The odometer in a car measures the number of miles driven by the car since it was made. During the trip, the odometer in Anita‘s car is modeled by the function Y=9500+55X where X represents the number of hours driven during the trip and y represents the odometer reading in miles. What is the meaning of the rate change in this function?
Answers
The given function is y=9500+55x, where x is in hours driven and y is in miles.
Therefore, the slope of the function is
[tex]\frac{miles}{number\text{ of hours driven}}[/tex]The answer is the number of miles driven each hour during the trip, the first option.Related Questions
Find the value of x b) 3x = 27
Answers
3x = 27
3x = 27 x
3x = 27/3
x. = 9
The city of Raleigh has 10,000 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 450 randomly selected registered voters was conducted. 166 said they'd vote for Brown, 257 said they'd vote for Feliz, and 27 were undecided.
Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.Round your
answer to four decimal places.
This sample statistic suggests that we might expect
voters to vote for Brown.
of the 10,000 registered
Answers
The sample statistic for the number of respondents who said they would vote for Brown is 0.3689, and the number of respondents who indicated they would vote for Brown is 3689.
The population in this survey are the registered voters in Raleigh. There are 10000 registered voters in Raleigh from which a sample is group selected of 450 randomly selected registered voters was conducted in which 166 said they'd vote for Brown, 257 said they'd vote for Feliz, and 27 were undecided.
So, according to the given data
The sample statistic is the number who would vote for Brown divided by the total number in the sample, means
[tex]\frac{166}{450}[/tex]
0.3689
To find sample statistic suggests that we might expect voters to vote for Brown of the 10,000 registered, we multiply the sample statistic (0.3689) with the total number of voters (10000) means
0.3689 * 10000 = 3689.
Therefore we can conclude that the sample statistic for the proportion of voters surveyed who said they'd vote for Brown is 0.3689 and the voters to vote for brown is 3689.
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I need help with the following questions. Please show your work.
1) Find the inverse of f(x)=3 sqrt x-1/2
2) Let f(x)-2/2x-1
Show that this function is one-to-one algebraically.
3) Determine whether f(x)=3x-5 and g(x)=x/3+5 are inverses. Explain how you know.
please help
Answers
Considering the given functions, we have that:
1) The inverse of function f(x) is defined by: [tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
2) It is shown in the Item 2 section that the function is one-to-one.
3) The functions are not inverses, due to the result of their composition.
Item 1 - Inverse functionThe find the inverse of a function, we exchange x and y on the original function, and then isolate y.
The original function is given by:
[tex]y = 3\frac{\sqrt{x - 1}}{2}[/tex]
Exchanging x and y, we have that:
[tex]x = 3\frac{\sqrt{y - 1}}{2}[/tex]
Now we do the procedures to isolate y, as follows:
[tex]3\sqrt{y - 1} = 2x[/tex]
[tex]\sqrt{y - 1} = \frac{2x}{3}[/tex]
[tex](\sqrt{y-1})^2 = \left(\frac{2x}{3}\right)^2[/tex]
[tex]y - 1 = \frac{4x^2}{9}[/tex]
[tex]y = \frac{4x^2}{9} + 1[/tex]
[tex]f^{-1}(x) = \frac{4x^2}{9} + 1[/tex]
Item 2 - One-to-one functionTo verify if the function is one-to-one, we first find the numeric values at x = a and x = b, then:
f(a) = -2/(2a - 1).f(b) = -2/(2b - 1).Now we have to verify how many outcomes of a and b are possible for them to be equal. Since they have the same numerator, they will be equal when the denominators are equal, that is:
2a - 1 = 2b - 1.
Simplifying the one and then by 2:
a = b.
Only equal when a = b, hence the function is one-to-one. (this is the algebraic proof).
Item 3 - Are they inverses?The functions will be inverses if the composition of the functions result in x, that is, if inputting function g(x) into function f(x) results in x.
The result of the composition is given by:
f(g(x)) = f(x/3 + 5) = 3(x/3 + 5) - 5 = x + 15 - 5 = x + 10.
x + 10 is different of x, hence the two functions are not inverses.
