In order to gain popularity among BHSEC students, a new pizza place near Aven offer a special promotion. The cost of a large pizza (in doll students, a new pizza place near Avenue D plans to Momotion. The cost of a large pizza (in dollars) as a function of time (measured in days since December 10th) is described by Let C(t) as follows: 9. Osis3 c(t)= 9+1, 3<158 21+41.8
Answers
For the function C(t) = {9, 0 ≤ t ≤ 3
C(t) = {9 + t, 3 < t ≤ 8
C(t) = {20 8 < t < 28
a) If you want to give their pizza a try, in order to get the best price you should buy a large pizza on date(s) February 10, February 11, February 12, and February 13.
b) The cost of large pizza on February 18th will be $17.
c) A large pizza will cost $13 on the date February 14.
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
The given function is C(t) = {9, 0 ≤ t ≤ 3
C(t) = {9 + t, 3 < t ≤ 8
C(t) = {20 8 < t < 28
a) According to the function above, the promotion's lowest price for a large pizza is $9.
When t = 0, t = 1, t = 2, and t = 3, this is how much the pizza will cost.
We are aware that the symbol t stands for the duration since February 10th.
Therefore, t = 0 relates to February 10, t = 1, t = 2, and t = 3 correspond to February 11, February 12, and February 13, respectively.
Therefore, February 10, February 11, February 12, and February 13 are the best dates to test the new pizza joint in order to receive the best price.
b) Eight days after February 10th, or t = 8, is February 18th.
When 3 < t ≤ 8, the function C(t) = 9 + t can be used to calculate the price of a large pizza in dollars.
At that point, C(t) = 9 + 8 = 17 dollars when t = 8.
Therefore, on February 18, a big pizza will cost $17.
c) Because the function above says that for these values of t, C(t) = 9, we know that 13 ≠ 9 and thus a big pizza cannot cost 13 dollars when 0 ≤ t ≤ 3.
Similar to the previous example, it is also known that 13 ≠ 20 indicates that a big pizza cannot cost 13 dollars when 8 < t < 28 because C(t) = 20 for these values.
As a result, it is known that the only circumstance in which a large pizza may cost 13 dollars is when t falls within the range 3t–8 for which C(t) = 9 + t.
Enter 13 as the cost into this equation and solve for t in order to determine the day on which a large pizza will cost 13 dollars -
13 = 9 + t
t = 13 - 9
t = 4
When t = 4, this indicates that a large pizza costs $13.00.
Given that t represents the number of days since February 10, it is known that t = 4 represents February 14.
Therefore, on February 14th, a big pizza will cost $13.
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Related Questions
Solve the absolute value equation for x. |4 − 2x| + 6 = 18 Enter your answers in the blanks in order from least to greatest. x=□ or □
Answers
The solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:
x = -4 or x = 8
What is inequality?
A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.
We can solve this absolute value equation by first isolating the absolute value term on one side of the equation and then solving for both possible cases. Here are the steps:
|4 − 2x| + 6 = 18
|4 − 2x| = 12 (subtract 6 from both sides)
Now we have an absolute value equation with no constant term. We can split this equation into two cases: one where the expression inside the absolute value is positive, and one where it is negative. For each case, we can solve for x:
Case 1: 4 - 2x > 0
If 4 - 2x is positive, then we can drop the absolute value bars and write:
4 - 2x = 12
-2x = 8
x = -4
So one solution is x = -4.
Case 2: 4 - 2x < 0
If 4 - 2x is negative, then we must flip the inequality when dropping the absolute value bars:
-(4 - 2x) = 12
-4 + 2x = 12
2x = 16
x = 8
So the other solution is x = 8.
Therefore, the solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:
x = -4 or x = 8
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How do I solve this problem?
Answers
Answer:
sup dudes pls what state is this and plus is this logarithms
What is a distribution that has both mean and median of (-15)?
Answers
A distribution that has both mean and median of (-15) is referred to as a perfectly symmetrical distribution.
What is a Perfectly symmetrical distribution?This is referred to as a type of distribution in which the values of the mean and the median are the same as they are the central component of inferential statistics.
In this scenario, we were given the mean and median to be of the same value which is (-15) which therefore denotes that the type of distribution is a perfectly symmetrical one.
