Answer:
f^-1(x) = 4x-3
Step-by-step explanation:
f(x) = (x+3)/4
y = (x+3)/4
Exchange x and y
x = (y+3)/4
Solve for y
4x = y+3
Subtract 3
4x-3 = y
The inverse
f^-1(x) = 4x-3
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92.
Round your answers to two decimal places.
(a) State the point estimate for the population mean cost of fast food bills at this restaurant $
(b) Calculate the 95% margin of error. $
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
$
≤ µ ≤ $
(d) What sample size is needed if the error must not exceed $1.00?
n =
First, we find the point estimate, given by the sample mean. Then, with this, and the standard deviation of the population given, we can find the margin of error, and then, we can find the confidence interval and the minimum sample size necessary.
Doing this, we get that:
a) The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
b) The 95% margin of error is $1.64.
c) The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
d) The sample size needed is 135.
Question a:
The point estimate for the population mean is the sample mean, which is of $18.21.
The point estimate for the population mean cost of fast food bills at this restaurant is $18.21.
Question b:
We have to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a p-value of , so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{5.92}{\sqrt{50}} = 1.64[/tex]
The 95% margin of error is $1.64.
(c) State the 95% confidence interval for the population mean cost of fast food bills at this restaurant.
The lower end of the interval is the sample mean subtracted by M. So it is 18.21 - 1.64 = 16.57
The upper end of the interval is the sample mean added to M. So it is 18.21 + 1.64 = 19.85
The 95% confidence interval for the population mean cost of fast food bills at this restaurant is: $16.57 ≤ µ ≤ $19.85.
(d) What sample size is needed if the error must not exceed $1.00?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.96\frac{5.92}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.96*5.92[/tex]
[tex](\sqrt{n})^2 = (1.96*5.92)^2[/tex]
[tex]n = 134.6[/tex]
Rounding up:
The sample size needed is 135.
For a question in which you find a confidence interval using the z-distribution, you can check https://brainly.com/question/24175328
To find the minimum sample size for a confidence interval, you can check https://brainly.com/question/22667000
I don't get this question i need some help please!!!
Answer:
2 sqrt(2) = x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/4
4 sin 45 = x
4 ( sqrt(2)/2) =x
2 sqrt(2) = x
Answer: D
Use sine to find the x-value:
[tex]sin(45)=\frac{x}{4} \\\\4*sin(45)=x\\\\x=\frac{\sqrt{2} }{2} *4=2\sqrt{2}[/tex]
SOMEBODY PLEASE HELP ME!!!! I NEED THIS!!!!
Answer:
47.1
Step-by-step explanation:
We know side LM corresponds with side OP with a factor of some number. The value of side LM is 8, and the value of side OP is 29. If we divide the two numbers, we will find the scale factor of which triangle NOP is larger than KLM. 29/8 simplifies to 3.625. Now, to find the value of side PN, we must find the side it corresponds to on triangle KLM. Because K corresponds with N, and M corresponds with P, we know the side that PN corresponds with on triangle KLM is side KM. Side KM has a value of 13, so side PN must be 3.625 times larger than 13.
13 times 3.625 = 47.125. The question says to round to the nearest tenth, so the answer would be 47.1
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism. Please explain.
a) 315 cm2 squared
b) 480 cm2 squared
c) 510 cm2 squared
d) 570 cm2
Answer:
Option (C)
Step-by-step explanation:
Surface area of a right prism = 2(Area of the triangular base) + Ph
Here, P = Perimeter of the base
h = Height of the prism
Area of the triangular base = [tex]\frac{1}{2}(\text{Height})(\text{Base})[/tex]
= [tex]\frac{1}{2}(5)(12)[/tex]
= 30 cm²
Height of the prism = 15 cm
Perimeter of the base = (5 + 12 + 13)
= 30 cm
Surface area of the right prism = 2(30) + 30(15)
= 60 + 450
= 510 cm²
Therefore, Option (C) will be the correct option.
