Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷) that represents a value or a quantity. It can be a single number or variable, or a combination of them, and can also include functions, parentheses, and other mathematical symbols. For example, 3x + 7 is an expression, where 3 and 7 are constants, x is a variable, and + is an operator. Expressions can be simplified, evaluated, or used as part of a larger mathematical statement or equation.
We can use the formula for Pearson correlation coefficient r to calculate it for the given data:
r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)]
where n is the number of observations, Σ represents the sum of the indicated values, and X and Y represent the two variables being correlated. Using the data from the table, we can calculate the following:
n = 5
ΣX = 25, ΣY = 25.8
ΣX² = 275, ΣY² = 288.68
ΣXY = 139.2
Substituting these values into the formula, we get:
[tex]$r = (5 * 139.2 - 25 * 25.8) \sqrt{[(5 * 275 - 25^2)(5 * 288.68 - 25.8^2)]} $[/tex]
r ≈ 0.915
Therefore, the Pearson correlation coefficient r for the data is approximately 0.915. Since the value is positive and close to 1, we can say that there is a strong positive correlation between the number of times the commercial is run on TV and the number of car sales.
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Marley's car gets 25 miles per gallon, and they expect to drive 1350 miles for their next vacation. If the average price of gasoline is $2.549, how much should they budget for gas for the trip?
A. $63.73
B. $54
C. $137.65
D. $337.50
After grading the take-home assignments, Mr. Montes randomly selects 5 take-home
assignments to analyze. He considers the student's responses to the three multiple choice
questions, which are as shown.
Student 1:
(C, A, C)
a. Set 1n Set 2
Student 2:
{C, B, B}
b. Set 2 U Set 3
Student 3:
{C, B, C)
7. The correct responses for the multiple choice questions are, in order, C, B, and A. If Set 1
represents the subset of these students who answered C for number 1, Set 2 represents the subset
of these students who answered B for number 2, and Set 3 represents the subset of students who
answered A for number 3, find each of the following. Explain what each notation means in
context of this scenario.
c. The complement of Set 1
Student 4:
{C, B, A}
Student 5:
{C, A, A}
8. Amisha was too tired to work on the take home assignment Mr. Montes gave her, so she
randomly selected answers without reading any of the questions. Suppose that you wanted to
find the odds that Amisha answered at least 3 of the 5 questions correctly. Do you think you
would use a permutation or a combination? Why?
Answer:
b
Step-by-step explanation:
my brain
try to answer all the questions below!
Part 1
a. In function notation, we have that R(3) > D(3)
b. In function notation, we have that R(0) - D(0) = 25
Part 2
The drone is 20 feet above the ground when the rocket hit the ground.
Part 3
a. R(t) = D(t) when the graphs intercept at t = 4.75 s
b. It tell us that the drone and rocket are at the same height at that time.
What is a function notation?A function notation is the representation of a statement as a mathematical equation using symbols.
Part 1
a. To write the statement at 3 seconds the toy rocket is higher than the drone in function notation.
Since
R(t) represents height of toy rocket and D(t) represents height of drone.At t = 3, the toy rocket is higher than the drone.
So, in function notation, we have that R(3) > D(3)
b. To write the statement at the start the toy rocket is 25 feet above the drone.
Since R(t) represents height of toy rocket and D(t) represents height of drone.At the start t = 0, and the toy rocket is 25 feet above the drone.
So, in function notation, we have that R(0) - D(0) = 25
Part 2.
To find the height of the drone when the rocket hit the ground,
Since
R(t) represents height of toy rocket and D(t) represents height of drone.We find R(t) = 0 and find the time t, where it intercepts the height of the drone.
So, from the graph R(t) = 0 at t = 5. And at t = 5, D(t) = 20
So, the drone is 20 feet above the ground when the rocket hit the ground.
Part 3.
a. The value of t at which R(t) = D(t) is where the graphs intercept.
The graphs intercept at t = 4.75 s
b. Since R(t) = D(t) at t = 4.75 s, it tell us that the drone and rocket are at the same height at that time.
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-4x = 64
How should you show your work to isolate the variable and solve the equation?
