The function that represents the number of people at the fair after x hours is f(x) = 68 + 1.5x
What is the function that represent the number of people at the fair?
The function that represents the number of people at the fair is known as a linear function. A linear function is any function that graphs to a straight line. The dependent variable in the linear function increases by a constant number.
Linear functions can be represented by : y = mx + c
Where:
y = dependent variable c = constantf(x) = 68 + (1.5x)
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A line that includes the points (j,
–
7) and (5,3) has a slope of
10
7
. What is the value of j?
Answer:
j = 7.8.
Step-by-step explanation:
The slope of the line = difference in y-values / corresponding difference in x-values.
Slope = (7-3) / (j-5) = 10/7
so 10(j - 5) = 7*4
10j - 50 = 28
10j = 78
j = 7.8.
30 points.
Please quick help
Using translation concepts, the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
For the translations, we have that:
It was shifted 4 units right, hence x -> x + 4.It was shifted 1 unit down, hence y -> y - 1.Then the expression for h(x) is given as follows:
[tex]h(x) = \sqrt{x + 4} - 1[/tex]
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PLS HELP PLS
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
The scale factor from Figure A to Figure B is 4
How to determine the scale factor from Figure A to Figure B?From the question, we have the following statement:
Figure B is a scaled copy of Figure A.
The corresponding side lengths of figure A and figure B are:
Figure A = 10
Figure B = 40
The scale factor from Figure A to Figure B is then calculated as:
Scale factor = Figure B/Figure A
Substitute the known values in the above equation
Scale factor = 40/10
Evaluate the quotient
Scale factor = 4
Hence, the scale factor from Figure A to Figure B is 4
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The surface area of a sphere is 320 square centimeters. what is the radius of the sphere? round your answer to 2 decimals places. the radius is centimeters.
Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.
What is the radius of the sphere?The surface area of a sphere is simply the total area that covers its outer surface.
The surface area of a sphere is expressed as;
A = 4πr²
Where r is radius and π is pi. ( π = 3.14 )
Given the data in the question;
Area A = 320cm²Radius r = ?We substitutes the given values into the equation above.
A = 4πr²
320cm² = 4 × 3.14 × r²
320cm² = 12.56 × r²
r² = 320cm² / 12.56
r² = 25.477707cm²
r = √25.477707cm²
r = 5.05cm
Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.
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Answer:
The radius is 5.05 centimeters.
Hope this helps!
Step-by-step explanation:
List all the possible outcomes for spinning the spinner and flipping a fair coin.
The list of the possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin goes as follows,
AH, BH, CH, DH, AT, BT, CT, DT
The possible outcomes for spinning a spinner (assuming that the spinner has four sectors, A, B, C, D) are: A, B, C, D (4 outcomes)
Now, the possible outcomes for flipping a fair coin are: Tales (T) and Heads (H) (2 outcomes)
For each possible outcome of the spinner, there can be two possible outcomes associated, because of the flipping of the fair coin. Hence, the total possible outcomes for spinning the spinner with four sectors A, B, C, D, and flipping a fair coin are 4 × 2, i.e. 8 outcomes.
These possible outcomes are AH, BH, CH, DH, AT, BT, CT, DT.
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A researcher reports that her obtained chi square of -17.56 is significant because it exceeds the critical chi square of -3.841 for an alpha of .05 with 2 degrees of freedom. What mistake has been made
The mistake that the researcher made is that; neither critical nor obtained Chi squares can have negative values
How to check the chi - square statistic?
A chi-square statistic is one way to show a relationship between two categorical variables. In statistics, there are two types of variables: numerical (countable) variables and non-numerical (categorical) variables.
The chi-squared statistic is a single number that tells you how much difference exists between your observed counts and the counts you would expect if there were no relationship at all in the population.
Now, Chi square (χ²) is the sum of a set of squared values, and as such it can never be negative. The minimum chi - squared value would be obtained if each Z = 0 so that χ² would also be 0. There is no upper limit to the χ² value. Similarly, the critical chi square cannot also be negative.
