Answer:
168 km
Step-by-step explanation:
Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:
x/42 +y/105 = 2.5
x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours
Multiplying the first equation by 210, we have ...
5x +2y = 525
Multiplying the second equation by 420, we get ...
15x +7y = 1680
Subtracting 3 times the first of these equations from the second, we have ...
(15x +7y) -3(5x +2y) = (1680) -3(525)
y = 105
Putting this into the very first equation, we get ...
x/42 + 105/105 = 2.5
x/42 = 1.5 . . . . . . subtract 1
x = 63 . . . . . . . . .multiply by 42.
The total distance to Tyler's parents' house is ...
63 km + 105 km = 168 km
Tyler's total travel distance is approximately 168 km.
Calculating Total Distance Traveled
To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.
→ The total distance is:
[tex]D = d_u + d_m[/tex]
First, using the normal journey:
→ Urban Area:
Speed = 42 km/h
Time = [tex]t_u[/tex] / 42,
→ Motorway:
Speed = 105 km/h
Time = [tex]t_m[/tex] / 105,
→ Total time for normal journey:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
We have:
→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]
→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]
When there is fog:
→ Urban Area:
Speed = 28 km/h
Time = [tex]t__uf}[/tex] / 28
→ Motorway:
Speed = 60 km/h
Time = [tex]t_{um[/tex] / 60
Total time for foggy journey:
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60
Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:
→ 2.5+1+0.5=4 hours
Thus,
→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4
Solving the Equations
We now have two equations:
→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]
→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]
Let's solve these equations step-by-step.
First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):
→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]
→ [tex]5t_u+2t_m=525[/tex] (eq. 1)
Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):
→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]
→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)
We now solve these two linear equations:
→ [tex]5t_u+2t_m=525[/tex]
→ [tex]15t_u +7t_m =1680[/tex]
First, let's solve Equation 1 for [tex]t_m[/tex] in terms of [tex]t_u[/tex]:
→ [tex]d_m=(525-5d_u)/2[/tex]
Substitute this expression into Equation 2:
→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]
Multiply through by 2 to clear the fraction:
→ [tex]30t_u +7(525-5t_u )=3360[/tex]
→ [tex]30t_u +3675-35t_u =3360[/tex]
→ [tex]-5t_ u +3675=3360[/tex]
→ [tex]-5t_u=3360-3675[/tex]
→ [tex]-5t _u=-315[/tex]
→ [tex]t_u=63[/tex]
Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:
→ [tex]5(63)+2t_m =525[/tex]
→ [tex]315+2t_m =525[/tex]
→ [tex]2t_m =210[/tex]
→ [tex]t_m=105[/tex]
Thus, the total distance Tyler travels is:
[tex]= t _u +t_m[/tex]
[tex]=63+105[/tex]
[tex]=168\ kilometers[/tex]
Bina kept a list of her expenses and income for one month. If she started the month with no money, how much money did she have left at the end of the month?
Answer:
Step-by-step explanation:
Income less expenses
Answer:
15
Step-by-step explanation:
i got it right pls mark brainliest
What is the determinant of
15
18
154
Answer:
The determinant is 15.
Step-by-step explanation:
You need to calculate the determinant of the given matrix.
1. Subtract column 3 multiplied by 3 from column 1 (C1=C1−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&3&1\\-5&5&3\end{array}\right][/tex]
2. Subtract column 3 multiplied by 3 from column 2 (C2=C2−(3)C3):
[tex]\left[\begin{array}{ccc}-25&-23&9\\0&0&1\\-5&-4&3\end{array}\right][/tex]
3. Expand along the row 2: (See attached picture).
We get that the answer is 15. The determinant is 15.
Answer:
The answer is 15
Step-by-step explanation:
A simple random sample of size nequals=200200 drivers were asked if they drive a car manufactured in a certain country. of the 200200 drivers surveyed, 105105 responded that they did. determine if more than half of all drivers drive a car made in this country at the alpha equals 0.05α=0.05 level of significance. complete parts (a) through (d).
Answer:
Is there supposed to be a photo
Step-by-step explanation:
The length of each side of a square increases by 2.5 inches to form a new square with a perimeter of 70 inches. The length of each side of the original square was inches.
Check the picture below.
Answer:
15
Step-by-step explanation:
70 = 4 x (a + 2.5)
70 = 4a + 10
70-10 = 4a
60 ÷ 4 = a
15= a
A box at a miniature golf course contains contains 4 red golf balls, 8 green golf balls, and 7 yellow golf balls. What is the probability of taking out a golf ball and having it be a red or a yellow golf ball? Express your answer as a percentage and round it to two decimal places.
Answer:
=57.89%
Step-by-step explanation:
The total number of golf ball is 4+8+7 = 19
P (red or yellow) = number of red or yellow
------------------------------------
total number of golf balls
= 4+7
-----
19
=11/19
Changing this to a percent means changing it to a decimal and multiplying by 100%
= .578947368 * 100%
=57.8947368%
Rounding to two decimal places
=57.89%
The probability of drawing a red or yellow golf ball from the box can be calculated by dividing the total number of red and yellow balls (11) by the total number of balls in the box (19), resulting in a probability of 11/19 or approximately 57.89%.