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Please I really need help
Determine which integers in the set S: {-40, "-10," 20, 40} will make the inequality 1/5 (m - 5) <_ 1/10 (m - 20) false.
S:{-40, -10}
S:{-10, 20}
S:{20, 40}
S:{-40, 40}
Answers
The integers in the set S that make the inequality false are 20 and 40, so the correct option is the third one.
Which elements in the set will make the inequality false?Here we have the following inequality:
(1/5)*(m - 5) ≤ (1/10)*(m - 20)
First, let's simplify the inequality:
(1/5)*(m - 5) ≤ (1/10)*(m - 20)
(10/5)*(m - 5) ≤ (m - 20)
2*(m - 5) ≤ (m - 20)
2m - 10 ≤ m - 20
2m - m ≤ -20 + 10
m ≤ -10
So the only solutions are the values of m that are equal to or smaller than -10.
And the set is {-40, "-10," 20, 40}, then the elements of that set that make the inequality false are 20 and 40 (both are larger than -10).
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Evaluate the function when x=-2; f(x)=4x+3
Answers
Answer:
Replace the variable x with -2 in the expression
f(-2) =4(-2)+3
f(-2) = -8+3
f(-2) = -5 (final answer)
Identify the mean of the following numbers: 15, 18, 24.
Answers
Answer:
19
Step-by-step explanation:
So first add the numbers and find sum. 15+18+24=57. Then you have to divide it by the number of numbers that are in the set which is 3. 57/3=19
Answer:
The mean is 19!
Step-by-step explanation:
The mean is 19!
Between which two whole numbers is square root of 12?
Which of the two numbers is a better estimate for square root of 12 explain.
Answers
Answer:
3 and 4Step-by-step explanation:
square root 12 lies between (square root 9 and 16) so it is between 3 and 4
A farmer picked 725 pounds of apples one week. Hepicked 693 pounds of pears in the same week. Whichcalculation can be used to find out how many morepounds of apples than pears he picked?
Answers
a farmer picked 725 pounds of apple,
also
heyya cann anyone help me with this
Answers
Answer:
a = 132°
Step-by-step explanation:
this is a straight line and straight lines always measure up to 180°....so you subtract 48° from 180° and you get 132°
Answer:
132°
Step-by-step explanation:
We know that,
angles in a straight line are added upto 180°.
Accordingly,
[tex]48 + a = 180[/tex]
Subtract 48 by both sides and make a the subject.
[tex]a = 180 - 48 \\ a = 132 \degree[/tex]
$2,300 at 7% interest for 9 years. What would the interest be?
Answers
We want to find the simple interest accrued on $2,300 at 7% interest for 9 years.
The formula for simple interest is given as;
[tex]I=\frac{P\times R\times T}{100}[/tex]Inserting the values, we have;
[tex]I=\frac{2300\times7\times9}{100}=\text{ \$1449}[/tex]Therefore, the interest is $1449
Of 734 students, 442 are taking mathematics. What angle (in degrees) of a circle would show the percent of students taking mathematics? (Round your answer to the nearest whole degree.)
Answers
We need to find the angle (rounded to the nearest whole degree) of a circle that would represent the percent of students taking mathematics.
Since a complete turn around the circle has 360º, we have the following proportion:
Number of students Angle
734 360º
442 x
Then, cross multiplying the above values, we obtain:
[tex]\begin{gathered} 734x=442\cdot360\degree \\ \\ x=\frac{442\cdot360\degree}{734} \\ \\ x\cong217\degree \end{gathered}[/tex]Answer: 217º
Answer:
217°
Step-by-step explanation:
The fraction of students taking math is 442/734
we need this same fraction of the 360 degrees in a circle
442/734 * 360 = 217°
Kate and Hellen buy a car. Kate pays £1200 and Helen pays the remaining 23 of the
total cost. How much does the car cost in total?
Answers
Answer:1223 pounds?
Step-by-step explanation:
View the image to answer.
