The relation represents y as a function of x as for each value of x there is a unique value of y.
What is a function?A function y = f(x) is defined as a one to one relation between sets X and Y. The set X is called the domain while Y is called the range of f(x).
The given data is as follows,
A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).
Here x is the element of domain and y is of the range of the given relation.
Here, the values of y are distinct for different values of x.
Hence, the given relation represents y as a function of x because for each value of x there is a single value of y.
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Identify the variation as direct, inverse, joint or combined x/y =c
O joint
O direct
O combined
O inverse
NEXT QUESTION
The Mid-High JV Team is playing in the state championship for football. In order
to beat their all-time points in a season record, they need to score more than 60
points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a
touchdown with an extra point (p) scores 7 points, which inequality best represents
the possible ways the team can score more than 60 points.
The inequality best represents the possible ways the team can score more than 60 points.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given that, the Mid-High JV Team is playing in the state championship for football.
In order to beat their all-time points in a season record, they need to score more than 60 points in the game.
Considering a field goal (f) scores 3 points, a touchdown (t) scores 6 points, and a touchdown with an extra point (p) scores 7 points.
We need to find the inequality best represents the possible ways the team can score more than 60 points.
3f+6t+7p>60
Hence, 3f+6t+7p>60 is the inequality best represents the possible ways the team can score more than 60 points.
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Name each polynomial by degree and number of terms.
-6x^4-2x^2+2
A. quintic binomial
B. quadratic binomial
C. quartic trinomial
D. quartic monomial
Reason:
It's a quartic because the largest exponent is 4 (so the degree is 4).
It's a trinomial since it has 3 terms.
coach jenson bought 15 shirts for $180 for the basketball team. the unit rate for the shorts was 1.50 less than the unit rate for shirts. choach jenson bought the same number of shorts as shirts to complete each uniform. What was the total cost of the uniforms for the team? explain your answer
Answer:
$337.50
Step-by-step explanation:
To find the total cost of the uniforms, you will need to find the unit price of the shirts and the unit price of the shorts and then multiply each by the number of shirts and shorts, respectively.
The unit price of the shirts is the total cost divided by the number of shirts, or $180 / 15 shirts = 12/shirt.
The unit price of the shorts is
$12/shirt - $1.50/shirt = 10.5/shirt.
Since the coach bought the same number of shirts and shorts, the total number of shirts and shorts is 15 shirts + 15 shorts = 30 shirts and shorts.
The total cost of the shirts is $12/shirt * 15 shirts = $12*15 = 180.
The total cost of the shorts is $10.5/shirt * 15 shirts = 157.5
The total cost of the uniforms is the sum of the cost of the shirts and the cost of the shorts, or $180 + 157.5= 337.5.
Therefore, the total cost of the uniforms for the team is $337.5.
What is the range of this function?
One brand of orange juice is sold in four different sizes. The 8 ounce carton costs $0.99. The 48-ounce carton costs $2.49. The 64-ounce carton costs $3.75. Which size is the Best Buy? Explain how you determine your answer
On number 3 i need to find the following:
DF=
JH=
GJ=
m
m
please help and explain
Answer:
DF= 16m
JH= 14m
GJ= 19m
Step-by-step explanation:
turn the triangles until they overlap each other
since they are congruent, the measure of one angle will be the same for the other one
Answer:
DF= 16m JH= 14m GJ = 19m
Step-by-step explanation:
We know the two figures are equal to each other. So to find the missing sides just refer to the other figure with the included side.
The force the attraction between two magnets is F Newtons. This force is inversely
proportional to the square of the distance, d centimetres, between the magnets.
(a) When the magnets are a certain distance apart, the force is 10 Newtons.
What is the force when the distance is doubled ?
(b) (i) Write down a formula connecting F,d and a constant k.
(ii) When the magnets are 3 cm apart, the force is 2 Newtons.
Find the force when they are 5 cm apart.
1a
f is inversely proportional to d² so when d is d f=10N and when d is doubled F is 5/2N
1bi K=Fd²
1bii
since K=fd² when d is 3cm and F is 2N k=18
then when d=5
F is 18/25N
a set of 15 different integers has a median of 25 and a range of 25. what is the greatest possible integer that could be in this set? 32 37 ...
The greatest possible integer that could be in this set is 43.
The group of 15 different integers in this instance has a range of 25 and a median of 25. The greatest value that can be entered will be limited by that range.
With a median of 25, we can deduce that 7 numbers fall within the range of 25 and above, and 7 numbers fall within this range.
We must increase the smallest value in order to increase the largest value. Here's how to accomplish it:
18 19 20 21 22 23 24 25
With 18 as the lowest value and a range of 25, 43 would be the highest value.