Answer:
-16
Step-by-step explanation:
1. multiply the minus sign on both sides now we have 4x=-64
2. divide 4 on both sides
You're done! x=-16
The ratio of the number of male and female children in the colony is 6:4:3 respectively and the minimum number of members in the colony is 200, then what will be the minimum number of children in the colony?
The minimum number of children in the colony is 47 given the ratio 6 : 4 : 3
Calculating the minimum number of children in the colony?Given that
Ratio = 6 : 4 : 3
We are given the ratio of male to female to children as 6:4:3.
Let the common ratio be x, so the actual number of males, females, and children respectively will be 6x, 4x, and 3x.
Total number of members in the colony = 6x + 4x + 3x = 13x.
We are given that the minimum number of members in the colony is 200.
So,
13x = 200
x = 200/13
The actual number of children in the colony 3x is
Children = 3 * (200/13) = 46.15
Children = 46.15
However, since we cannot have a fraction of a child, we round to the nearest whole number.
Therefore, the minimum number of children in the colony is 47.
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Find the Area.
12 ft
12 ft
Answer:
144ft^2
Step-by-step explanation:
Answer:
144^2 feet
Step-by-step explanation:
To find the area you would multiply length x width for your answer. I hope this helps!
a section of an exam contains four true false questions. A completed exam paper is selected at random, and four answers are recorded.
the probability that all answers are False?
the probability that exactly three or four answers is false?
the probability that at lastt answer is true is ?
We can use the binοmial distributiοn tο mοdel this situatiοn, where each questiοn is a Bernοulli trial with a prοbability οf success (getting the cοrrect answer) οf 0.5.
A prοbability simple definitiοn is what?A prοbability is a numerical representatiοn οf the likelihοοd οr chance that a specific event will take place. Bοth prοpοrtiοns ranging frοm 0 tο 1 and percentages ranging frοm 0% tο 100% can be used tο describe prοbabilities.
Let X be the number οf False answers in the cοmpleted exam paper.
Prοbability that all answers are False:
[tex]P(X = 4) = (0.5)^4 = 0.0625[/tex]
Prοbability that exactly three οr fοur answers are False:
P(X = 3 οr X = 4) = P(X = 3) + P(X = 4)
[tex]= 4C3(0.5)^3(0.5)^1 + (0.5)^4[/tex]
= 0.25 + 0.0625
= 0.3125
Prοbability that at least οne answer is True (which is the cοmplement οf the event that all answers are False):
P(at least οne True) = 1 - P(all False) = 1 - 0.0625 = 0.9375
Prοbability that the last answer is True:
This prοbability can be calculated using cοnditiοnal prοbability, where we find the prοbability that the last answer is True given that we knοw that at least οne answer is True:
P(last answer is True | at least οne True) = P(last answer is True and at least οne True) / P(at least οne True)
P(last answer is True and at least οne True) = P(last answer is True) = 0.5
P(at least οne True) = 0.9375 (calculated in part 3)
Sο, P(last answer is True | at least οne True) = 0.5 / 0.9375 = 0.5333 (rοunded tο fοur decimal places).
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Graciela needs to design a can with radius 2
inches and surface area as close to 100
square inches as possible. What is the height of the can? (Use π=3.14
, and round your answer to the nearest inch.)
The height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.
What is cylinder?
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.
The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrhwhere r is the radius of the base, h is the height, and π is approximately 3.14.
In this case, the radius is given as 2 inches, and we want to find the height that will give us a surface area as close to 100 square inches as possible. So we need to solve for h in the equation:
100 = 2π(2)² + 2π(2)h
Simplifying this equation:
100 = 8π + 4πh
92 = 4πh
h = 23/π
h ≈ 7.32
Rounding this answer to the nearest inch, we get:
h ≈ 7 inches
Therefore, the height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.
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Can I please get some help???
Answer: B) 2
Step-by-step explanation:
In the image, we see a box and whisker plot. The middle line represents the median. Looking at the numbers on the side, and the placement of the middle line, we can see that the median in this situation is 2.
Julia made a die for a game. It had 5 faces, labeled 1-5. Because of the shape of the die, it was biased in favor of rolling a 3. We do not know the amount of bias. She experimented to estimate how likely it was for a 3 to be rolled and her results are in the above table. Using her experimental results, find the best estimate of the probability of rolling a 3.
