(scores[i], best))
Sample execution:
Enter scores: 40 55 70 58 Student 0 score is 40 and grade is C Student 1 score is 55 and grade is B Student 2 score is 70 and grade is A Student 3 score is 58 and grade is B
# copy pastable code link: https://paste.ee/p/UVTbP
Hence the answer is a program that reads a list of scores and then assigns grades based on the following scheme is listed above.
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) find the number of ways to distribute 10 identical cards into 3 boxes, where each box has at least one card.
Numbers of ways to distribute 10 identical cards into 3 boxes is 36
Combination is is a way of selecting items from a collection where the order of selection does not matter.
Formula of combination:
Let a x-combination of a set is a subset of x distinct elements of S. If the set has n elements, the number of x-combinations is equal to the binomial coefficient.
ⁿCₓ = n(n-1)(n-2)(n-3). . . (n-x+1) / (x-1)(x-2)(x-3) . . . .(1)
which can be written as ⁿCₓ = n! / (n-x)! x! , when n > x
ⁿCₓ = 0 , when n < x
Where n = distinct object to choose from
C = Combination
x = spaces to fill
According to the question,
Number of identical cards : n =10
Number of box cards are being distributed : x = 3
Number of ways to distribute when no condition is given : ⁿ⁺ˣ⁻¹Cₓ₋₁
If we place one one card in each box then
Number of cards left with us = 10 - 3
= 7
Now, condition of at least one cards in each box is satisfied ,
Then total number of ways to distribute 7 cards into 3 = ⁷⁺³⁻¹C₃₋₁
=> ⁹C₂ = 9! / (9 - 2)! 2!
=> 9×8×7! / 7!2!
=> 9×8/2
=> 9×4
=>36 ways
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How do you solve rational root problems?.
A rational root is such a number that makes any polynomial function equal to zero.
let us consider a general polynomial equation-
P(x) = anxn + an− 1xn − 1 + … + a1x1 + a0
hence, the rational roots must be of the form = [tex]\pm[/tex] (factors of a0) / (factors of an).
let us now take an example,
[tex]F(x) = 4x^3 - 6x^2 + 9x + 10[/tex]
here ao = 10, and factors of 10: 1,2,5,
an = 4 and the factors of 4: 1,2,4
Hence, we have Possible Rational Roots:
[tex]$$\pm\left\{1, 2, 5, 10,\frac{1}{2}, \frac{1}{4}, \frac{5}{2}, \frac{5}{4}\right\}$$[/tex]
In this way, we have the rational numbers which can be possible solutions for our function f(x).
Now we substitute each of these rational numbers one by one to check if it satisfies the equation as follows.
[tex]F(1) = 4(1)^3 - 6(1)^2 + 9(1) + 10=17\neq 0[/tex]
Hence, it doesn't satisfy the equation, it means it's not the root of the equation.
Similarly, we can check for the rest of the numbers.
we will get f(-1/2)=0, f(5)=0, f(5/4)=0 and f(-2)=0
Hence, x=5,5/4,-1/2 or -2 are the solutions for the equation F(x).
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How many sides and angles does a circle have?.
The number of sides in a circle is 0.
The number of angles in a circle is 0.
What is the Radius of a circle?
Any circular object's radius is the measurement from the center to its outermost border or boundary. A radius is a dimension that applies to spheres, semispheres, cones with circular bases, and cylinders with circular bases in addition to circles.
It is possible to define a circle as the locus of a point moving in a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its center. The fixed point is referred to as the center of the circle.
The angle formed by any two-circle radii is known as the central angle. The arc length, or the distance between the two places where the two radii cross the circumference, and the radius length must be determined in order to determine the central angle.
So, we can say that:
Since a circle is made up of arcs, which form a continuous line that joins at both ends, it has no sides. The distance between each circle's component components and its center is equal. A side must have two angles, one on either side of the line, and a line.
Hence,
The number of sides in a circle is 0.
The number of angles in a circle is 0.
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Is it important to solve or address the problem why or why not?.
Is it easier for you to visualize the reaction by using pictures words or symbols?.
Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
What is photosynthesis?
Photosynthesis is the process in which green plants prepare their own food in the presence of sunlight and light energy is converted into chemical energy by the process of cellular respiration.