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How do you know if results are practically significant?
Answers
In order to determine the practical significance requires considering both the effect size measures and the context of the study
One way to determine practical significance is by using effect size measures. Effect size is a standardized measurement of the magnitude of a treatment or intervention.
A common equation used to calculate effect size is Cohen's d, which is the difference between the means of two groups divided by the standard deviation.
Another equation used is the odds ratio, which is the ratio of the odds of an event occurring in one group compared to another.
Additionally, it is important to consider the context of the study when evaluating practical significance.
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The heights of the bars of a histogram correspond to ______ values.
Answers
The heights of the bars of a histogram correspond to Frequency values.
A histogram is a type of graph used to show the distribution of a dataset. It is used to display the frequency of values within the data set by depicting the number of observations that fall within a set of ranges.
The heights of the bars of a histogram correspond to the frequency of values within the data set.
A histogram is used to illustrate the distribution of data within a set by showing the number of data points that fall within a specified range of values (called bins).
The height of each bar in the histogram represents the frequency of values within the bin range. A taller bar indicates that more data points fall within that range. The area of each bar is also proportional to the frequency of the values in the bin.
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Suppose that the data y = (y1,..., yn) are a sample from a normal distribution with unknown
mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean
0 and standard deviation σ0.
(a) For an uninformative prior, do we need a large or small value for σ0? [2]
(b) We want the prior probability P(|θ| ≤ A+10) to be 0.95, where A is the third-to-last digit
of your ID number. What value for σ0 should we choose? [4]
(c) A colleague prefers a Cauchy distribution as a prior. What is a possible reason for this
preference?
Answers
the data y = (y1,..., yn) are a sample from a normal distribution with unknown mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean 0 and standard deviation σ0.
y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1 y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1
We have two cases for Ф,
1. Ф=1; it implies that Pr(Ф=1)=0.5, while y~N(1,α²)
2. Ф=2; it implies that Pr(Ф=2)=0.5, while y~N(2,α²)
Now,
For 1st case of α=2,
We have marginal probability density formula
p(y)=∑p(yIФ)p(Ф)
=p(yIФ=1)p(Ф=1)+p(yIФ=2)p(Ф=2)
=N(yI1,2²)(1/2)+N(yI2,2²)(1/2)
=(1/2)[N(yI1,2²)+N(yI2,2²)]
Now.
For Pr(Ф=1Iy=1) at α=2
We have,
=p(Ф=1Iy=1)
=[p(y=1,Ф=1)]/[p(y=1)]
=[p(y=1IФ=1)p(Ф=1)]/[p(y=1)]
={(1/)exp[(-1/(2*2²))(1-1)²(1/2)]}/{(1/)(1/2)[exp[(-1/(2*2²))(1-1)²]+exp[(-1/(2*2²))(1-2)²]}
=0.53 Answer
Now, to describe the changes in shape of Ф when α is increased and decreased deviation
The formula for posterioir density is p(ФIy)=p(yIФ)p(Ф)/p(y)
=exp[(-1/(2α²)(y-Ф)²]/{exp[(-1/(2α²)(y-1)²]+exp[(-1/(2α²))(y-2)²]}
Now at Ф=1 and solving the equation, we get
p(Ф=1Iy)=1 / {1+exp[(2y-3)/2α²]}
Similarly at Ф=1 and solving the equation, we get
p(Ф=2Iy)=1 / {1+exp[(2y-3)/2α²]}
Conclusion:
α² → ∞ ⇒p(ФIy) → p(Ф) = 1/2
α² → 0 ⇒ two cases
y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1
y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1
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Kevin was solving for the area of the triangle below.
The formula for area of a triangle is A = bh. Kevin's answer
for the area of this triangle was 40 inches².
Is Kevin's solution correct? Why or why not?
If not, what was his mistake?
If not, what is the correct solution for the area of this
triangle?
Answers
Kelvin's solution is correct because he multiplies the base of the triangle by the height of the triangle.
What is the area of the triangle?Area of triangle= base × height
The base of the triangle= 5 in
The height of the triangle = 8 in
Area of triangle= base × height
= 5 in × 8 in
= 40 square inches
Consequently, the area of the triangle as calculated by kelvin is correct.
