A power function is in the form of f(x) = kx^n, where k = all real numbers and n = all real numbers. You can change the way the graph of a power function looks by changing the values of k and n.
What is a power function?The power function is a function that links the true value of a parameter to the probability of rejecting a null hypothesis about the value of that parameter.
A power function is a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. (A number that multiplies a variable raised to an exponent is known as a coefficient.) As an example, consider functions for area or volume.
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A 16,000-gallon pool is being filled at a rate of 50 gallons per minute. At this rate, how many minutes will it take to fill this pool 3\4 full?
The amount of time it will take 16000 gallons to fill the pool 3/4 full is 320 minutes.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the amount of time it takes to fill 3/4 of the pool , we use the formula below.
Formula:
R = g/t............. Equation 1Where:
R = Rate at which the pool is being fiiledg = Gallons required to fill 3/4 of the poolt = TimeFrom the question,
Given:
g = (16000)×3/4 = 12000 gallonsR = 50 gallons per minuteSubstitute these values into equation 1 and solve for t
50 = 16000/tt = 16000/50t = 320 minutesHence, the time it will take is to fill the pool 3/4 full 320 minutes.
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Two quantities, x and y, are directly proportional. If x is doubled, what happens to y? clear check it is multiplied by 4. It is multiplied by 12. It depends on the starting value of x. It is doubled.
The two quantities x and y, are directly proportional. If x is doubled, then value of y will also be doubled.
Define the term directly proportional?If two quantities become directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.
The relationship between two values where their ratio equals a constant number is known as a direct proportion and direct variation. It is symbolized by the proportional sign (∝). Since the other variable is reversed in this case, the inversely proportional relationship is really represented by the same symbol.For the given situation;
x and y are in the direct proportional relation.
Thus,
x ∝ y
Thus,
x = k y
k = proportionality constant.
Thus,
multiplying both side by 2
2 x = 2 k y
Y also becomes twice .
If x is multiplied by 4 then,
4 x = 4 k y
y also get 4 times.
Thus, if x is doubled, then value of y will also be doubled and if x get 4 timed y also become 4 times.
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Find the number of elements inA_1 ∪ A_2 ∪ A_3if there are 100 elements in each set and if a) the sets are pairwise disjoint. b) there are 50 common elements in each pair of sets and no elements in all three sets. c) there are 50 common elements in each pair of sets and 25 elements in all three sets. d) the sets are equal.
a) Number of elements in the union of all three sets when the sets are pairwise disjoint is 300
b) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and no elements in all three sets is 150
c) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and 25 elements in all three sets is 175
d) Number of elements in the union of all three sets when the sets are equal is 100
What do you mean by relation and function?
(INPUT, OUTPUT) is a representation of an ordered pair.
The relationship between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT. Although all relations are functions, not all functions are relations. A function is a relationship that states that there should only be one output for each input, or we could refer to it as a particular category of relationship (a collection of ordered pairs) that adheres to a rule.
Given are three distinct sets, A1, A2, and A3, each with 100 members. The number of elements in the uninon set, A1 U A2 U A3, are as follows, according to the circumstances.
First off, if we remember the formula, it will be really simple to determine how many components make up the union set;
n(A1 U A2 U A3) = n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 ),
a) This states that we dont have any common elemets in any pair of these sets,
n( A1 ∩ A2 ) = 0, n( A2 ∩ A3 ) = 0 , n( A1 ∩ A3 ) = 0 and also n( A1 ∩ A2 ∩ A3 ) = 0 and as given n( A1 ) = n( A2 ) = n( A3 ) = 100 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 0 - 0 - 0 + 0
= 300
b) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and n( A1 ∩ A2 ∩ A3 ) = 0 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 0
= 150
c) We have
n( A1 ) = n( A2 ) = n( A3 ) = 100
n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and
n( A1 ∩ A2 ∩ A3 ) = 25 .
Hence the no of elements in the union set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 50 - 50 - 50 + 25
= 175
d) This states that all the common elemets are present in the three sets, so
n( A1 ) = n( A2 ) = n( A3 ) = 100 as well as n( A1∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = n( A1 ∩ A2 ∩ A3 ) = 100
Hence the no of elements in the unino set A1 U A2 U A3 will be
n(A1 U A2 U A3)
= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )
= 100 + 100 + 100 - 100 - 100 - 100 + 100
= 100
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Describe the error sadie made, and explain how to find the correct answer.