The process of photosynthesis takes place in green plants only due to presence of chlorophyll and materials such as sunlight, water, carbon dioxide is required for the process of photosynthesis.
The equation of photosynthesis is represented below:
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
The process of food manufacturing in plant is done through photosynthesis and the plants are known as autotrophs as they are the producers.
In the process of photosynthesis the reactant have 6 carbon dioxide molecules and six water molecules, and light energy converted into chemical energy due to presence of chlorophyll.
Therefore, Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
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A jacket normally costs £79.50.
In a sale there is 30% off the normal price.
What is the sale price of the jacket?
Answer:
£55.56
Step-by-step explanation:
30% off means you pay 70% of the full price.
70% = 0.7
£79.50 * 0.7 = £55.56
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount Erica owed for 6 years if $5300 is loaned to her at the rate of 8% is $8,551.56.
How to find the amount Eric owes for 6 years?The amount Erica owes for 6 years if 5300 dollars is loaned to her at the rate of 8% compounded monthly can be computed as follow:
Therefore, it is compounded 12 times.
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
where
p = principalr = rate t = timen = number of time compoundedTherefore,
p = 5300 dollars
t = 6 years
n = 12
r = 8%
Therefore,
[tex]A = p(1 +\frac{r}{n} )^{nt}[/tex]
[tex]A = 5300(1+ \frac{0.08}{12} )^{(12)(6)}[/tex]
A = 5300(1 + 0.0067)⁷²
Therefore,
A = $8,551.56
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A mail-order company charges $5 per order plus $2 per item in the order, up to a maximum of 4 items. write a function rule to describe the situation. find a reasonable domain and range for the function.
The function to describe the order of the mail-order company is given by f(x) = 5 +2x , {x | x ≤ 4 } .
The charge per order = $5 .
Cost of each item = $2
Cost of x items = 2x
Total cost for the order = 5 + 2x
Function to represent this situation : f(x) = 5 + 2x
Now it is given that the maximum of 4 items can be ordered.
Domain: {1,2,3,4}
At x = 1 , f(x) = $7
At x = 2 , f(x) = $9
At x = 3 , f(x) = $11
At x = 4 , f(x) = $13
Range of the function: {7,9,11,13}
A rule is referred to as a function if it produces a distinct result for each input x. In mathematics, a function is represented by a mapping or transformation.
The set of all potential values that can be passed into a function while it is specified is known as the domain. The entire set of values that the function's output is capable of creating is referred to as the "range."
The range of potential values for a function's outputs is known as the co-domain.
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Answer:
Domain: {1, 2, 3, 4}
Range: {7, 9, 11, 13}
Step-by-step explanation:
How do you find the roots and multiplicity of a polynomial?.
To find the roots and multiplicity of a polynomial, we first need to find its factors.
To do this, we use the factoring method of our choice (such as the quadratic formula, factoring by grouping, etc.), and then we determine how many times each factor occurs. The roots of the polynomial are the factors that have a multiplicity of 1, and the multiplicity of a root is the number of times that it occurs as a factor.
A polynomial is an equation that can be written in the form:
ax² + bx + c = 0
where a, b, and c are real numbers and x is a variable. The roots of a polynomial are the values of x that make the equation true. The multiplicity of a root is the number of times that the root appears as a solution to the equation.
To find the roots of a polynomial, you can use the Quadratic Formula:
x = (-b +/- sqrt(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the equation. The +/- sign indicates that there are two roots, one with a positive sign and one with a negative sign.
The multiplicity of a root can be found by counting how many times the root appears as a solution to the equation. For example, if the root x = 2 appears twice as a solution, then the multiplicity of the root is 2.
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The lengths of the four sides of a quadrilateral (in meters) are consecutive integers. If the perimeter is 50 meters, find the value of the shortest of the four side lengths.
(also, what do those numbers mean that are next to the subject when i'm asking a question?)
please helo me with both of them thank u
Answer:
13: 22 < x < 74
14: Side DF, Side DE, side EF
Step-by-step explanation:
So for the first one, you add 26 + 48 which equals 74. Then, you subtract 48 - 26 which equals 22. So the range is 22 < x < 74.
For the second one, the angle corresponds to the side across from it. The smallest side will be across from the smallest angle. So, the order is side DF, side DE , and then side EF.