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give 3 examples each.
Answer:
see below
Step-by-step explanation:
You want examples of use of the rules of logarithms:
[tex]\begin{array}{ll}\vphantom{\dfrac{M}{gN}}1.&\log_b{(MN)}=\log_b{(M)}+\log_b{(N)}\\2.&\log_b{\left(\dfrac{M}{N}\right)}=\log_b{(M)}-\log_b{(N)}\\\vphantom{\dfrac{b}{g}}3.&\log_b{(M^a)}=a\cdot\log_b{(M)}\end{array}[/tex]
The point of these is that M and N and 'a' and 'b' can be anything. (Generally, 'b' will be a positive number greater than 1.) For the purpose here, we can let M ∈ {x^3y, (1+r)}, N ∈ {(x-4), r/n}, a ∈ {4, -3}, b ∈ {2, e}.
Using these values in various combinations, your examples could be ...
1. Product rule[tex]\log_2{((x^3y)(x-4))}=\log_2{(x^3y)}+\log_2{(x-4)}\\\\\ln{((1+r)(r/n))}=\ln{(1+r)}+\ln{(r/n)}\\\\ \log_2{((x^3y)(r/n))}=\log_2{(x^3y)}+\log_2{(r/n)}[/tex]
2. Quotient rule[tex]\log_2{\left(\dfrac{x^3y}{x-4}\right)}=\log_2{(x^3y)}-\log_2{(x-4)}\\\\\\\ln{\left(\dfrac{1+r}{r/n}\right)}=\ln{(1+r)}-(\ln{(r)}-\ln{(n)})\\\\\\ \log_2{\left(\dfrac{x^3y}{r/n}\right)}=\log_2{(x^3y)}-(\log_2{(r)}-\log_2{(n)})}[/tex]
3. Power rule[tex]\ln{(x^3y)^4}=4\ln(x^3y)=4(3\ln{(x)}+\ln{(y)}=12\ln{(x)}+4\ln{(y)}\\\\\log_2{(1+r)^{-3}}=-3\log_2{(1+r)}\\\\\log_2{(x^3y)^{-3}}=-3\log_2{(x^3y)}=-9\log_2{(x)}-3\log_2{(y)}[/tex]
Which model represents a function?
Model III represents a function by vertical line test.
What is Vertical line test?
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
The vertical line test concludes that a curve in the plane represents the graph of a function if and only if no vertical line intersects it more than once.
According to the given question:
Graph I has vertical line intersections more than one on many points of the curve. Therefore, Graph I does not represents a function.
Model II has two values for the domain point that is -5 has two images 2 and 10. Hence it does not represents a function.
Graph III has only one intersection by vertical lines on the curve. Therefore, Graph III represents a function.
Graph IV has two intersection points if a vertical line passes through the curve. Hence, Graph IV does not represents a function.
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PLEASE HELP!!!!!!!!!!!
CROSS CONDUCT PROPERTY
By cross multiplication, the result for each pair of rational numbers are listed below:
x = 14 x = 114 / 5 x = 97 / 19 x = 318 / 5 x = 27 / 4 x = 2 x = 109 / 5 x = 94 / 11How to use cross multiplication
Cross multiplication is a property involving multiplication and division between the terms of two rational numbers of the form:
a / b = c / d
Where a, b, c, d are real numbers. Combinations between a numerator and a denominator are multiplications and combinations between two numerators and two denominators are divisions. Now we proceed to solve on each case:
Case 11
4 / x = 2 / 7
4 · 7 = 2 · x
28 = 2 · x
x = 14
Case 12
19 / 10 = x / 12
19 · 12 = 10 · x
228 = 10 · x
x = 114 / 5
Case 13
(x - 1) / 6 = 13 / 19
(x - 1) · 19 = 13 · 6
(x - 1) · 19 = 78
x - 1 = 78 / 19
x = 1 + 78 / 19
x = 97 / 19
Case 14
5 / 17 = 19 / (x + 4)
5 · (x + 4) = 19 · 17
x + 4 = 323 / 5
x = 318 / 5
Case 15
10 / (2 · x - 9) = 20 / 9
10 · 9 = 20 · (2 · x - 9)
90 / 20 = 2 · x - 9
27 / 2 = 2 · x
27 / 4 = x
x = 27 / 4
Case 16
12 / 18 = (3 · x + 4) / 15
2 / 3 = (3 · x + 4) / 15
10 = 3 · x + 4
3 · x = 6
x = 2
Case 17
(x - 20) / 3 = (x - 11) / 18
18 · (x - 20) = 3 · (x - 11)
18 · x - 360 = 3 · x - 33
15 · x = 327
x = 109 / 5
Case 18
6 / (x + 16) = 7 / (3 · x + 3)
6 · (3 · x + 3) = 7 · (x + 16)
18 · x + 18 = 7 · x + 112
11 · x = 94
x = 94 / 11
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"Cara" opened a savings account and deposited "$800.00" as principal. The account earns 10% interest, compounded annually. What is the balance after 4 years
This year consumers purchased 7,234,267,990 strawberries. Last year consumers purchased 2,000,900,999 strawberries. Which is the best estimate of how many more strawberries were sold this year than last year?