From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.
The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:
P(rolling a 3) = Number of times 3 was rolled / Total number of rolls
P(rolling a 3) = 45 / 100
P(rolling a 3) = 0.45 or 45%
Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.
x.cot a. tan (90°+a) = tan (90°+a). cot (180°-a) + x.sec (90°+a).
If the angle -270° rotates 180° counter-clockwise, what is the new measurement of the co-terminal angle?
___°
Starting with the angle of -270°, adding 360° gives us 90° (which is a coterminal angle with -270°).
If we rotate 180° counter-clockwise from 90°, we end up at the angle of 270°. Therefore, the new measurement of the coterminal angle is 270°.
I hope this helps :)
3^-2 find the equivalent expression from these choices
The fourth expression 3⁻⁷/3⁻⁵ is equivalent to 3⁻².
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, operators, and functions that are combined in a particular way to represent a mathematical value or relationship. Expressions can be simple or complex, and they can involve any number of mathematical operations.
Expressions can be used to represent many mathematical concepts:
Arithmetic operations: addition, subtraction, multiplication, and divisionExponents and logarithmsTrigonometric functions: sine, cosine, and tangentAlgebraic equations: variables and constantsCalculus: derivatives, integrals, and limitsNow,
To find the equivalent expression of 3⁻², we can simplify each of the given choices using the rules of exponents:
1. 3⁻²/3³ = 1/3²⁺³ = 1/3⁵
2. 3⁻⁷/3⁵ = 3⁻⁷⁻⁵ = 3⁻¹²
3. 3³/3⁻¹² = 3³⁺¹² = 3¹⁵
4. 3⁻⁷/3⁻⁵ = 3⁻⁷⁺⁵ = 3⁻²
Out of the given choices, the fourth choice 3⁻⁷/3⁻⁵ is equivalent to 3⁻².
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What are algebraic expressions that are equivalent to 7x-2?
The algebraic expressions that are equivalent to 7x-2 are -2 + 7x, 14x/2 - 4/2 and 5x + 2x - 2
How to determine the equivalent expressionsThe expression in the question is given as
7x - 2
The above expression is linear
Here are some algebraic expressions that are equivalent to 7x-2:
14x/2 - 4/2
When evaluated, we have
14x/2 - 4/2 = 7x - 2
5x + 2x - 2:
We can break up 7x into 5x and 2x, then combine 5x and 2x to get 7x.
So, we have
5x + 2x - 2 = 7x - 2
Hence, the expressions are 14x/2 - 4/2 and 5x + 2x - 2
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Part II: According to the tax tables below, how much would Melvin pay in federal
income taxes if filing separately? How much would Sylvia pay if filing separately?
How much would Melvin and Sylvia pay combined if filing separately?
According to the tax tables below, Melvin would have to pay in federal income taxes if filing separately $5,131 and Sylvia $6,750. The total would be $11,881
How to identify how much tax Melvin and Sylvia have to pay?To identify how much Melvin and Sylvia have to pay in taxes, we must look carefully at the table. In this, the different incomes are classified and on the right side are shown how much the tax is depending on the condition of the citizen. These options are: single, married filling jointly, married filling separately and head of a household.
In accordance with the above, we must look at which number coincides in the row of married filling separately with the value of the income of each one of them. According to the above, Melvin has to pay 5,131 in taxes while Sylvia has to pay 6,750.
Note: This question is incomplete. Here is the complete information:
Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $35,750 last year, while Sylvia had a gross income of $41,700.
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PLEASE HELP SUPER CONFUSED
Answer:
4.5
Step-by-step explanation:
6+2=8
8/2=4
1.5x4=6
6-1.5=4.5
prove that every bounded sequence contain a convergent subsequence
Answer:
To prove that every bounded sequence contains a convergent subsequence, we will use the Bolzano-Weierstrass theorem.
Bolzano-Weierstrass theorem: Every bounded sequence in Euclidean space has a convergent subsequence.
Proof: Let (a_n) be a bounded sequence in Euclidean space, which means that there exists some M > 0 such that |a_n| <= M for all n. We will use the bisection method to construct a subsequence that converges to some limit L.