Hope this helps!!! :)
Work out the perimeter of a semicircle with radius 3 cm.
Give your answer in terms of pi .
The perimeter of a semicircle with radius 3 cm is 6π cm.
What is semi-circle?
When a line travelling through the Centre of a circle reaches its two ends, a semicircle is created. Thus, a circle can be formed by combining two semicircles.Half of the area of a circle is contained within a semicircle. Since r2 is the radius of a circle, A semicircle's area is therefore 1/2(πr2), where r is its radius π has a value of 3.14, or 22/7.Half of the circle's circumference plus its diameter add up to a semicircle's perimeter. Since a circle's circumference is 2πr or πd, A semicircle's perimeter is therefore 1/2 (πd) + d, or πr + 2r, where r is its radius.Given :
Radius = 3cm
Circumference or Perimeter of a circle = 2πr
= 2 * π * 3
= 6π cm
Hence, the perimeter of a semicircle with radius 3 cm is 6π cm.
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Please help will mark Brainly
The value of y - intercept is: -5
What is Y Intercept?It is distance between point on Y axis where graph cuts it and origin generally denoted by c.
Here in this question initially f(x) was = x
later we took new function g(x) = f(x-5) = x-5
therefore we call g(x) = x - 5now we need to find y intercept and we know that on y axis (x - coordinate = 0)
just put x=0 in above equation g(0) = -5
which is value of y intercept
y = -5
why this is y intercept?because one point is origin(0,0) and other is this one(0,-5)we need to calculate distance between these 2 that after finding from distance formula we get answer as 5 but here intercept is negative so, our final answer is -5
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jill buys a mobile phone that weighs 210g to 2 significant figures. she puts the phone inside a protective case that weighs 15.4g to 1 decimal place. work out the smallest possible total weight, in grams (g) of the phone, and the case combined
The smallest possible total weight of the phone and case combined is 225.4g.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
To find the smallest possible total weight of the phone and case combined, we need to add the weight of the phone and the case.
The weight of the phone is given to 2 significant figures, so we can assume that it has an uncertainty of +/- 0.05g. The weight of the case is given to 1 decimal place, so we can assume that it has an uncertainty of +/- 0.05g as well.
Adding the two weights together, we get:
210g + 15.4g = 225.4g
To find the smallest possible total weight, we need to round this to the nearest 0.1g, since the weight of the case is given to 1 decimal place. Rounding to the nearest 0.1g gives us:
225.4g rounded to 1 decimal place = 225.4g
Therefore, the smallest possible total weight of the phone and case combined is 225.4g.
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The lowest overall weight that may be achieved is [tex]220.35g[/tex].
What does weight actually mean?The amount and quantity of bulk or heaviness; the weight of something. Physics. In an area with constant gravitational acceleration, mass is typically defined as the force of gravity, which is equal to the body's mass times the local velocity of gravity.
What does weight vs. weigh mean?With a few exceptions like statistics, grades, and blankets, we can generally keep weigh or weight distinct through using weight as a verbs and mass as a noun.
As the weight of the smartphone is stated to be [tex]210g[/tex] to two significant numbers, we may conclude that its true weight is between [tex]205g[/tex] & [tex]215g[/tex].
We may estimate that the case weighs between [tex]15.35g[/tex] to [tex]15.45g[/tex] because it is said to weight [tex]15.4g[/tex] to one decimal point.
So, [tex]205g + 15.35g = 220.35g[/tex] is the absolute minimum weight that the phone and case may weigh together.
Hence, [tex]220.35g[/tex] is the lowest feasible overall weight.
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how many different 4 card hands can be dealt from a deck of 52 cards? the order of the cards does not matter in this case.
Answer:
270,725 hands.
Step-by-step explanation:
(52 x 51 x 50 x 49)/(4 x 3 x 2) = 13 x 17 x 25 x 49 = 270,725
Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = x4, y = x7
The volume of the solid formed by revolving the region about the x-axis is 2/45π.
Given:
Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y = x^4, y = x^7
In addition, we must identify if the axis of revolution is vertical or horizontal.
In this case, the axis of revolution is on the x-axis, when y=0
The axis of revolution is Horizontal.