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How do you convert acres to miles?
Answers
The convert acres to miles 0.0015625.
What is meant by miles ?
The mile is a customary unit of measurement in the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is often referred to as the international mile or statute mile to distinguish it from other miles. In 1959, the statute mile was formally redefined with respect to SI units as precisely 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.The Romans split a mile into 5,000 Roman feet, but in Elizabethan England, where furlongs were valued more highly, the statute mile was changed in 1593 to be equal to 8 furlongs, or 5,280 feet.To learn more about miles refer to
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Area of a circle 12 mm diameter
Answers
Answer:
Area of a circle= 1/4*π d^2
A=1/4*π*12^2=
A=1/4*π*144=113.1
Step-by-step explanation:
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In a certain species of plant, the color purple (p) is dominant to the color white (p). According to the punnett square, what is the probability of an offspring being white?.
Answers
Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.
what is the probability of an offspring being white?.Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.
It is used to know the result of the genotype of the offspring having either having single or multiple traits.
The correct answers are:
1.Option C. 0%
In the Punnett square the cross is between the purebred dominant and purebred recessive parent.
This will result in all the offspring having a heterogeneous genotype trait carrying purple color. Hence 0% will carry white color.
2. Option D. 25%
It can be explained as:
Due to the presence of heterogenous parent species. It will result in 25% of offspring carrying white color.
Therefore, in question 1, 0% of plants will be white while in another question 25% of the offspring will carry the white color trait.
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Here are graphs of three exponential equations.
Match each equation with its graph.
6,000
4,000
2,000
Column A
1.
2
3
-
f(x) = 100 (3)^x
g(x) = 100 (35)^x
h(x) = 100 (4)^x
B
U
3
Column B
a. C
b. A
C. B
Answers
Answer:
f(x) = 100 (3)^x <===> C
f(x) = 100 (3.5)^x <===> B
f(x) = 100 (4)^x <===> A
Step-by-step explanation:
Since the base of each of the exponential functions is the same, the higher the base, the higher up the graph will be with respect to another base with a lower value
This can be easily determined by choosing a specific value for x for each equation and seeing what the f(x) value is
Let's choose x = 2
For f(x) = 100 (3)^x, at x = 2 we get f(2) = 100(3)^2 = 100 x 9 = 900
For f(x) = 100 (3.5)^x, at x = 2 we get f(2) = 100(3.5)^2 = 100 x 12.25 = 12.25
For f(x) = 100 (4)^x, at x = 2 we get f(2) = 100(4)^2 = 100 x 16 = 1600
So for a specific value of x, the higher the base, the higher the graph is relative to the x-axis
So the matches are:
f(x) = 100 (3)^x <===> C
f(x) = 100 (3.5)^x <===> B
f(x) = 100 (4)^x <===> A
given the linear system y[n] = 0.25y[n-1] x[n] for n > 0 and y[-1]=0 system is described by the impulse response h[n] = [0.25]nu[n]. determine if the system is stable or not
Answers
The system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.
The stability of a linear system can be determined by analyzing the magnitude of its impulse response −
|h[n]| ≤ M for some finite M
In this case, the impulse response is h[n] = 0.25nu[n], where nu[n] is the unit step function. Since the magnitude of h[n] is 0.25 for all n, the system is stable since 0.25 is a finite number that is less than any M.
To summarize, the system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.
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4. What percentage of the earth's surface is covered by water?
a. 86%
b. 71%
c. 67%
d. 58%
e. 52%
Answers
Answer: option b. 71%
Step-by-step explanation:
Given the following Venn diagram, where A and B are each represented by an oval:IV LT IIIWhich regions make up ( AExam ImageB )c?a) III and IVb) I, II and IVc) I, II and IIId) II
Answers
A and B are each represented by an oval:IV LT III regions make up
the answer is (d) II.
What is Venn diagram ?
A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
The set (A union B) complement is defined as the set of all elements in the universal set that are not in A union B. In set notation, it can be expressed as (A union B)^c = U - (A union B), where U is the universal set and c represents the complement.