Thus, we can conclude that the mistake that the researcher made is that neither critical nor obtained Chi squares can have negative values
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If f(3x)=f(3) + f(x) then show that f(1)-f(3)-f(9) -f(27) = f (81).
The claim is wrong, or your question is incorrectly entered.
[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]
[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]
[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]
[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]
Then
[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]
at least if [tex]f(3)\neq0[/tex].
Find a power series representation for the function
Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].
[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]
By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have
[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
Then the series expansion of [tex]f(x)[/tex] is
[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.
Find the power series representation for the function:In the question the given function is,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
We know that series representation of sin x and eˣ are:
[tex]sin x = \sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1}[/tex][tex]e^{x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]
= [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Substituting the series representation in the function we get,
⇒ f(x) = x³sin(x) + e³ˣ⁺²
⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]
Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².
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Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?
Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
What is a credit card?A credit card is a payment card that is issued to users (cardholders) to allow them to pay merchants for products and services based on the cardholder's incurred debt (i.e., promise to the card issuer to pay them for the amounts plus the other agreed charges). The card issuer (typically a bank or credit union) opens a revolving account and offers the cardholder a line of credit, from which the cardholder can borrow money to pay a merchant or for a cash advance.
The answer to why Lynn wants to wait would be:
The answer will be (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card. A and B don't make sense, because who cares about what happens to the store's money, and C can't be true because we don't know what kind of a person Lynn is. Most people don't forget to pay their bills.Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
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The complete question is shown below:
Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?
a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.
b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.
c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.
d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
What is the greatest common factor of 30, 22, and 8?
Answer:
2
Step-by-step explanation:
just because all three numbers are even
Hope this helps
The greatest common factor of 30, 22, and 8 will be 2.
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
For example in 6 and 12 6 is the highest common factor.
The factor of 30 ⇒ 2,3,5
The factor of 22 ⇒ 2,11
The factor of 8 ⇒ 2,4
The only common factor among 30,22 and 8 is 2 so it will be the greatest common factor.
Hence "The greatest common factor of 30, 22, and 8 will be 2".
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Please solve the attachment which is given, and give me the answer. Thank you for your lovely time! <3
Answer:
1. 36 liters
2. 3 kg
Step-by-step explanation:
because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters
also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)
Answer:
1.) 36 litres
2.) 3 kg
Step-by-step explanation:
In this case there is a ratio of 1:3 of mass to volume. If we know the mass, the volume is 3 times that. If we know the volume, the mass is that divided by 3.
pls help with math rn neeedddd
Answer:
40° to the left and 3/2 units down
Step-by-step explanation:
See attached image.
5a<2a is a negative or positive
Answer:
Positive
Step-by-step explanation:
5a < 2a
Divide 2 on both sides
5/2a < a
Use a composite figure to estimate the area of the figure. The grid has squares with side lengths of 1.5 cm.
The area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex]
Given that the grid has squares with side lengths of 1.5 cm.
We are required to find the area of the composite figure.
The area of the composite figure is approximate to the area of the rectangle plus the are of the semicircle at the top of the rectngle plus the semicircle at the right side of the rectangle.
Finding the area of the rectangle.
A=(3*1.5)(4*1.5)=27 [tex]cm^{2}[/tex]
Finding the area of the semicircle at the top of the rectangle.
A=1/2 π[tex](2*1.5)^{2}[/tex]=4.5 π [tex]cm^{2}[/tex]
Finding the area of the semicircle at the right of the rectangle.
A=1/2 π[tex](1.5*1.5)^{2}[/tex]
=2.53π [tex]cm^{2}[/tex]
Total area =27+4.5π+2.53π
=27+7.03π
Use π=3.14
=27+7.03*3.14
=49.1 [tex]cm^{2}[/tex]
Hence the area of the composite figure in which the length of squares is 1.5 cm is 49.1 [tex]cm^{2}[/tex].
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Coach Salinas wants to compare the kicking statistics for kickers on their team. Which 2 ways could Coach Salinas find the kicker with the greatest goal success rate?