Find the fourth proportion to : 2,3,16
Answer is 24
Step by step:
2,3,16
Let the fourth proportion be x
2/3 = 16/x
or, 2x = 3×16
or, x = 3×16/2
or, x = 3×8
or, X = 24
Find two numbers that have 2, 5, and 7 as factors.
Step-by-step explanation:
One easy way to find a number that has all of these numbers as factors is to multiply them all together, so 2 * 5 * 7 = 10 * 7 = 70, which is one number.
To find the other number, we can multiply the number we already have by any integer greater than 1, e.g. 2, to get 70* 2= 140 as our other number, making our numbers 70 and 140
If you were going to install a new window in your bathroom, what needs to be measured? What
else might you need to consider?
measure horizontally
measure vertically
measure depth..
Please help! Question in image below:
Answers also below:
Answer:
11, 18, 25, 32, .....
Option D
Step-by-step explanation:
The formula for the nth term of an AP is a+(n-1)d
a+(n-1)d=a+(n-1-1)d+7
a+nd-d=a+nd-2d+7
d=7
As the common difference is 7.
The only option given which is in an AP is the 4th option
Write an inequality for the shaded region shown in the figure.
Answer:
y ≥ x^2 - 1
Step-by-step explanation:
First, we can see that the shaded region is above what seems to be a parabola, and we also can see that the lines of the parabola are solid lines (which means that the points on the curve itself are solutions, so the symbol ≥ is used)
Then:
y ≥ a*x^2 + b*x + c
where a*x^2 + b*x + c is the general quadratic equation.
Now let's find the equation for the parabola:
f(x) = a*x^2 + b*x + c
We also can see that the vertex of the parabola is at the point (0, -1)
This means that:
f(0) = -1 = a*0^2 + b*0 + c
= -1 = c
then we have that c = -1
Then:
f(x) = a*x^2 + b*x - 1
Now we can look at the graph again, to see that the zeros of the parabola are at +1 and -1
Which means that:
f(1) = 0 = a*1^2 + b*1 - 1 = a + b - 1
f(-1) = 0 = a*(-1)^2 + b*(-1) - 1 = a - b - 1
Then we got two equations:
a + b - 1 = 0
a - b - 1 = 0
from this we can conclude that b must be zero.
Then:
b = 0
and these equations become:
a - 1 = 0
a - 1 = 0
solving for a, we get:
a = 1
Then the quadratic equation is:
f(x) = 1*x^2 + 0*x - 1
f(x) = x^2 - 1
And the inequality is:
y ≥ x^2 - 1
Given f(x) = 6x + 2, find f(x – 3).
A. f(x – 3) = 6x – 1
B. f(x – 3) = 6x – 16
C. f(x - 3) = x - 1
D. f(x – 3) = 6x2 – 16x - 6
Answer: B. f(x - 3) = 6x - 16
Concept:
When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.
Solve:
Given function and value
f(x) = 6x + 2
f(x - 3)
Substitute the value into the given expression
f(x - 3) = 6 (x - 3) + 2
f(x - 3) = 6x - 18 + 2
f(x - 3) = 6x - 16
Hope this helps!! :)
Please let me know if you have any questions
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answer:
The solutions of this system of equation is (-5,3) and (-1,-5).
Answer: (-3,-1) and (-5,3)
Step-by-step explanation:
A camera with a price of d dollars is discounted 25%. write two expressions to represent the price of the camera with the discount.
Answer:
17d/20
Step-by-step explanation:
100-25=85
85/100×d
=17/20×d
=17d/20
Which word MOST affects the tone of this sentence?
A slender woman walked into the room wearing a pink dress and a gaudy hat.
A- room
B- gaudy
C- woman
D- slender
Answer:
B
Step-by-step explanation:
PLEASE ANSWER!!!!! A car traveled s kilometers in 6 hours with a speed of v kilometers per hour. Express the dependence of s on v. Using the formula, find: v for s=363
In this question, the relations between velocity, distance and time are explored to first express the dependence of s on v, given the data in the exercise, and then to find the value of v for which s = 363.