Step 1: Divide the interval [-M, M] into two subintervals, [-M, 0] and [0, M]. Since (a_n) is bounded, at least one of these intervals contains infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_1.
Step 2: Divide I_1 into two subintervals of equal length, and again, at least one of these subintervals must contain infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_2.
Step 3: Repeat this process for each subinterval, dividing it into two subintervals of equal length and choosing the one that contains infinitely many terms of the sequence. We obtain a sequence of nested intervals I_1 ⊃ I_2 ⊃ I_3 ⊃ ... that contain infinitely many terms of the sequence.
Step 4: Since the length of each interval is decreasing and they are nested, the intersection of all the intervals is a single point L. By construction, every term of the sequence (a_n) belongs to one of the intervals I_k, which means that there exists a subsequence (a_nk) that converges to L.
Therefore, every bounded sequence in Euclidean space has a convergent subsequence, as required.
Step-by-step explanation:
Find the value of the unknown.
162000=750×6^y
Answer:
[tex]\boxed{\textsf{y = 3}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for y.}[/tex]
[tex]\textsf{We should begin by \underline{simplifying} the equation.}[/tex]
[tex]\textsf{First, begin by dividing 750 from \underline{both sides} of the equation.}\\[/tex]
[tex]\Large\underline{\textsf{Divide:}}[/tex]
[tex]\mathtt{\frac{162000}{750} = \frac{750 \times 6^y}{750} .}[/tex]
[tex]\mathtt{216=6^y}[/tex]
[tex]\Large\underline{\textsf{Continue Dividing By 6:}}[/tex]
[tex]\mathtt{\frac{216}{6} = 36 (^{y-1})}[/tex]
[tex]\mathtt{\frac{36}{6} = 6 (^{y-2} )}[/tex]
[tex]\Large\underline{\textsf{Identify y:}}[/tex]
[tex]\mathtt{6^1 = 6. \ 6^{1+2} = 216. \ (6^3)}[/tex]
[tex]\boxed{\textsf{y = 3}}[/tex]
PLEASE ANSWER ASAP PLEASE
value from least to greatest is
A<B<C<D
Define fractionA fraction is a numerical quantity that represents a part of a whole or a ratio of two quantities. It is expressed in the form of one number, called the numerator, divided by another number, called the denominator, and is typically written as a/b, where "a" is the numerator and "b" is the denominator.
Part a)
Let 5.7 (bar on 7) be x
x=5.777777... .....(1)
Multiply the equation by 10,
10x=57.77777... ....(2)
(2)-(1),
9x=52
x=52/9=5.777777778
Partb)
Let 5.75 (bar on 75) be x
x=5.75757575... .....(1)
Multiply the equation by 100,
100x=575.75757575.. ....(2)
(2)-(1),
99x=569.99
x=190/33=5.757575758
Part c)
Let 5.75 (bar on 5) be x
x=5.7555555... .....(1)
Multiply the equation by 10,
10x=57.55555555... ....(2)
Multiply the equation by 10,
100x=575.5555.. ....(3)
(3)-(2),
90x=52
x=259/45=5.755555556
Hence, value from least to greatest is
A<B<C<D
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The answer of the given question based on the ordering from the least to greatest the answer is the correct answer is (A) DBCA.
What is Decimal system?The decimal system is a number system that uses the base 10, meaning that there are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used to represent any quantity. This system is also called the base-10 numeral system, denary system, or Hindu-Arabic numeral system.
In the decimal system, each digit represents a different power of 10. For example, in the number 357, the 7 represents the units, 5 represents the tens, and 3 represents the hundreds.
This system is widely used in everyday life, in which numbers are expressed in decimal form, such as money, time, and measurements. It is also used in mathematics, science, and engineering as the standard way of expressing numbers.
The correct order from least to greatest will be :
A. 5.7
D. 5.75
B. 5.75
C. 5.75
Therefore, the correct answer is (A) DBCA.
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The area of a circle increases at a rate of 5 cm²/s. a. How fast is the radius changing when the radius is 3 cm? b. How fast is the radius changing when the circumference is 1 cm?