In a Venn diagram, the complement of a set is represented by the region outside of the set. In the given Venn diagram, the region outside of A and B is represented by region IV, so (A union B) complement = IV.
Therefore, A and B are each represented by an oval:IV LT III regions make up the answer is (d) II.
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Evaluate lim f(x) and lim f(x) for the following function. Use co or co where appropriate. Then give the horizontal asymptote(s) of f (if any).
f(x)= 3x^3+8/4x^3+√ 64x^64
Answers
The limit of f(x) as x approaches positive infinity and negative infinity is equal to 3/4, and the horizontal asymptote of the function is y=3/4.
The horizontal asymptote of a function is a horizontal line that the function approaches as x approaches infinity or negative infinity.
The function f(x) is given by
=> f(x)= 3x³ + 8/4x³ + √ 64x⁶⁴.
To evaluate the limits, we need to consider what happens as x approaches positive infinity and negative infinity.
In this case, as x approaches positive infinity or negative infinity, the x³ term in the numerator and denominator will dominate and the limit of the function will be equal to 3/4.
This means that the function has a horizontal asymptote of y=3/4.
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A humane society has 73 dogs and cats to be adopted. The number of cats is 10 more than twice the number of dogs. How many of each animal is up for adoption?
Answers
Answer:
52 cats
Step-by-step explanation:
Let d be the number of dogs, then c = 2d + 10 is the number of cats.
The total number of animals is 73, so we have d + c = 73.
Substituting c = 2d + 10 into this equation, we get d + 2d + 10 = 73.
Combining like terms, we get 3d + 10 = 73.
Solving for d, we have 3d = 63, so d = 21.
Thus, there are 21 dogs and 2 * 21 + 10 = 52 cats up for adoption.
) suppose harry has 3 apples and 2 bananas. would he be willing to trade an apple for a banana? show why or why not.
Answers
Total Utility of Harry remains the same and so he would indifferent to this exchange.
Now, According to the question:
MUa(H) = ∂UH/∂a = ∂(2ab)/∂a = 2b
MUb(H) = ∂UH/∂b = ∂(2ab)/∂b = 2a
"Information available from the question"
a = 3 apples and b = 2 bananas
For a = 3 and b = 2
MUa(H) = 2b = 4; MUb(H) = 2a = 6
Total Utility(H) = MUa(H) + MUb(H) = 4 + 6 = 10
New distribution after exchange --> a = 2 and b = 3.
MUa(H) = 2b = 6; MUb(H) = 2a = 4
Total Utility(H) = MUa(H) + MUb(H) = 6 + 4 = 10
Total Utility of Harry remains the same and so he would indifferent to this exchange.
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The given quesion is incomplete, complete question is:
Tom, Jim , and Harry, the only three people on a desert island with two consumption goods, apples and bananas, have utility functions UT, UD, and UH, respectively, where:
UT(xa,xb) = 6xa+9xb
UD(xa,xb) = 8xa+12xb
UH(xa,xb) = xaxb2
a)Suppose harry has 3 apples and 2 bananas. would he be willing to trade an apple for a banana? show why or why not.
Let u = 26 [ 4 -2] and A= -5 9 . Is u in the plane in R3 spanned by the columns of A? Why or why not? 1 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal for each matrix element.) O A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. O B. No, the reduced row echelon form of the augmented matrix is , which is an inconsistent system
Answers
No, u is not in the plane spanned by the columns of A.
To check if u is in the plane spanned by the columns of A, we first need to construct the augmented matrix of the system A · x = u, where x is the vector of unknowns. The augmented matrix is:
[−5 9 | 26 4 −2]
The reduced row echelon form of this augmented matrix is:
[1 0 | 2 -1]
This is an inconsistent system,the reduced row echelon form of the augmented matrix is , which is an inconsistent system so it does not have any solutions. This means that u cannot be written as a linear combination of the columns of A, so it is not in the plane spanned by the columns of A.