Answers
The function f,g and h are defined by f(x)=xSin(1/x²), g(x)=x²Sin(1/x) and h(x)=Sinx/x. The 1st and 2nd inequality are satisfying the function, Option A is correct.
Given that,
The function f,g and h are defined by
f(x)=xSin(1/x²)
g(x)=x²Sin(1/x) and
h(x)=Sinx/x
We have to find which inequality can be used with squeeze theorem to find the limit of the function.
The inequality are
1. -|x|<f(x)<|x|
2. -x²<g(x)<x²
3. -x<h(x)<x
The squeeze (or sandwich) theory states that if f(x)g(x)h(x) for all numbers and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them. Theorem: We can use them to achieve challenging limits, such as sin(x)/x at x=0, by "squeezing" sin(x)/x between two better functions and using them to find the limit at x=0.
First we see the 1st inequality.
The range of sin function is from -1 to 1
-1<Sin(1/x²)<1
-x<xSin(1/x²)<x
-|x|<xSin(1/x²)<|x|
-|x|<f(x)<|x|
The 1st inequality satisfy the function.
Now, we see the 2nd inequality.
The range of sin function is from -1 to 1
-1<Sin(1/x)<1
-x²<x²Sin(1/x²)<x²
-x²<g(x)<x²
The 2st inequality satisfy the function.
Now, we see the 3nd inequality.
The range of sin function is from -1 to 1
-1<Sinx<1
-1/x<Sinx/x<1/x
-1/x<h(x)<1/x
The 3st inequality does not satisfy the function.
Therefore, the 1st and 2nd inequality are satisfying the function, Option A is correct.
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A bicyclist rides 11.2 kilometers
east and then 5.3 kilometers south.
What is the magnitude of the
bicyclist's resultant vector?
Hint: Draw a vector diagram.
[ ? ] kilometers
Round your answer to the nearest tenth.
Answers
The magnitude of the bicyclist's resultant vector is 12.5 km.
Given that, a bicyclist rides 11.2 kilometers east and then 5.3 kilometers south.
What is vector?A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction.
Now, using Pythagora's theorem
The magnitude of the bicyclist's resultant vector is
x² = (11.2)² + (5.3)²
⇒ x² = 125.44 + 28.09
⇒ x² = 153.53
⇒ x = √153.53
⇒ x = 12.47
⇒ x ≈ 12.5 km
Therefore, the magnitude of the bicyclist's resultant vector is 12.5 km.
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Answer:
12.4 km (nearest tenth)
Step-by-step explanation:
The resultant vector of the bicyclist after riding 11.2 km east and then 5.3 km south is:
b = 11.2i - 5.3jThe magnitude of a vector b is written | b |.
Magnitude is a scalar, and it’s always positive.
The i and j components of a vector form a right triangle, so use Pythagoras’ theorem to find a vector’s magnitude.
[tex]\begin{aligned} |\textbf{b}|&=\sqrt{11.2^2+5.3^2\\&=\sqrt{125.44+28.09\\&=\sqrt{153.53}\\&=12.4\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, the magnitude of the bicyclist's resultant vector is 12.4 km (nearest tenth).
Find the value of r. Justify your answer.
6×(r×3)=3×(6×9)
Answers
Answer:
r = 9
Step-by-step explanation:
6 × (r × 3) = 3 × (6 × 9) , that is
6 × 3r = 3 × 54
18r = 162 ( divide both sides by 18 )
r = 9
En los juegos olimpicos del 2012 en londres usain bolt gano medalla de oro al recorrer 100 metros en 9.69 segundos cual fue su velocidad ?
Answers
Answer:
la respuesta es 10.3199...