Answer:
1. the radius is increasing at a rate of approximately 0.265 cm/s when the radius is 3 cm
2. the radius is increasing at a rate of approximately 0.159 cm/s when the circumference is 1 cm
Step-by-step explanation:
We can use the formulas for the area and circumference of a circle to solve these problems:
a. To find how fast the radius is changing when the radius is 3 cm, we can use the formula for the area of a circle:
A = πr^2
Taking the derivative of both sides with respect to time, t, we get:
dA/dt = 2πr dr/dt
where dr/dt is the rate of change of the radius.
We know that dA/dt = 5 cm²/s, and when the radius is 3 cm, we can plug in these values to solve for dr/dt:
5 = 2π(3) dr/dt
dr/dt = 5/(6π) cm/s ≈ 0.265 cm/s
Therefore, the radius is increasing at a rate of approximately 0.265 cm/s when the radius is 3 cm.
b. To find how fast the radius is changing when the circumference is 1 cm, we can use the formula for the circumference of a circle:
C = 2πr
Taking the derivative of both sides with respect to time, t, we get:
dC/dt = 2π dr/dt
where dr/dt is the rate of change of the radius.
We know that when the circumference is 1 cm, C = 1 cm, so we can plug in these values to solve for dr/dt:
1 = 2π dr/dt
dr/dt = 1/(2π) cm/s ≈ 0.159 cm/s
Therefore, the radius is increasing at a rate of approximately 0.159 cm/s when the circumference is 1 cm.
please help me.............
The Tοtal number οf tickets tο play will be 15.
What is inequality?Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.
At a schοοl fair, there are different games tο play that each require 5 tickets tο play.
Jοrdan wants a bag οf pοpcοrn that requires 26 tickets and tο use the rest οf the tickets tο play games.
Jοrdan has 101 tickets.
Fοr tickets tο play will be 101-26 = 75
Sο the Tοtal number οf tickets tο play will be 75/5 = 15.
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PLS HELP , in need to solve by using substitution and with checks
Answer:
(x, y) = (-1/2, 5/2)
Step-by-step explanation:
To solve this system of equations using substitution, we can use the first equation to express y in terms of x, and then substitute that expression into the second equation to get an equation in terms of x alone.
Starting with the first equation, we have:
y = x + 3
We can now substitute this expression for y into the second equation:
3x + 3y = 6
3x + 3(x + 3) = 6
Simplifying the right-hand side:
3x + 3x + 9 = 6
6x = -3
x = -1/2
Now that we have solved for x, we can substitute this value back into the first equation to find y:
y = x + 3
y = -1/2 + 3
y = 5/2
Therefore, the solution to the system of equations is (x, y) = (-1/2, 5/2).
To check our solution, we can substitute these values back into both equations and verify that they hold true:
y = x + 3
5/2 = -1/2 + 3
5/2 = 5/2
This equation holds true, so the first equation is satisfied by our solution.
3x + 3y = 6
3(-1/2) + 3(5/2) = 6
-3/2 + 15/2 = 6
6 = 6
This equation also holds true, so the second equation is satisfied by our solution as well.
Therefore, we can conclude that our solution is correct.
The equations have two variables, x and y, and we can use substitution to solve for one variable in terms of the other. By substituting the expression for y into the second equation and solving for x, we get the value of x as -1/2. We can then substitute this value back into the first equation to get the value of y, which is 5/2. This means that the solution to the system of equations is (x, y) = (-1/2, 5/2) and we can check that this solution satisfies both equations.
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]
A game Is played using one die. If the die is rolled and shows 3, the player wins $15. M the die shows any number other than 3, the player wins nothing. Complete parts (a) through (0)
a. If there is a charge of $3 to play the game, what is the game's expected value?
Answer:
0
Step-by-step explanation:
Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)
In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).
The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.
Therefore, the expected value is:
Expected Value = (1/6) x $15 + (5/6) x (-$3)
Expected Value = $2.50 - $2.50
Expected Value = $0
3. Karem drives his car 96 miles in 1 ½ hours. If Karem continues to drive at this rate, how many miles will he travel in 2 ½ hours?
Answer:
160 miles
Step-by-step explanation:
To find the unit rate, we want to know how many miles can we go in i hour.