Sadie didn't simplify the expression properly and made mistakes during the simplification. The correct answer after simplification will be [tex]3a^{3} b\sqrt{6ab }[/tex]
Whenever we are about to simplify an expression, we should do it till the most simplified answer we got and follows the maths rules properly.
Sadie simplified the expression [tex]\sqrt{54a^{7}b^{3} }[/tex].
He first made an error during the simplification step at
[tex]\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex] where it should be [tex]3^{2}[/tex] not [tex]3^{3}[/tex].
Secondly, he came to the answer [tex]3a b \sqrt{6 a^5 b}[/tex] but we can simplify it more by simplifying [tex]a^{5}[/tex].
We can find the correct answer by simplifying the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] by the following:
[tex]\sqrt{54a^{7}b^{3} }[/tex] = [tex]\sqrt{3^2 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex]
= [tex]3 \cdot a \cdot|b| \sqrt{6 \cdot a^5 \cdot b}[/tex]
= [tex]3 a b \sqrt{6.a^4.a.b}$[/tex]
= [tex]3.a.b.a^{2} \sqrt{6ab}[/tex]
[tex]= 3a^{3}b\sqrt{6ab}[/tex]
So the most simplified answer to the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] is [tex]3a^{3}b\sqrt{6ab}[/tex].
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Your question is incomplete, but most probably your full question is:
Sadie simplified the expression [tex]\sqrt{54 a^7 b^3}[/tex], , where [tex]$a \geq 0$[/tex] as shown:
[tex]\sqrt{54 a^7 b^3}=\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}=3 a b \sqrt{6 a^5 b}[/tex]
Describe the error Sadie made, and explain how to find the correct answer.
What is the relationship between attending training and preferred source of ordering parts? which of these would be an appropriate Null Hypothesis?
1.
There is a relationship between attending training and the preferred source of auto parts.
2.
There should be a relationship between attending training and the preferred source of auto parts.
3.
There is no relationship between attending training and the preferred source of auto parts.
4.
There will be no difference in the number of auto parts ordered.
The correct option is,
There is no relationship between attending training and the preferred source of auto parts.
What is Null Hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.
Null hypothesis always states that there is no significant difference between given observations. This also means that there is no such relationship between the two sets. That is, there is no effect of value in one set increases on value of another set will increase or decrease.
Hence the Null Hypothesis for given statement , "the relationship between attending training and preferred source of ordering parts " is :
H0 : There is no relationship between attending training and the preferred source of auto parts.
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the least squares regression line is the line which minimizes the sum of the squared residuals for all the points in the scatterplot. the vertical distance between a point in the scatterplot and the predicted value on the regression line is the residual for the point. least square estimates from simple linear regression are the slope b1 estimates, on average, the change in the y variable associated with one unit increase in x variable.
The correct statements for least square estimates is the 3rd and 4th statements.
What is least square estimates?Least square estimates is method to predicted the observed Y value with minimized the sum of squared errors when using the fitted line.
The first and second statements is about simple linear regression. Simple linear regression is refers to linear line as parameter for fitting a model.
All statements are correct, but since the question asks for which statement is correct for least squares estimation, only the third and fourth statements are correct.
Thus, the 3rd and 4th statements is correct for least square estimates.
Your question is incomplete, but most probably your full question was (image attached)
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the michner corporation is trying to choose between the following two mutually exclusive design projects: table Picture
If the required return is 10 percent then the profitability index for project 1 is 1.140 and project 2 is 1.284. If the company applies the profitability index decision rule, then project 2 should the firm accept.
In the given question, the michner corporation is trying to choose between the following two mutually exclusive design projects.
A1. Profitability index
Profitability index = present value of cash flow/initial investment
Project 1
Present value of future cash flows = 37600/(1+0.1)³
Present value of future cash flows = 93,505.634
Initial investment = 82,000
Now substitute values in formula
Profitability index = 93,505.634/82,000
Profitability index = 1.140.