Th find the kicker with the greatest goal success rate, Coach Salinas should:
identify the kicker who has the best accuracyidentify the kicker has the highest number of field goals per game.What is statistics?
Statistics refers to the method of collecting data for the purpose of analysis, making of inferences and drawing of conclusions about the data collected.
Statistics usually involve numerical data in large quantities.
Statistical data can be used to make predictions about future events. They are also used to make decisions. For example, the statistical data of soccer players such as games/goal ratio, number of complete dribbles per match, number of successful take-ons, number of tackle or interceptions per game can be used in deciding which soccer player a football team should buy.
In the given scenario, Coach Salinas wants to compare the kicking statistics for kickers on their team in order to find the kicker with the greatest goal success rate.
To do this, Coach Salinas should:
determine the kicker who has the best accuracydetermine the kicker has the highest number of field goals per game.In conclusion, statistical data is important in making decisions.
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Answer:
A and D are the answers.
Step-by-step explanation:
Is the following number rational or irrational?
√64
√64 is rational.
Hope this helps :)
❄ Hi there,
let us consider this –
Is [tex]\sqrt{64}[/tex] a rational or irrational number?
Well, to answer that we need to work out [tex]\sqrt{64}[/tex].
And we know that
[tex]\sqrt{64} =8[/tex]
and 8 is a rational number.
That's it!
❄
Solve for x. You must show all of your work to receive credit.
Step-by-step explanation:
the inner WU arc angle is 23x - 5.
the outer WU arc angle is 37x + 5.
together they must be 360°, as this is the full circle.
so, we have
360 = 23x - 5 + 37x + 5 = 60x
x = 6
therefore, the angle at V is
V = 5x + 17 = 5×6 + 17 = 30 + 17 = 47°
inner WU arc angle = 23x - 5 = 133°
outer WU arc angle = 37x + 5 = 227°
this also fits with
V = (outer arc angle - inner arc angle)/2 =
= (227 - 133)/2 = 94/2 = 47°
if a car is moving at 52mph, how fast is the car moving in m/s?
**Disclaimer** Hi there! I assumed the unit [ mph ] represents miles per hour and [ m/s ] represents meters per second. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.
Answer: [tex]\Large\boxed{23~m/s}[/tex]
Step-by-step explanation:
Given information
Speed = 52 mph
Given conversion factors
1 mile ≈ 1609 meters
1 hour = 3600 seconds
Convert the unit from mph to m/s using conversion factors
The basic idea is that you utilize the factors and cancel out unnecessary units
[tex]\dfrac{52~miles}{1~hour} \times\dfrac{1~hour}{3600~seconds} \times\dfrac{1609~meters}{1~miles}[/tex]
Simplify by multiplication
[tex]=\dfrac{52~miles}{3600~Seconds} \times\dfrac{1609~meters}{1~miles}[/tex]
[tex]=\dfrac{52\times 1609~meters}{3600~Seconds}[/tex]
Simplify the fraction
[tex]=\dfrac{83668~meters}{3600~Seconds}[/tex]
[tex]\Large\boxed{\approx23~m/s}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Adam says that the number 4 has for factors. explain why this statement is incorrect
Adam says that the number 4 has four factors. The above statement is incorrect as 4 only three factors 1,2, and 4.
What are the factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.Factors can be found using either division or multiplication. Rules of divisibility can also be applied. There are a finite number of factors for all integers.The factor of a number is never more than the number; it is always less than or equal to the number.Every integer, excluding 0 and 1, has a minimum of two factors: 1 and the actual number.Multiplication and division are used to find factors.To learn more about Factors with the given link
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Solve the given differential equation by using an appropriate substitution. the de is homogeneous. (y2 yx) dx − x2 dy = 0
The solution for the given differential equation is lnlxl = [tex]\frac{-x}{y} +C[/tex]
Given,
[tex](y^{2} +y^{x} )dx - x^{2} dy =0[/tex]
Here,
x = vy, dx = vdy + ydv
y = ux, dy = udx + xdu
Then,
[tex]((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du[/tex]
Now,
[tex]\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du[/tex]
l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{u^{-1} }{(-1)} +C[/tex]
l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{-1}{u} +C[/tex]
y = ux
u = [tex]\frac{y}{x}[/tex]
That is l[tex]n[/tex]l[tex]x[/tex]l [tex]=\frac{-x}{y} +C[/tex]
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Please help with this question!