The estimated value was 9,000,000,000 strawberries sold this year than last year.
As per the given information, the required solution would be as:
We must calculate the most accurate estimate of the number of strawberries sold this year and the previous year.
Rounding up to the closest full number is the best approximation.
This year, 7,234,267,990 strawberries were purchased.
Last year, 2,000,900,999 strawberries were purchased.
Based on the above value, the estimated number of strawberries sold this year and the previous year is:
= 7,000,000,000 + 2,000,000,000
= 9,000,000,000
Thus, the estimated value was 9,000,000,000 strawberries sold this year than last year.
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Which expression is equivalent to the following complex fraction? 1 + startfraction 1 over y endfraction divided by 1 minus startfraction 1 over y endfraction.
On solving the provided question, we got that - question is based on the solving the fraction, so the correct option is [tex]\frac{y+1}{y-1} \\[/tex] that is is equivalent to the given complex fraction.
What is expression?Any mathematical statement made up of numbers, variables, and an operation between them is called an expression or an algebraic expression. As an illustration, the expression 4m + 5 consists of the terms 4m and 5, as well as the variable m, all of which are separated from one another by the arithmetic sign +.
Here the Expression, we have is -
[tex]\frac{ 1 + \frac{1}{y}}{1 - \frac{1}{y} }[/tex]
We must figure out the expression that equals the provided complex fraction.
The answer to the query is
Take the LCM of the numerator and denominator first.
We get,
[tex]\frac{ \frac{y+1}{y}}{\frac{y-1}{y} }[/tex]
[tex]\frac{y+1}{y} X \frac{y}{y-1}[/tex]
[tex]\frac{y+1}{y-1} \\[/tex]
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What is the slope of a line perpendicular to the line whose equation is 3x-6y=90. Fully simplify your answer.
Answer:
the slope is 0.5 or 1/2
Step-by-step explanation:
3x - 6y = 90
-6y = -3x + 90
y = 0.5x + 90
Answer:
slope= 1/2
Step-by-step explanation:
3x-6y=90
rewrite the equation into slope intercept form
y=1/2x-15
subtracting is the same as adding the opposites
y=1/2x+(-15)
since the equation is written in slope intercept form, y=mx+b, identify the slope of the line as the coefficient next to the variable x
y=1/2x+(-15), m=1/2
identify the y intercept of the lines as the constant term
y=1/2x+(-15),m(slope)=1/2,b=-15
Let g(x)=x²-5 and h(x) = 3x + 2. Find (hog)(x)
The value of the composite function is (hog)(x) = 3x²- 13.
What is a composition function?
Function composition is an operation used in mathematics that takes two functions, f, and g, and creates a function, h = gof, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.
The functions are g(x)=x²-5 and h(x) = 3x + 2
The composition function (hog)(x) can be written as (hog)(x) =h(g(x))
Putting g(x)=x²-5 in (hog)(x) =h(g(x)):
(hog)(x) =h(x²-5)
Now putting x= (x²-5) in h(x) = 3x + 2:
h(x²-5) = 3(x² - 5) + 2
h(x²-5) = 3x² - 15 + 2
h(x²-5) = 3x² - 13
Therefore (hog)(x) = 3x² - 13.
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How many square inches of gift wrap will be needed to cover a box that is 5in x 7in x 3in?
Answer:
65 sq.inches
Step-by-step explanation:
To find the total surface area of a box, you need to calculate the area of each of its faces and add them together. In this case, the box has three faces with dimensions 5 inches by 7 inches, and three faces with dimensions 5 inches by 3 inches.
The total surface area of the box is therefore:
(5 * 7) * 2 + (5 * 3) * 2 = 35 + 30 = 65 square inches
This means that you will need 65 square inches of gift wrap to cover the box.
Hope this helps you
Answer: 142 squared inches of gift wrap
Step-by-step explanation:
To find how many square inches of gift wrap you would need, you would use the formula for the surface area of the box (rectangle)
Formula: 2 ( length x width + width x height + height x length ) = Surface AreaNow plug the numbers in from the given dimensions
2 ( 7 x 5 + 5 x 3 + 3 x 7 ) = Surface AreaNow solve...