Select the method to find the volume. We select the Washer Method:
[tex]V = pi*\int\limits^b_a {(R(x))^2-(r(x))^2} \, dx[/tex]
From the image uploaded:
r(x) = x^7
R(x) = x^4
a = 0
b = 1
[tex]V = pi*\int\limits^1_0 {(x^4)^2-(x^7)^2} \, dx[/tex]
[tex]V = pi*\int\limits^1_0 {(x^8)-(x^{14})} \, dx[/tex]
[tex]V=pi*[(-1/15(1)^{15}+1/9(1)^9)-(-1/15(0)^{15}+1/9(0)^9)][/tex]
[tex]V = pi*[(2/45) - (0)][/tex]
V = 2/45*π
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A computer programming team has 17 members. (a) How many ways can a group of nine be chosen to work on a project? As in Example 9.5.4, since the set of people in a group is a subset of the set of people on the team, the answer is (b) Suppose nine team members are women and eight are men. (1) How many groups of nine can be chosen that contain five women and four men? As in Example 9.5.7a, think of forming the group as a two-step process, where step 1 is to choose the women and step 2 is to choose the men. The answer is (ii) How many groups of nine can be chosen that contain at least one man? As in Example 9.5.7b, consider the relationship between the set of groups that consist entirely of women and the set of groups with at least one man. This thinking leads to the conclusion that the number of groups with at least on man is (iii) How many groups of nine can be chosen that contain at most three women? A group of nine that contains at most three women can contain no women, one woman, two women, or three women. So, the number of groups of nine that contain at most three women is (c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain A and not B, B and not A, and neither A nor B leads to the conclusion that the total number of groups of that can be chosen to work on the project is (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project? As in Example 9.5.5, let A and B be the two team members who insist on working in a group together or not at all. How many groups contain both A and B? How many groups contain neither A nor B?
The number of groups that can be chosen from the team of 17 depends on the given conditions of the selection.
The correct responses are;
(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.
(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.
(ii) The number of groups of 9 that contain at least one man is 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.
(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.
Given,
The combination of n objects taking r at a time is given as follows
ₙCr = (ⁿr)
(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;
Number of ways of choosing groups of 9 = (17, 9) = 24,310 ways.
(b) (i) Number of women = 9
Number of men = 8
Number of groups of 9 containing 5 women and 4 men = (9, 5) x (8, 4)
(9, 5) x (8, 4) = 126 x 70 = 8820
Number of groups of 9 containing 5 women and 4 men = 8,820 groups.
(ii) The number of groups that contain at least one man is (17, 9) - (9, 9)
(17, 9) - (9, 9) = 24,310 - 1 = 24,309
The number of groups that contain at least one man are 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women if given as follows;
(8, 8) × (9, 1) + (8, 7) × (9, 2) + (8, 6) × (9, 3) = 2649
The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are (15, 9) + 2 × (15, 8)
(15, 9) + 2 × (15, 8) = 5,005 + 2 × 6,435 = 17,875
(d) Two team members must work together or not at all is (15, 7) - (15, 9)
(15, 7) - (15, 9) = 6,435 - 5,005 = 1,430
The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.
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you are interested in knowing what proportion of college students smoke. in a big university, you take a small random sample of 650 students and find that 25 of them smoke. based on the results of your survey, construct a 99% confidence interval for the proportion of college students who smoke.
A 99% confidence interval for the proportion of college students who smoke for the given standard deviation is (0.021. 0.045).
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
formula for confidence interval is :
m = p-bar ± z*√p(1-p)/n
given information =
n= 650
p - bar = 25/650 = 1/26
C.I. = 99% = 0.99
we need to find value of 0.99 in z -table
z = 2.33
substituting value ,
0.038 ± 2.33√( 0.038(1-0.038))/650
0.038 ± 2.33 * 0.075
0.038 ± 0.017
(0.021. 0.045)
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According to USA today, customers are not settling for automobiles straight off the production lines. As an ex. , those who purchase a $355,000 Rolls-Royce typically add $25,000 in accessories. One of the affordable automobiles to receive additions is BMWs mini cooper. A sample of 179 recent Mini purchasers yielded a sample mean of $5,000 above the $20,200 base sticker price. Suppose the cost of accessories purchased for all Mini Coopers has a standard deviation of $1,500.