-------------------------
Relation between velocity, distance, and time:
We have that velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
-------------------------
A car traveled s kilometers in 6 hours with a speed of v kilometers per hour.
This means that [tex]d = s, t = 6[/tex]
-------------------------
Express the dependence of s on v.
Taking the above values of d and t, and the formula, we have that:
[tex]v = \frac{d}{t}[/tex]
[tex]v = \frac{s}{6}[/tex]
[tex]s = 6v[/tex]
Thus, the dependence of s on v can be expressed as: [tex]s = 6v[/tex]
-------------------------
Using the formula, find: v for s=363
We have that:
[tex]s = 6v[/tex]
And thus
[tex]v = \frac{s}{6}[/tex]
Considering [tex]s = 363[/tex]:
[tex]v = \frac{363}{6} = 60.5[/tex]
Thus, for s = 363, v = 60.5.
For an example of a problem using this formula, you can check here: https://brainly.com/question/14307500
Answer:
v=s/6 is the formula
and if s=363, v=60.5
hope this helped!
The average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. Who is relatively taller based on their comparison to their gender, LeBron James at 81 inches or Candace Parker at 76 inches?
a) Candace is relatively taller because she has a larger z-score.
b) LeBron is relatively taller because he has a larger z-score.
c) LeBron is relatively taller because he has a smaller z-score.
d) Candace is relatively taller because she has a smaller z-score.
Answer:
b) LeBron is relatively taller because he has a larger z-score.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
LeBron James:
Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when [tex]X = 81, \mu = 69.5, \sigma = 2.7[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{81 - 69.5}{2.7}[/tex]
[tex]Z = 4.26[/tex]
Candace Parker:
Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when [tex]X = 76, \mu = 64.2, \sigma = 3.2[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{76 - 64.2}{3.2}[/tex]
[tex]Z = 3.69[/tex]
Who is relatively taller?
Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.
Plz help
I will be giving extra 50 points
it isn't possible to just give extra points in a simple and reliableway. anyways, let's starts.
a. is simple, just put the terms in order
r² +6r -5
because:
[tex] {r}^{2} + {6r}^{1} + {5r}^{0} [/tex]
anything to the power of 0 equals 1,
because it's the same as r/r, and 5 * r/r = 5*1
b. same logic as above
a²b² -5ab +33
c.
-c³ +ab +d +9
d.
-9y^5 - 2x³y²z +4x² +10x +1
^5 = to the power of five, it's the fastest way to type it without the special math input tool.
hope it helps you
Answer:
I agree with the above one.
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of howmany miles it lasts. Assume the standard deviation for the tire life of this particular brand is 6000miles. Determine the sample size needed to construct a 95% confidence interval with a margin oferror within 2000 miles.ShowWork:
Answer:
6 samples
Step-by-step explanation:
Given :
Sample size, = n
Standard deviation, = 6000
Margin of Error = 2000
Confidence interval, α = 95%
Zcritical at 95% = 1.96
n = (Zcritical * σ) / margin of error
n = (1.96 * 6000) /2000
n = 11760 / 2000
n = 5.88
n = 6 samples
ASAP ! PLSSSQ!!!!!!!
Answer:
16
Step-by-step explanation:
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
Help please, thanks
Answer: B. X It passes the vertical line test :)
Step-by-step explanation:
10(2x-3)=10
find the value of x
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
10(2x-3)=1020x-30=1020x=10+3020x=40x=40/20X=2It is given that,
→ 10(2x-3) = 10
Then find required value of x,
→ 10(2x-3) = 10
→ 20x-30 = 10
→ 20x = 10+30
→ 20x = 40
→ x = 40/20
→ [x = 2]
Hence, the value of x is 2.
what is the length of AB? round to one decimal place
Answer:
A=0
Step-by-step explanation:
DAC=BAD
A=0
Evaluate the expression when y=6 and x=4. x + 7y X s ?