Project 2
Present value of future cash flows = 11,200/(1+0.1)³
Present value of future cash flows = 27,852.742
Initial investment = 21,700
Now substitute values in formula
Profitability index = 27,852.742/21,700
Profitability index = 1.284
A2. Multiple choice.
The project with higher probability index should be accepted, therefore Project 2 should be accepted.
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a courier company charges $15 plus $1.60 per pound to deliver packages. identify the independent and dependent variables, and write a rule in function notation for the given situation.
The rule in function notation for the courier company charge on delivery is
C = 15 + 1.6x
Independent variables are the ones that you include in the model to explain or predict changes in the dependent variable.
The dependent variable is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and left-hand variable.
Given in the question,
A courier company charges $15 plus $1.60 per pound to deliver packages
Here , the dependent variable is cost of delivery because it is depending on how much a packages is weighting
The independent variable here is the weight of package because it doesn't depend on anything.
Let the cost of delivery be C and weight of package be x
The function for the charge will be :
C = 15 + 1.6x
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the regression sum of squares (ssr) can be greater than the total sum of squares (sst). group of answer choices true false
The given statement is False . That is regression sum of squares (ssr) can be greater than the total sum of squares (sst).
Regression sum of squares (ssr)
The sum of squares regression is the sum of the differences between the predicted value and the mean of the dependent variable.
SSR = ∑( yᵢ-cap - y-bar)² and i = 1 to N
Total Sum of Squares (SST) :
Total Sum of Squares is the deviation of the value of the dependent variable from the sample mean of the dependent variable. Essentially, the total sum of squares quantifies the total sample variation. It can be found using the formula:
SST = ∑(yᵢ - y-bar )²
The first is that the regression sum of squares cannot be computed as a total sum of squares. Let's find an explanation for this. We know that the sum of squares can be divided. There's the dualism of squares, some of the squares and regressions, sums of squares, dead food. A regression sum of squares is not formed, it is a total sum of squares. This means the statement is false. The next processing is the value, which is always positive, but we know that the value the confession of the adjustment, in the range -1 to 1.
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A line passes through (0, 2) and has a slope of 13 . what is the equation of the line in slope-intercept form? responses y=13x 2 y equals 1 third x plus 2 y=13x−2 y equals 1 third x minus 2 y=−13x 2 y equals negative 1 third x plus 2 i don't know.
A line passes through (0, 2) and has a slope of 13. What is the equation of the line in slope-intercept form?
y = 1/3x + 2 (y equals 1 third x plus 2)
y = 1/3x − 2 (y equals 1 third x minus 2)
y = −1/3x + 2 (y equals negative 1 third x plus 2)
y-intercept is : (0 , 2)
slope = 13 or 13/1 (this is positive so slope will be positive)
slope = rise/run = y/x
what is the distance from amelia to the top of the tower? type your answer in the box. use numerals instead of words. the distance from amelia to the top of the tower is feet.
The distance from Amelia to the top of the tower is 100 feet.
Define trigonometric identities.Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle. Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
Given,
Considering the query;
The tower has a 50-foot height.
Amelia's position and the top of the tower form a 30° angle.
Trigonometric identities, therefore;
Thus,
x = 50/sin30°
sin 30° = 50/x.
x = 50/0.5
x = 100 ft.
The distance from Amelia to the top of the tower is 100 feet.
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in a baseball league of 9 teams, how many games are needed to complete the schedule if each team plays 12 games with each other?
Total number of games for 9 teams so that each team will play 12 games in the baseball league will be 432
Total number of teams in the baseball league is 9
Total number of games that each team will play is 12
Since, each team will have option of 8 teams to play with since no team can play with itself
Therefore, number of games that each team will play after playing 12 games will be 8 x 12 = 96
Since there are 9 teams, therefore total number of games that two teams will play = 96 x 9 = 864
Now, as it takes two teams to play a game therefore the required number of games for the 9 teams = 864/2 = 432
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Sam runs a large chain of car repair shops. He pays his employees for 8 hours of work each day. The employees
have to log the amount of time they spend working on each job, which results in a number of billable hours for
each employee each day. Sam would like to estimate the mean number of billable hours for the large number of
employees at the company. To do so, he selects a random sample of 10 employees and asks them how many
billable hours they tend to have each day. From their responses, he constructs a 95% confidence interval for the
true mean number of billable hours for all employees in the company. Which of the following may have an impact
on the confidence interval, but is not accounted for by the margin of error?
response bias
nonresponse bias
sampling variation
undercoverage bias
Sampling variation will have more impact on confidence interval, but is not accounted for by the margin of error.