Step-by-step explanation:
solo divides 100 por 9.69
how to solve this equation (x2/3)6/5
Answers
Answer:
[tex] \frac{2}{5} {x}^{2} [/tex]
Step-by-step explanation:
x²/3(6/5)
=2/5x²
Answer:
[tex]=\frac{4x}{5}[/tex]
Step-by-step explanation:
[tex]\frac{\left(x\frac{2}{3}\right)\cdot \:6}{5}=\frac{4x}{5}[/tex]
Remove parentheses: :3
[tex]=\frac{x\frac{2}{3}\cdot \:6}{5}[/tex]
Multiply [tex]x\frac{2}{3} * 6 : 4x[/tex]
ANd u get
[tex]=\frac{4x}{5}[/tex]
hope thjis helps
~~Wadfads~~
A flagpole is anchored to the ground by a guy wire that is 12 m long. The guy wire makes an angle of 63 deg with the ground. How far from the base of the flagpole must the guy wire be anchored into the ground?
Answers
Answer: ~ 5.45 m
Step-by-step explanation: The pole would create an altitude for the triangle, and the wire attached from the ground to the pole would be create a hypotenuse of 12m. Since the wire makes a 63 degree angle with the ground, we can use a trig ratio to find the base. The base of the triangle would be the distance from the wire in the ground to the pole itself. Using cosine, (adjacent to 63 degrees over 12m) you can find the measure of the base.
cos (63 deg.) = x / 12
12 • cos (63 deg.) = x
5.44788599687 = x.
Hope this helps! (Added pic for clarity!)
Your good friend Carlos, offers you the opportunity to join his game. The rules are:
If you pick a spade from a shuffled pack, you win $9.00.
If you lose you owe him $2.00
Find the expected value you win the game?
Answers
If Your good friend Carlos, offers you the opportunity to join his game. The rules are: If you pick a spade from a shuffled pack, you win $9.00. If you lose you owe him $2.00 . The expected value you win the game is $.075.
Expected valueProbability of getting spade = 13/52
Probability of getting spade = 1/4
Probability of getting another thing = 1 - 1/4
Probability of getting another thing = 3 / 4
Now let find the expected value
E(x) = Σxp(x)
Expected value = 9 × 1/4 + (-2) (3 /4)
Expected value = 9 /4 - 6 /4
Expected value = 3 /4
Expected value = $0.75
Therefore the expected value is $0.75.
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a) Complete the table of values for y = x² - 2x - 3
-2 -1 0 1
2
3
4
0
X
y
-3
5
Answers
Answer:
On worksheet: 5, -3, -4, 0
Step-by-step explanation:
See attached worksheet.
weekly wages at a certain factory are normally distributed woth a mean of $400 and a standard deviation of $50. find the probability that a worker selected at random makes between $450 and $500
Answers
Answer:
See below
Step-by-step explanation:
450 is 1 standard deviation above mean : z - score +1 corresponds to
.8413 (from z-score table)
500 is 2 S.D. for z-score of 2 corresponds to .9772
.9772 - .8413 = .1359 or 13 . 59 %
Given the equation 13.25y = 79.5, determine the value of y.
Answers
Answer:
y = 6
Step-by-step explanation:
13.25 = 79.5 ( isolate y by dividing both sides by 13.25 )
y = 79.5 ÷ 13.25 = 6
y 12 11 10 9 18 5 NCS A 1 X -12-11-10-9-8-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 -1 3 ó do & och ich -10 -11 -12
Answers
To find out the equation of the line we need two points
so
we take
(1,-3) and (2,-9)
step 1
Find the slope
m=(-9+3)/(2-1)
m=-6/1
m=-6
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=-6
point (1,-3)
substitute
-3=-6(1)+b
solve for b
-3=-6+b
b=6-3
b=3
therefore
y=-6x+3Help plssssssssssssssssss
Answers
Answer:
2
Step-by-step explanation:
→ Find 2 points
( 3, 5 ) and ( 2 , 3 )
→ Find the change in y coordinates
3 - 5 = -2
→ Find the change in x coordinates
2 - 3 = -1
→ Divide y by x
-2 ÷ -1 = 2
a random variablegroup of answer choicesis the result of a measurement.can only be discrete.assigns one and only one numeric value to each experimental outcome.is a binomial, poisson, or hypergeometric variable.
Answers
A random variable assigns one and only one numeric value to each experimental outcome.
A random variable used in experimental trials assign numerical values to the members or elements of the trial. This random variable is used to study the outcome of a trial conveniently.