Answer:
NONE of these statements are true
[tex] \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)[/tex]
b) False[tex] \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} [/tex]
Im assuming this is an absolute valuec) True[tex] \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } [/tex]
Option C7/3=7:
what will seven over three equals seven divide be
Answer:
3(7/3=7:3)Step-by-step explanation:
7/3=7:
what will seven over three equals seven divide be
7/3 is a division (7:3)
so
your answer is :
3
(7/3=7:3)
A=5
b=12
c=10
d=2
2a to the power of 2-c
2a is 2 x a
Substitute a =5
2 x 5 =10
Now we have:
10^2-c
Substitute c = 10
(2 - 10 = - 8)
So,it's now 10^ - 8 (10 to the power of - 8)
Ans: 10^ - 8 (or 1 x 10^ -8)
Hope this helps!
the slope of the line p is__and the slop of the line q is__
Answer:
The slope of line p is 3 and the slope of line q is -3.
Express your answer in scientific notation. 0.00045-2.5x10^-5
Answer:
4.25 × 10^-4
Step-by-step explanation:
0.00045-2.5x10^-5
= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)
= (4.5 × 10^-4) - (0.25 × 10^{1-5} )
= (4.5 × 10^-4) - (0.25 × 10^-4)
= (4.5 - 0.25) × 10^-4
= 4.25 × 10^-4
What is the independent variable in the following function?
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
The independent variable in the function f(c) = 2c + 9 is c whereas the dependent variable is f.
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A sample of disinfecting bleach shows a density of 9.4 lb/gal. If 100 pounds of bleach is required for disinfection, how many gallons must be applied
the number of gallons that must be applied is 94 gallons.
What is density?Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.
It is denoted with rho, 'ρ'
The formula for density is given as;
Density = mass/ volume
From the information given, we have that
density = 9.4 lb/galmass = 100 pounds volume is unknownTo determine the volume, we need to make it the subject from the formula
Volume = density × mass
Volume = [tex]\frac{9. 4}{100}[/tex]
Volume = 0. 094
The number of gallons is given as;
= Volume × 1000
= 0. 094 × 1000
= 94 gallons
Thus, the number of gallons that must be applied is 94 gallons.
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An ellipse has a vertex at (4, 0), a co-vertex at (0, 2), and a center at the origin. Which is the equation of the ellipse in standard form?
Answer:
x^2/ 16 + y^2/4 = 1
Step-by-step explanation:
The major axis is 4 and that goes with the x variable. It is the major axis because 4 is a larger value than 2.
4 x 4 = 16
2 x 2 = 4
The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.
How to derive the standard form of the equation of the ellipse
In this problem we know the coordinates of a vertex, a co-vertex and the center of an ellipse. Based on this information, we find an ellipse whose major axis is parallel to the x-axis. whose formula in standard form is:
(x - h)² / a² + (y - k)² / b² = 1 (1)
Where:
(h, k) - Center of the ellipsea - Major semiaxis lengthb - Minor semiaxis lengthThe major semiaxis has a length of 4 units and the minor semiaxis has a length of 2 units. If we know that (h, k) = (0, 0), a = 4 and b = 2, then the equation of the ellipse is:
x² / 16 + y² / 4 = 1
The equation of the ellipse in standard form is x² / 16 + y² / 4 = 1.
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Consider the line 4x + 2y = 8.
What is the slope of a line perpendicular to this line?
Answer:
supposed to make the subject y then slope is -2
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Using a calculator, the line of best fit for the function is given by:
y = 51.7x - 5.7.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator. For this problem, a linear regression is used because the data only increases.
From the given table, the points are:
(1, 68), (2,97), (3, 134), (4, 176), (5, 241), (6,335).
Inserting these points on the calculator, the line of best fit for the function is given by:
y = 51.7x - 5.7.
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