What is Sampling variation?
Because each sample is unique, sampling variation describes how much a sample estimate (a statistic) is likely to change from sample to sample.What factors lead to sampling variation?
Sample Sizes and Variability
The variability of samples fluctuates as sample sizes are raised or lowered. For instance, if you select a sample size of 10 persons from a population of 1,000, you would almost certainly get a completely different conclusion than if you take a sample size of 100.What does the sample variation reveal?
To evaluate population group differences, statistical tests like variance tests and the analysis of variance (ANOVA) use sample variance. To determine whether the populations they represent significantly differ from one another, they use the variances of the samples.To know more about sample variation check the below link:
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g(x) = 3x^2+ 5
f(x) = x - 2
Find | g
The value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The first function is
g(x) = [tex]3x^2[/tex] + 5
The second function is
f(x) = x - 2
The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable and another variable is dependent variable. The function consist of the different variable, numbers and mathematical operators
Then the value of (gof)(x) is
g(f(x) = g(x-2)
Then,
g(x - 2) = 3 × [tex](x-2)^2[/tex] + 5
Expand the terms
g(x - 2) = 3 × ([tex]x^2[/tex] - 4x + 4) +5
g(x - 2) = [tex]3x^2[/tex] - 12x + 12 +5
Add the terms
g(x - 2) = [tex]3x^2[/tex] - 12x + 17
Hence, the value of (gof)(x) is [tex]3x^2[/tex] - 12x + 17
The complete question is
If g(x) = 3x^2+ 5
f(x) = x - 2
Find the value of (gof)(x)
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Is linear and quadratic function the same?.
No. Linear functions and quadratic functions are not the same.
Given,
Linear function;-A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).
Quadratic function;-A polynomial function of degree 2 known as a quadratic function is expressed in the generic form f(x)=ax2+bx+c. Where a0, real numbers a, b, and c are used. The graph of the quadratic function f(x)=x2 that squares an input value is shown below.
Difference between linear and quadratic function;When we graph a linear function, we get a straight line, however with a quadratic function, we get a parabola. In contrast to the slope of a linear polynomial, the slope of a quadratic polynomial is dynamic.
That is,
Linear functions and quadratic functions are not the same.
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The random variable X is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that X is between 72 and 84? (a) 0.683 (b) 0.954 (c) 0.271 (d) 0.340
The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
In the question ,
it is given that ,
The random variable X is said to be normally distributed ,
the mean is given as , μ = 70 , and
standard deviation of normal distribution is (σ) = 10
probability that X is between 72 and 84 is written as P(72 < X < 84)
= P((72 - 70)/10 [tex]<[/tex] Z [tex]<[/tex] (84 - 70)/10)
= P(0.2 < Z < 1.4)
= P(0 [tex]<[/tex] Z [tex]<[/tex] 1.4) – P(0 [tex]<[/tex] Z [tex]<[/tex] 0.2)
From the z table , we get the values as
= 0.4192 – 0.0793
= 0.3399
≈ 0.340
Therefore , The probability that the X is between 72 and 84 is 0.340 , the correct option is (d) .
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Fwam took a taxi from his house to the airport. The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. The total fare was $33. 05, not including the tip. Write and solve an equation which can be used to determine mm, the number of miles in the taxi ride.
The taxi company charged a pick-up fee of $3. 80 plus $2. 25 per mile. So, the number of miles in the taxi ride with the total fare $33. 05 is 13 miles.