96 ÷ 1 [tex]\frac{1}{2}[/tex]
1 [tex]\frac{1}{2}[/tex] can be written
[tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{2}[/tex] 1 is the same as [tex]\frac{2}{2}[/tex]
Now we have
96 ÷ [tex]\frac{3}{2}[/tex] if we get a common denominator, in this case 2, we can just divide a cross.
96 is equal to [tex]\frac{192}{2}[/tex] ([tex]\frac{96}{1}[/tex] x [tex]\frac{2}{2}[/tex])
Now we have
[tex]\frac{192}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{64}{1}[/tex] = 64
We now know the unit rate is 64 miles in one hour.
The distance in 2 [tex]\frac{1}{2}[/tex] hours would be
64 + 64 + [tex]\frac{1}{2}[/tex](64)
64 + 64 + 32
160
Helping in the name of Jesus.
what is the value of X when 7=3x_2
Answer:
7+2=3x-2+2
9/3=3x/3
3=x
A bag contains several marbles 7 of which are blue 18 are yellow and 12 are green
If 3 marbles are chosen without replacement what is the probability that they are all yellow
Answer:
The answer would be 8.1% (8.108% if you need the exact percentage.)
Step-by-step explanation:
All you would need to do is add 7 + 18 + 12 which = 37, and divide 3/37, which in percentage that gives you 8.1%. (8.108% if you need exact percentage.)
PLEASEEEE HELP!!!!
Enter your answer and show all the steps that’s you used to solve this problem in the space provided.
How do the graphs of y = 1/x and y = 5/x+6 compare?
The transformations that compares the functions y = 1/x and y = 5/(x + 6) are
The second function is shifted 6 units to the left and Dilated by 5 unitsWhat are transformations?
Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.
Since we have the functions
y = 1/x and y = 5/(x + 6),We want to see how the graphs of
y = 1/x and y = 5/x+6 compare?We proceed as folows.
Looking at the functions
y = 1/x and y = 5/(x + 6),We compare the transformations and see that
The second graph is shifted 6 units to the left since it has x + 6 units denominatorAlso, since we have 5 in the numerator, it is dilated by 5 units.So, the functions compare by
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Equation of the hyperbola?
The equation of the hyperbola x²/36 = 1. The equation of a horizontal line passing through (±6,0).
Describe Hyperbola?The resulting curve of a hyperbola consists of two separate branches that are mirror images of each other, and they are characterized by their asymptotes, which are straight lines that the curve approaches but never touches. The asymptotes intersect at the center of the hyperbola, which is also the point where the two branches are closest together.
Since the foci of the hyperbola are at (0,-6) and (0,6), and the transverse axis is vertical, the center of the hyperbola is at the midpoint of the foci, which is the point (0,0).
Also, since the asymptote of the hyperbola is the line y = -x, we know that the slopes of the asymptotes are ±1, and since the transverse axis is vertical, the slope of the transverse axis is 0. Therefore, we have a hyperbola with center (0,0), vertical transverse axis, and asymptotes y = x and y = -x.
The standard form of the equation for a hyperbola with center (0,0), transverse axis of length 2a, and asymptotes y = ±(a/x) is:
x²/a² - y²/b² = 1
where b² = a² - c², where c is the distance from the center to each focus.
In this case, since the distance between the foci is 12, we have:
c = 6
Also, since the transverse axis is vertical and the distance from the center to each vertex is a, we have:
a = distance from center to vertex = 6
Therefore, we have:
b² = a² - c² = 36 - 36 = 0
So the equation of the hyperbola is:
x²/36 - y²/0 = 1
Simplifying, we get:
x²/36 = 1
or
x² = 36
This is the equation of a horizontal line passing through (±6,0).
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Maureen drove for 1.5 hours at an average speed of 62 mph and then for another half hour at an average speed of 24 mph. How far did she drive altogether?
Answer:
105 mi
Step-by-step explanation:
distance = speed x time
total distance = (62 mi/hr)(1.5 hr) + (24 mi/hr)(0.5 hr) = 105 mi
30 min = 0.50 hr
NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6
. In an earlier study, the population proportion was estimated to be 0.41
.
How large a sample would be required in order to estimate the fraction of people who black out at 6
or more Gs at the 95%
confidence level with an error of at most 0.04
? Round your answer up to the next integer.