A. Calculate a 95% confidence interval for the average cost of accessories on Mini Cooper.
B. Determine the margin of error in estimating the average cost of accessories on Mini Coopers.
C. What sample size would be required to reduce the margin of error by 50%?
The 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746
The margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The required sample size should be 34574400 to reduce the
margin of error by 50%
Sample size, n = 179
Sample mean, x = 5,000
Population standard deviation, σ = 1,500
Confidence level, 1-α=0.95
⇒ Level of significance, α = 0.05
From the z-table, the tabulated value is given by
[tex]Z_{\alpha /2}[/tex] / [tex]Z_{0.025}[/tex]
=1.95
95% confidence interval for the average cost of accessories on Mini Cooper is
5,000±1.96×(1,500/√179)
= (5,000 ± 219.7459)
=($4790.254, $5219.746)
Therefore the 95% confidence interval for the average cost of
accessories on Mini Cooper is between $4790.254 and $5219.746.
Margin of error
= 1.96x(1,500/√179)
= 219.7459
Therefore, the margin of error in estimating the average cost of accessories on Mini Coopers is $219.7459.
The margin of error (E) is 0.50
⇒(0.50) √n=1.96(1500)
√n = 1.96(1500) /0.50
= n = (1.96(1500) /0.50)²
= n = (5880)²
= n = 34574400
Therefore, the required sample size should be 34574400 to reduce the
the margin of error by 50%
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What are the dangers you should look out for before using the AED?.
The dangers you should look out for before using the AED are do Not use an AED on a victim lying on a conductive surface, Do Not use an AED on a child under age 8 or under 90 pounds, o Not use an AED on a victim who has a nitroglycerine or other patch, and so on.
AED stands for Automated Outside Defibrillator. An AED analyzes the heart's rhythm and tells a first-help supplier to provide a stun to a victim of sudden cardiac arrest. This stun is called defibrillation and may offer assistance to the heart to reestablish an effective beat. It appears that early defibrillation increments a victim of sudden cardic arrest chances for survival. . Don't touch the victim whereas defibrillating. You or somebody else may get shocked. Do Not utilize liquor to wipe the victim's chest dry. Liquor is flammable. Do Not utilize an AED in a moving vehicle. Movement may influence the analysis. Do Not utilize an AED on a victim who is in contact with water. Move victims absent from puddles of water or swimming pools or out of the rain sometime recently defibrillating.
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(1 point) you have a spinner with red and blue regions. when you spin, it comes up blue 80 percent of the time. you do an experiment where you spin the spinner 120 times, and it comes up blue 101 times. (a) what proportion of spins came up blue in your sample?
84 percent of spins came up blue in your sample.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, You spin the spinner 120 times, and it comes up blue 101 times.
∴ The proportion of spins that came up blue in your sample is,
= (101/120).
= 0.84 Or 84% of the spins came up blue.
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For what values of r will the area of the shaded region be greater than or equal to 12 square units?
The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8
Given that,
We have to find the darkened region's area will be more than or equal to 12 square units for what values of r.
We can see a rectangle and a triangle in the given image.
The triangle is the part of the rectangle that is not coloured.
Thus;
Area of rectangle minus area of rectangle gives the area of the shaded area.
We know that formula for area of rectangle is;
Ar = length × width
Thus; Ar = 3 × r
Ar = 3r
Area of a triangle is;
At = ½ × base × height
At = ½ × r × 3
At = ½(3r)
Thus;
Area of shaded region = 3r - 1/2(3r)
Area of unshaded portion = 1.5r
We are informed that the unshaded area must have a minimum area of 12 and a maximum area of 12. Thus;
1.5r ≥ 12
r ≥ 12/1.5
r ≥ 8
Therefore, The values of r for which the shaded region will be greater than or equal to 12 square units is r ≥ 8
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The table shows the sales of a health and beauty supply company, in millions of dollars, for several years. Let x be the number of years since 2010.
Year 2011 2012 2013 2014 2015
Sales 12.2 19.1 29.4 37.3 45.7
a. Write the equation for the best-fit line for the data. Round to the nearest hundredth, if necessary.
y =
x +
Part B
Select the correct choices to complete the sentence.
b. Find and interpret the correlation coefficient.
r ≈ , 1 of 4.
Select Choice
The equation , 2 of 4.
Select Choice
the data very well. Its , 3 of 4.
Select Choice
value means that as the years since 2010 increase, sales, in millions of dollars, , 4 of 4.