2 ( 7 x 5 + 5 x 3 + 3 x 7 ) = 142Giving you the answer of 142 squared inches of gift wrap
Hope this is correct and helpful! ^^
Alex went bowling. He managed to get 3 strikes after 15 attempts. If you were to suggest the probability that he gets a strike on his next attempt, what type of probability would you be using?.
Theoretical Probability because its what should happen but experimental is what happens
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
it is binomial probability p=3/15 = 1/5 = 0.2
or at the very least geometric
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the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection.
For each binomial experiment described, find
A. the mean
B. the variance
C. the standard deviation
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
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what are the expected value and standard erro for the sampling distribution of the sample proportion?
The anticipated value and standard error are 0.75 and 0.0306, respectively.
Explain the term standard error?The population mean's likelihood to differ from a sample mean is indicated by the standard error of a mean, and simply standard error. It reveals how much what the sample mean will change if a study were to be repeated with fresh samples drawn from a single population.If n is the sample size and p is the genuine population proportion, then the sampling distribution of a sample proportion is thought to adhere to the normal distribution.
np ≥ 10n(1 - p) ≥ 10As per the given question;
population proportion P = 0.75 size of the sample n = 200Let P' represents the sample proportion.
Regarding the sample proportion's sampling distribution:
The anticipated value is calculated using,
μp = P
μp = 0.75
As a result, 0.75 is the expected value.
Now, for the standard deviation-
σp = √P(1 -P)/n
σp = √0.75(1 - 0.75)/200
σp = 0.0306
Because the standard error is specified as; the value is 0.0306.
As a result, again for sampling distribution for sample proportion, the anticipated value and standard error are 0.75 and 0.0306, respectively.
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The complete question is-
A random sample of size n = 200 is taken from a population with population proportion P = 0.75. Calculate the expected value and the standard error for the sampling distribution of the sample proportion.
Consider the graph of equation y=mx+b
How does changing the value of m affect the graph of the equation?
What are the solutions of It - 2001 - 50 = 0?
O A. -250 and -150
OB. 40 and 50
O C. -150 and 250
OD. 150 and 250
Answer:
Step-by-step explanation:
d
Answer:
d
Step-by-stedp explanation:
Find zeros of quadratic polynomial
x²+x -20
Answer:m,m,
Step-by-step explanation:
Answer:
Zeros:
x = -5x = 4Step-by-step explanation:
Given quadratic polynomial:
[tex]x^2+x -20[/tex]
The zeros of a function f(x) are the x-values that satisfy the equation f(x)=0.
Therefore, to find the zeros of the given function, set it to zero and solve for x.
Factor the quadratic:
[tex]\implies x^2+x-20=0[/tex]
[tex]\implies x^2+5x-4x-20=0[/tex]
[tex]\implies x(x+5)-4(x+5)=0[/tex]
[tex]\implies (x-4)(x+5)=0[/tex]
[tex]\boxed{\begin{minipage}{8.4 cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}[/tex]
Apply the Zero Product Property:
[tex]\implies x-4=0 \implies x=4[/tex]
[tex]\implies x+5=0 \implies x=-5[/tex]
Therefore, the zeros of the given quadratic polynomial are:
x = -5x = 4I need help please i don’t understand
I need some step to solve this please
Answer:
MN = 50
Step-by-step explanation:
You want the length of the base segment MN in triangle MNO, where MN is marked 41+3x and parallel midsegment PQ is marked 49-8x.
MidsegmentThe midsegment is half the length of the parallel base segment. That means the base segment is double the length of the midsegment:
MN = 2·PQ
41 +3x = 2(49 -8x)
41 +3x = 98 -16x
19x = 57 . . . . . . . . add 16x-41
x = 3
MN = 41 +3x = 41 +3·3 = 50
The length of MN is 50 units.
how can confidence intervals help researchers attain their purpose of using a sample to understand a population?
The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .
In the question ,
we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,
we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .
the confidence interval are useful because ,
(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .
(ii) they make data analyses richer and help us to make more informed decisions about the research questions .
Therefore , the reason how confidence interval helps is mentioned above.
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To eliminate a variable in the system, should you add the equations or subtract the equations?
3x - 2y = 17
-3x - 4y = 7
Answer: You should add the equation
Step-by-step explanation: I see here that you already have perfect 3x and -3x, so the best way is to add them and eliminate the x to find the y first and then put the y back in the equation and solve for the x!
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a student was marked tardy five different time in a 40 day period. What percent of the times was the student tardy
Answer:
12.5%
Hope this helps!
Answer:
The percentage of times the students marked will be 12.5%.
Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
A student was marked tardy five different times in a 40-day period.
Percentage of 5 among 40 →
(5/40) x 100 = 12.5%