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A city currently ha 132 treetlight. A part of an urban renewal program, the city council ha decided to intall 4 additional treetlight at the end of each week for the next 52 week. Ue thi information to complete the following tatement. Round to the nearet whole number a needed. The city will have (blank) treetlight at the end of 46 week. The city will have 232 treetlight at the end of (blank) week
Answers
They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
According to the data problem,
At the end of 46 week the city will have: 132 streetlight + (4 streetlight/ week * 46 weeks)
At the end of 46 week the city will have: 132 streetlight + 184 streetlight
At the end of 46 week the city will have: 316 streetlight
232 streetlight at the end of the week = (232 streetlight - 132 streetlight) / 4 streetlight /week
232 streetlight at the end of the week = 100 streetlight /4 streetlight /week
232 streetlight at the end of the week = 25 weeks
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Correctly written question:
A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. The city will have (blank) streetlights at the end of 46 weeks. The city will have 232 streetlights at the end of (blank) week
:(help pleaseeeeeeeeeee
Answers
The values of the letters are:
A = $37.5
B = $16.95
C = 5
D = $15.34
How to determine the values of the letter?A sales tax is a tax paid to the government for the sales of certain goods and services.
Total price = Quantity * Unit Price
Unit price = Total price / Quantity
Quantity = Total price / Unit price
A = Total price = 3 * 12.5 = $37.5
B = Unit price = 33.90 / 2 = $16.95
C = Quantity = 31.00 / 6.20 = 5
15% VAT = 15% of Total Price
D = 15/100 * 108.28 = $15.34
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Calculate the volume of this cylinder. Give your answer to 1 d.p. and remember to give the correct unit
Answers
Solution is in the attachment!!
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
Slope = 3/2 , y-intercept = 0
Answers
Answer:
y = [tex]\frac{3}{2}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = [tex]\frac{3}{2}[/tex] and y- intercept c = 0 , then
y = [tex]\frac{3}{2}[/tex] x + 0 , that is
y = [tex]\frac{3}{2}[/tex] x
A teacher asks three students to complete the following statement about the nature of the roots
of a quadratic equation.
If q
2
– 4pr > 0, the roots of the quadratic equation px2 + qx + r = 0 will be...
Zain answers, "always positive".
Vipul answers, "positive, if p, q, and r are positive".
Suman answers, "negative, if p, q, and r are positive".
Who answered correctly
Answers
If q² – 4pr > 0, the roots of the quadratic equation px² + qx + r = 0 will be: "negative, if p, q, and r are positive". Therefore, Suman answered correctly.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
Generally speaking, the standard form of a quadratic function is given by ax² + bx + c = 0.
Assuming the roots of the quadratic function are a and b. Therefore, the sum of the roots of the quadratic function would be equal to -q/p;
a + b = -q/p
ab = r/p
This ultimately implies that, the nature of the roots would depend on the value of p, q and r, which make Zain's answer to be wrong.
Additionally, if p, q, and r are positive, a + b would be negative, and one or both roots must be negative, which make Vipul's to be wrong.
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81000 km of black plastic cylindrical water piping with internal diameter 13 mm and walls of thickness
2 mm is required for a major irrigation project. The piping is made from bulk plastic which weighs
0.86 tonnes per cubic metre. How many tonnes of black plastic are required?
Answers
The number of tones of the black plastic that is required here is 9567.3 tones .
What is the number required?The volume of one meter of piping can be calculated as follows:
V = π * (r^2) * l
Where r is the radius of the pipe (6.5 mm), and l is the length (1 meter).
So, the volume of one meter of piping is:
V = π * (6.5^2) * 1 = 134.96 mm^3
Since 1 m^3 = 10^9 mm^3, the volume in m^3 of one meter of piping is:
V = 134.96 / 10^9 = 0.00013496 m^3
Therefore, the total volume of 81000 km of piping is:
V = 0.00013496 * 81000 * 10^3 = 11,124.16 m^3
And the total weight of the piping is:
W = V * 0.86 tones/m^3 = 9567.3 tones
So, 9567.3 tones of black plastic is required.
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To investigate the influence of distracted driving, 13 volunteers were asked to participate in a study involving a driving simulator. The participants drove at a safe speed but were told to stop the car at a random moment during the simulation. The scatterplot shows the reaction time and the simulated car’s stopping distance (in feet) for each volunteer. The value of r for the scatterplot is 0. 935.
How would the correlation change if the stopping distances were recorded in meters, rather than feet?