Answer:
4 + 42s
Step-by-step explanation:
When y = 6 and x = 4,
x + 7y * s4 + (7*6) * s4 + 42 * sWhat is the slope of the line that goes through the points (1,-5) and (4,1)?
Answer:
The slope is 2
Step-by-step explanation:
The Slope formula is y2-y1/x2-y1.
1. Plug the numbers into the slope equation which is 1-(-5)/4-1=2
Consider the triangle.
Which statement is true about the lengths of the sides?
O Each side has a different length.
O Two sides have the same length, which iS less than
the length of the third side.
O The three sides have the same length.
O The sum of the lengths of two sides is equal to the
length of the third side.
Answer:
the last one
Step-by-step explanation:
this is because it is an equalactral triangle meaning that the line at the side is the only one which its degrees is 90 so if u add 45 and 45 its 90(hope this helps)
Answer:
Two sides have the same length, which iS less than
the length of the third side.
Step-by-step explanation:
Hypotenuce is a sode opposite to right angle, which is always bigger then any side of right triangle. since both angles are the same, Adjacent and Opposite are similar size as well.
Solve, expressing your answer in an exact form involving a natural logarithm and showing your steps: 3*e^1/2t+4=27
Answer:
3 e^t/2 + 4 = 27
e^t/2 = 23 / 3
Taking natural log of both sides
t/2 = ln 23/3 = ln 7.667 = 2.037
t = 4.074
Check:
3 e^4.074/2 + 4 = 27
27 = 27
Solve 3x to the second power +17x-6=0
The solution of the equation 3x² + 17x - 6 = 0 are, x = 1/3 and x = - 6.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
We have to given that;
The quadratic equation is,
⇒ 3x² + 17x - 6 = 0
Now, We can solve the equation as;
⇒ 3x² + 17x - 6 = 0
⇒ 3x² + (18 - 1)x - 6 = 0
⇒ 3x² + 18x - x - 6 = 0
⇒ 3x (x + 6) - 1 (x + 6) = 0
⇒ (3x - 1) (x + 6) = 0
This gives two solutions,
⇒ 3x - 1 = 0
⇒ x = 1/3
And, x + 6 = 0
⇒ x = - 6
Learn more about the quadratic equation visit:
brainly.com/question/1214333
#SPJ2
Add or subtract the following mixed numbers using the first method. (Add the whole numbers; add the fractions; combine the parts of the sum for the answer.) Be sure your answers are in mixed number format and reduced to lowest terms.
2 2/3 +4 1/8 =
6 19/24
Step-by-step explanation:
Find the LCM(lowest common multiple) of 3 and 8 which is 24Multiply the denominator of 2/3 by 8 and 1/8 by 3Whatever you do to the denominator you have to do to the numerator, so you also have to multiply the numerator of 2/3 by 8 and 1/8 by 3 = 2 16/24 + 4 3/24Add the whole numbers (4+2= 6)Add the fractions (16/24 + 3/24= 19)Put them together and the answer is 6 19/24I can't really explain things properly, but I hope it helps
Find the period of the function y = 3/2 tan(1/3^x).
А) pi
B) pi/3
C) 3pi
D pi/6
==========================================================
Explanation:
I'm assuming you meant to say
y = (3/2)*tan( (1/3)x )
If so, then that equation is in the form
y = A*tan(Bx)
The B coefficient is B = 1/3 and it directly ties together to the period T.
T = pi/B
T = pi/(1/3)
T = pi*(3/1)
T = 3pi .... answer is choice C
Side note: This formula only works for tangent and cotangent functions.
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 2 million barrels of oil in the well; six years later 1,000,000 barrels remain.
Required:
a. At what rate was the amount of oil in the well decreasing when there were 1,200,000 barrels remaining?
b. When will there be 100,000 barrels remaining?
Answer:
A. It was decreasing by -138,629.44 barrels
B. 26 years of time
Step-by-step explanation:
Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.
A. At 1200000
Bt = 1200000
-1/6ln2 x 1200000
Solve this using a calculator
= -138,629.4361
So the amount of oil is decreasing by -138,629.44 barrels