A random variable assigns one and only one numeric value to each experimental outcome. This assigned numeric value may not be exact. In an experimental trial the possible outcomes are denoted by a random variable. So these values are just practically assigned and not theoretically exact.
There are discrete and continuous random variables. They are usually denoted by capital letters such as X, Y,.. etc. These random variables are used to calculate the probability of each outcome in a trial.
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Jim estimates the width of his wall to be 8 feet. The actual wall measures 8.25 feet wide. What is Jim’s percent error?
Answers
Jim's percent error is 3.03%.
What is the percentage error?The percentage error is given as the difference between the actual value and the estimated value divided by the actual value, multiplied by 100%.
The percentage error is a relative value that compares the actual value and the estimated value to explain any deviations.
Estimated width of wall = 8 feet
The actual width of the wall = 8.25 feet
The difference in estimate = 0.25 feet (8.25 - 8)
Percentage Error = 3.03% (0.25/8.25 x 100)
Thus, we can conclude that Jim made a percentage error of 3.03% in his estimate of the width of the wall.
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giving out brainliest!
−5x > –25
Answers
Answer:
the answer is x < 5
Step-by-step explanation:
-5x/-5 < -25/-5
Cancel terms that are in both the numerator and denominator
Divide the numbers
x < 5
Given the function g(x) = −3x + 4, compare and contrast g(−2) and g(4). Choose the statement that is true concerning these two values.
1. The value of g(−2) is smaller than the value of g(4)
2. The value of g(−2) is the same as the value of g(4).
3. The values of g(−2) and g(4) cannot be compared.
4. The value of g(−2) is larger than the value of g(4).
Answers
The function g(x) = −3x + 4, after putting the values we find out that the value of g(-2) is greater than the value of g(4). Hence, option 4 is correct.
What is a function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for creating physical links in the sciences.
According to the given information in the question,
g(x) = -3x + 4
Substitute g(-2) in the above equation,
g(-2) = -3(-2) + 4
g(-2) = 10
Now, substitute g(4) in the above equation,
g(4) = -3(4) + 4
g(4) = -8
Hence, it is clear that the value of g(-2) is larger than the value of g(4).
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se the given frequency distribution to find the (a) class width. (b) class midpoints. (c) class boundaries. temperature (f) frequency question content area bottom part 1 (a) what is the class width?
Answers
The class width is 5 for the given frequency distribution.
What are class boundaries?
The values used to demarcate classes are called class borders. The difference between a class's upper-class limit and its lower-class limit indicates the extent of the gap between classes.(a) Class width is the same for all the classes. It is the difference between the lower class limit of two consecutive classes
Therefore Lower limit of 50 - 54 = 50
Lower limit of 55 - 59 = 55
Class width = 55 - 50
Class width = 5
If calculated all have the same class width.
(b) Midpoint is the average of the sum of lower and upper-class limits of the class.
Temp Freq Midpoint
50-54 1 52
55-59 3 57
60-64 5 62
65-69 11 67
70-74 7 72
75-79 7 77
80-84 1 82
(c) Class boundaries are to make the classes continuous mostly. We can find this by first calculating the difference between the upper-class limit and the lower-class limit of the next class and taking its average.
Add this average to the upper limit and subtract this average from the lower limit
Lower boundary for 50 - 54 = 50 - 0.5 = 49.5
Upper boundary for 50 - 54 = 54 + 0.5 = 54.5
Temp Freq Class Boundaries
50-54 1 49.5-54.5
55-59 3 54.5-59.5
60-64 5 59.5-64.5
65-69 11 64.5-69.5
70-74 7 69.5-74.5
75-79 7 74.5-79.5
80-84 1 79.5-84.5
The class width is 5 for the given frequency distribution.
Complete question: Use the given frequency distribution to find the
(a) class width.
(b) class midpoints.
(c) class boundaries.
Temperature (°F) Frequency
32-36 1
37-41 3
42-46 5
47-51 11
52-56 7
57-61 7
62-66 1
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due now pls help meee!!!!!
Answers
Answer:
just guess but it might be c