How to determine the number of miles in the taxi ride?Write and solve an equation
Supppse, the number of miles = x
Total fare = a pick-up fee + fare per mile × the number of miles
Total fare = 3.80 + 2.25 x
Determine the number of miles
Total fare = 3.80 + 2.25 x
33.05 = 3.80 + 2.25 x
2.25 x = 33.05 - 3.80
2.25 x = 29.25
x = 29.25/2.25
x = 13
The number of miles in the taxi ride is 13 miles.
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What number is 80% of 25?.
1. Select all the correlation coefficients that indicate that an increase in one variable
results in a decrease in the other.
A. r=-0.9894
B. r=-0.5776
C.r=0.2361
D. T= 0.4429
E. r= 0.9919
The correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
What is correlation coefficient and how to interpret it?Correlation coefficient is a measure of how similar two datasets are acting.
When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.
When the correlation coefficient comes out below 0, then values are negatively correlated. SO,
All of the given option are negatively correlated.
If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated.
Therefore, the correlation coefficients that indicate that an increase in one variable results in a decrease in the other;
B. r=-0.5776
C.r=0.2361
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Line m is parallel to the y-axis, and its slope is _____. negative undefined positive 0
Answer:
undefined slope
Step-by-step explanation:
a vertical line parallel to the y- axis has an undefined slope
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $24.65 for 29 pounds of laundry and $36.55 for 43 pounds of laundry. In words, describe the graph of the proportional relationship. A line from (0, 0) going through (24.65, 29) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars) A line from (0, 0) going through (29, 24.65) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds) A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds) A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
The best description of the graph of the proportional relationship is: D. A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) while the y-axis is labeled Cost (in dollars).
What is the Graph of a Proportional Relationship?The graph that represents a proportional relationship is a straight line graph that passes through the origin (0, 0) and has a constant of proportionality, k, which is y/x.
Thus, given that the relationship between total cost for laundry service (y) is proportional to the weight of laundry (x), it means that the graph that will pass represent this would have the following features:
X-axis would be labelled weight (in pounds)Y-axis is labelled cost (in dollars)The line will pass through the following points, (0, 0), (29, 24.65), (43, 36.55)Therefore, the best description in words is: option D (last option).
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Answer:
Its A i did the practice exam test
Step-by-step explanation:
the guy above was wrong and didn't even make sense so here you go ;)
a single card is drawn from a standard deck of 52 cards. what are the odds against drawing an odd numbered card?
Answer:26%
Step-by-step explanation:
For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maximum absolute values of the shear and bending moment.
The maximum absolute values of the shear and bending moment is 2P and 3Pₐ respectively.
(a) Diagram is shown in image.
From A to B:
+∑Fy = 0: V = -P
+∑M₁ = 0: M = -P
From B to C:
+∑Fy = 0:
-P-P-V = 0
⇒ V = -2P
+∑M₂ = 0:
Pₓ+P(x - a)+M =0
⇒
M = -2Pₓ + Pₐ
(b) The maximum bending moment occurs in a beam, when the shear force at the section is zero or changes the sign because at point of contra fixture the bending moment is zero.
Therefore
|V|max = 2P
|M|max = 3Pₐ
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I will give brainlest to first person to answer correctly!
Answer:
R = 1
Step-by-step explanation:
R = y/x
Substitute the x and y values, for example, the first row
5.8/5.8 = 1
Therefore the answer is 1
What is the image point of (-9, -5) after the transformation T -5,0 of D2?
(-14, -5) is the image point of (-9, -5) after the transformation T(-5,0)
How to find the image of a point after transformation?Transformation is defined as the change in the position of a point, a line or a geometric figure
Given: point (-9, -5) with transformation T (-5,0)
This implies there is a change in the position of the original point by (-5, 0). Thus, the image point can be determined as follows:
image point = (-9, -5) + (-5,0)
= (-9+(-5), -5+0)
= (-14, -5)
Therefore, the image point is (-14, -5)
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the cost in dollars of a class party is 59 13n, where n is the number of people attending. what is the cost for 44 people?
The total cost of 44 people in the class party will be $631
The total cost in dollars of a class party is 59 + 13n
Where n = number of people attending in the class party
Let F(n) be the function representing the total cost in dollars of a class party
Such as, F(n) = 59 + 13n
As per the question, the total cost of attending the 44 people will be:
For 44 people we have n = 44
As we had, F(n) = 59 + 13n
Here, F(n) will be treated as a function in which n will be its domain while F(n) will give the output as a range.