A. The value of the correlation coefficient would not change.
B. Since the points would be more spread out, the value of the correlation coefficient would decrease.
C. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would increase.
D. Since the number of meters would be less than the number of feet, the value of the correlation coefficient would decrease
Answers
The value of the correlation coefficient would not change.
The following would be the correlation change if the stopping distances were recorded in meters, rather than feet.
Hence, option (A) is the correct choice.
Correlation is a statistical number derived based on historical data (profitability), and, contrary to popular belief, it is not constant and can change over time.
Correlation is a statistical term that reflects how much two or more variables vary in relation to one another.
The correlation coefficient is evaluated on a scale ranging from + 1 to - 1. The degree of correlation between two variables is denoted by + 1 or -1. When one variable rises as the other rises, the correlation is positive; when one falls as the other rises, the correlation is negative.
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Gayle bought a shirt that was originally marked as $18. She had a coupon to receive 15% off the price. Gayle
had to pay 7. 5% sales tax on her shirt. What price did Gayle pay for the shirt?
Answers
sssssssssaStep-by-step explanation:
The equation s equals three fourths times f represents the proportional relationship between the amount of sugar (s) and flour (f) in a recipe. Which table represents the equation of the proportional relationship?
Sugar Flour
1 six fourths
2 three fourths
Sugar Flour
six fourths 1
three fourths 2
Sugar Flour
three fourths 1
six fourths 2
Sugar Flour
1 three fourths
2 six fourths
Answers
The table that represents the equation of the proportional relationship is; Table 4
How to find the proportional relationship?A proportional relationship is defined as a mathematical relationship that exists between two variables in which their ratio is always equal.
We have that the equation s equals three fourths times f. This is expressed as;
s = ³/₄f
where;
s is the amount of sugar
f is the amount of flour
Table 1;
when f = 1
s = ³/₄(1)
s = ³/₄
when f = 2
s = ³/₄(2)
s = 6/4
Thus, table 4 is correct
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for each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false. (a) ∀x∃y(y 2 x). (b) ∀x∀y(x < y → ∃z(x < z < y)
Answers
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
An integer, also called a "round number" or “whole number,” is any positive or negative number that does not include decimal parts or fractions. For example, 3, -10, and 1,025 are all integers, but 2.76 (decimal), 1.5 (decimal), and 3 ½ (fraction) are not.
(a) ∀x∃y( [tex]y^{2}[/tex] ≥ x)
[tex]y^{2}[/tex] ≥ 0
When x ≥ 0 , [tex]y^{2}[/tex] = x is True.
When x < 0 , without [tex]y^{2}[/tex] = x is True.
(b) ∀x∀y(x < y → ∃z(x < z < y)
When x ≠ z ≠ y , x < z < y is True.
When z = x or z = y , x < z < y is False.
When x = y and x = z , y = z
Therefore,
A domain of discourse for a domain integer statement is,
(a) True : x ≥ 0 and False x < 0
(b) True : x ≠ z ≠ y and False x ≠ y = z
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Catori is a landscape photographer. One weekend at her gallery she sells a total of 52 prints for a total of $2,975. How many of each size print did Catori sell?
Answers
Answer:
15 prints
Step-by-step explanation:
Let's call the number of small prints sold as "x".
The number of medium prints sold is then (52 - x) prints.
We know that the total revenue from all the prints sold is $2,975, so we can set up the following equation:
$2975 = (x * $50) + ((52 - x) * $75)
Expanding and solving for x:
$2975 = $50x + $3900 - $75x
$2975 = $3900 - $25x
$-925 = -$25x
x = 37
So, Catori sold 37 small prints and (52 - 37) = 15 medium prints
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A four-sided figure is resized to create a scaled copy. The proportional relationship between any given side length in the original figure, f, and the corresponding side length in the scaled copy, s, can be represented by the equation s=11/2 f. What is the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy?
Answers
The constant of proportionality is 7.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".
A four-sided figure is resized to create a scaled copy.
The proportional relationship between any given side length in the original figure f, and the corresponding side length in the scaled copy, s, can be represented by the equations s=1/7f.
To find the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy
The equation we get as, f=7s
Therefore, the constant of proportionality is 7.
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