Select Choice
.
a. The equation for the line of best-fit is:
y = 8.52x + 11.7.
b. The correlation coefficient is of: 0.9987, hence there is a strong positive correlation between the variables.
How to find the equation of the line of best fit and the correlation coefficient?To obtain the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.
The points in this problem are given on the table as follows:
(0, 12.2), (1, 19.1), (2, 29.4), (3, 37.3), (4, 45.7).
As we consider the input x as the number of years since 2011.
Then, using the calculator, the equation is given as follows:
y = 8.52x + 11.7.
Using a correlation coefficient calculator, the numeric value of the coefficient is of:
r = 0.9987.
Hence the correlation between the variables is classified as follows:
Positive, as the correlation coefficient is positive.Strong, as the correlation coefficient is greater than 0.6.More can be learned about regression equations at https://brainly.com/question/26755306
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Bill has lost 40 pounds in 8 weeks. What is his weekly rate?
Answer: 5
Step-by-step explanation:
So all you have to do is divide 40 by 8 and you get the answer
An experiment compared the adhesion of 2 types of paint, a and b, to 3 types of metal, 1, 2, and 3, used in automobiles. Thirty sheets of metal were used in the experiment: 10 of metal 1, 10 of metal 2, and 10 of metal 3. Half of each metal type will receive paint a and the other half will receive paint b. The adhesion of the paints was measured, and the measures were compared. How many experimental units are in the experiment?.
There are 35 experimental units are in the experiment.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given there are 2 types of paints, and 3 types of metal, Thirty sheets of metal were used in the experiment.
We have to apply the addition operation in order to find the number of experimental units.
The number of experimental units in the experiment is found as,
=2+3+30
=5+30
=35
Thus, there are 35 experimental units are in the experiment.
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Write an equivalent expression for 8(1/7y - 7)
Answer: 8/7y - 56
Step-by-step explanation: To find the equivalent expression, we multiply 8 by both of the values in the parenthesis.
8 × 1/7y = 8/7y
8 × (-7) = -56
Now to express it as an equation:8/7y - 56 is our final answer.
Find the critical point of the function f(x, y) = X2 + y2 + 3xy - 7.5x Use the Second Derivative Test to determine whether the point a local maximum test fails a local minimum a saddle point
The critical point of the function f(x, y) = x^2 + y^2 + 3xy - 7.5x is (0, 0) because the partial derivatives of f with respect to x and y are both equal to 0 at this point.
What is the critical point?In mathematics, a critical point is a location along a function or curve where the derivative of the function is either equal to 0 or undefined. Accordingly, a critical point occurs where the slope of the function is either 0 or not specified, producing a flat or vertical tangent line. Critical points are significant because they frequently point to locations where the function changes course or exhibits a local extreme value, such as a maximum or minimum. Taking the function's derivative and then solving for the values of x where the derivative equals zero or is undefined will help you locate key spots. The critical points of the function are at these values of x.
How to solve?
To use the Second Derivative Test, we need to calculate the Hessian matrix of the function at the point (0, 0).
The Hessian matrix for f(x, y) at (0, 0) is given by:
H = [2 3]
[3 2]
λ1 = 5, λ2 = -1
Since the Hessian matrix has one positive and one negative eigenvalue, the point (0, 0) is a saddle point.
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What are the steps for using a compass and straightedge to construct a regular hexagon inscribed?.
The steps to construct a regular hexagon inscribed are-Construct a horizontal line I and a point H on this line I, draw a circle having to intersect line I with it's center at point H, label the point of intersection of the circle and the left of point H, point J.
Detailed steps to construct a regular hexagon inscribed using a compass are:
Construct a horizontal line I and a point H on this line I.Construct a circle which will intersect line I with it's center at point H.Name the point of intersection of the circle and the left of point H, point J.Construct a circle by taking center point at point J and with a radius of HJ. Construct a circle by taking center at point K having a radius of HJ.Name the point of intersection of circles H and J that lies above line I, point M, and the point of the intersection that lies below line I, point N. Name the point of intersection of circles H and K that lies above line I, point O, and the point of their intersection that lies below line I, point P. Construct and JM, MO, OK, KP, PN, and NJ to complete regular hexagon JMOKPN.To know more about regular hexagon, visit here:
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