F(44) = 59 + 13(44)
= 59 + 572
= 631
Total cost will be $631
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The y-intercept of f(x)=3(1/2)x is ____________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = 3(1/2)x is less than the y-intercept of the graphed function.
What is the Y-intercept of a Function?The y-intercept of function, y = mx + b, is the value of b, which is the point on the graph where the line intersects the y-axis.
Given the function, f(x) = 3(1/2)x, the y-intercept is 0 because if we examine the equation given in slope-intercept form as y = mx + b, there is no value of b, or rather, the value of b is equal to 0.
In the given graph above, the line of the function intercepts the y-axis at 4. This implies that the y-intercept of the function on the graph is 4.
Therefore, f(x) = 3(1/2)x has a y-intercept that is less than that of the function in the given graph.
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A box contain 576 marble of 6 different color. If there are 254 boxe how many marble are in all the boxe
Answer:
146304 marbles
Step-by-step explanation:
We do not need to worry about the color part, at least right now
One box contains 576 marbles
To find how many are in 2 boxes we would do 576 * 2
To find 254, we would do 576 * 254
Now, I would suggest using lattice multiplication here. If you do not know how to do that, long multiplication works fine.
I can't show that here, but I can show the answer:
576 * 254 = 146304
So, there are 146304 marbles is 254 boxes
find two positive numbers that satisfy that the product is 147 and the sum of the first number plus three times the second number is a minimum.
Two positive numbers that satisfy x=21 and y=7
XY = 147
x +3y = x + 3(147/x) = (x²+ 441)/x = f(x)
0= f'(x) = (x ( 2x) - x² - 441)/x²
= 2x² - x² -441)/x²
= (x² - 441)/x²
So then x² - 441 = 0
x = 21 , as x>0
x=21 and y=7,
the max sum is 21 +3(7) = 42
Related to best a regular and a primary-order (linear) time period, in which m is the slope and b is the y-intercept. every so often, the above is referred to as a "linear equation of variables," where y and x are the variables. a linear feature is defined as a feature that has both one or two variables without exponents. it is a function that graphs to the direct line.
A linear equation in two variables is of the shape Ax + by way of + C = zero, in which A and B are the coefficients, C is a consistent term, and x and y are the two variables. Linear functions are those whose graph is an instant line. A linear feature has the subsequent shape. y = f(x) = a + bx. A linear characteristic has one impartial variable and one based variable. The independent variable is x and the base variable is y.
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suppose and . what does the tangent line approximation give as an approximation for ? 29.2 what does the tangent line approximation give as an approximation for ? (4*.1)/.1
Using tangent line approximation formula,
the tangent line approximation at x= 29.2 is
L(x) = 2x - 1 or L(29.2) = 57.4
Given a function f differentiable at tangent
x=a, we can find that the slope of the tangent of y=f(x) at (a,f(a)) can be found by writing . ). The resulting tangent line through (a,f(a)) and the gradient m=f'(a) is the point-gradient given by
y−f(a)=f'(a)(x−a) has an equation of the form This can also be expressed as y=f'(a)(x−a)+f(a).
Replacing the variable y by the expression L(x) yields
points (a, f( a)) called L(x)=f′(a)(x−a)+f(a). , L(x) is just the new name for the tangent, and
f(x)≈L(x) for x near a.
For example, suppose the function y=f(x) is known to have a tangent approximation at the point (1, 3) given by L(x)=3−2(x−1), but the function Other things about f.
we have given that,
f(x) = 2x - 1
x= 29.0 near to 29.2
f(29.0) = 58 - 1 = 57
f'(x) = 2
so, the point is (29.0, 57) and slope of tangent is 2 .
tangent line , 57 = 2(29) + b
=> b = -1
then equation is 2x - 1 = y
we to calculate tangent line approximation give as an approximation for at x = 29.2
tangent line approximation,
y = 2 (29.2) - 1 = 57.4
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Complete question:
suppose and f (x) = 2x - 1 , what does the tangent line approximation give as an approximation for x= 29.2??