Explanation:To calculate the probability of drawing a red or yellow golf ball from the box, we first need to figure out the total number of balls in the box. This is found by adding up the number of each color of balls: 4 red balls + 8 green balls + 7 yellow balls = 19 total balls.
Next, we consider the total number of red and yellow balls, which is 4 red + 7 yellow = 11.
To find the probability, we divide the number of desired outcomes (red or yellow balls) by the total number of outcomes (total balls). So, the probability is 11/19.
To express this as a percentage rounded to two decimal places, we can multiply the result by 100, which gives us approximately 57.89%. So, there is a 57.89% chance of drawing a red or yellow ball from the box.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ11
Identify the area of the figure rounded to the nearest tenth. HELP PLEASE!!
This is equivalent to an 11x15 rectangle with 2 circles each of radius 2cm cut out of it (4 semi-circles = 2 circles in area).
11x11 rectangle = 165cm^2 area.
2 circles of 2cm radius = 2*4pi = 8pi = 25.13
165 - 25.13 = 139.87 [tex]\approx[/tex] 139.9 [tex]cm^2[/tex] (A)
Answer:
139.9
Step-by-step explanation:
First find the area of the circles.
A = pi*r^2
So pi*2^2
2^2 = 4
4*pi = 12.57
Then divide 12.57 by 2 because its only half a circle.
12.57/2 = 6.285
Then multiply 6.285 by 4 since there are 4 half circles.
6.285*4 = 25.14
Now find the area of the square.
A = lw
A= 15*11
A = 165
Now subtract 165 and 25.14.
165 - 25.14 = 139.86
Now round 139.86 to the nearest tenth
So 139.9
Compare the functions below: Which function has the smallest minimum?
A. F(x)
B. G(x)
C. H(x)
D. All three functions have the same minimum value
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
f(x) = -3 sin (x-pi) +2
Sin has a minimum value of -1, but since it is multiplied by a negative, we want its maximum value
sin has a maximum of 1
f (min) = -3(1) +2 = -1
g(x) has a minimum at x =3
g(minimum) = -1
h(x) = (x+7)^2 -1
The smallest a squared value can be is zero
= 0 -1
h(min) =-1
Answer:
D. All three functions have the same minimum value
Step-by-step explanation:
Just did this :)
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?
Answer:
(14.7 , 16.9)
Step-by-step explanation:
it is given that [tex]\bar{x}=15.8[/tex] tons
σ=3.8 tons
n=49
at 95% confidence level α=1-.95=0.05
[tex]z_\frac{\alpha }{2}=z_\frac{0.05}{2}=z_{0.025}\\[/tex]
=1.96 ( from the standard table)
at 95% confidence level the coefficient interval for μ is
[tex]\bar{x}\pm z_\frac{\alpha }{2}\times \frac{\sigma }{\sqrt{n}}[/tex]
[tex]15.8\pm 1.96\times \frac{3.8}{ \sqrt{49}}[/tex]
[tex]15.8\pm 1.1[/tex]
(14.7, 16.9)
A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answer:
The dimensions of enclosed area are 200 and 400/3 feet
Step-by-step explanation:
* Lets explain how to solve the problem
- There are 800 feet of fencing
- We will but it around a rectangular field
- We will divided the field into 2 identical smaller rectangular plots
by placing a fence parallel to one of the field's shorter sides
- Assume that the long side of the rectangular field is a and the
shorter side is b
∵ The length of the fence is the perimeter of the field
∵ We will fence 2 longer sides and 3 shorter sides
∴ 2a + 3b = 800
- Lets find b in terms of a
∵ 2a + 3b = 800 ⇒ subtract 2a from both sides
∴ 3b = 800 - 2a ⇒ divide both sides by 3
∴ [tex]b=\frac{800}{3}-\frac{2a}{3}[/tex] ⇒ (1)
- Lets find the area of the field
∵ The area of the rectangle = length × width
∴ A = a × b
∴ [tex]A=(a).(\frac{800}{3}-\frac{2a}{3})=\frac{800a}{3}-\frac{2a^{2}}{3}[/tex]
- To find the dimensions of maximum area differentiate the area with
respect to a and equate it by 0
∴ [tex]\frac{dA}{da}=\frac{800}{3}-\frac{4a}{3}[/tex]
∵ [tex]\frac{dA}{da}=0[/tex]
∴ [tex]\frac{800}{3}-\frac{4}{3}a=0[/tex] ⇒ Add 4/3 a to both sides
∴ [tex]\frac{800}{3}=\frac{4}{3}a[/tex] ⇒ multiply both sides by 3
∴ 800 = 4a ⇒ divide both sides by 4
∴ 200 = a
- Substitute the value of a in equation (1)
∴ [tex]b=\frac{800}{3}-\frac{2}{3}(200)=\frac{800}{3}-\frac{400}{3}=\frac{400}{3}[/tex]
* The dimensions of enclosed area are 200 and 400/3 feet
At a school dance, the ratio of boys to girls is 7 to 5. What fraction of students at the dance consists of girls? (You must use the fraction form of a ratio
Answer:
5/12
Step-by-step explanation:
The fraction that is girls is the ratio of girls to the total of boys and girls:
girls/(boys+girls) = 5/(7+5) = 5/12
If RT = 6 and RS = 9, then RX =
A - sqrt(54)
B - 13.5
C - 7.2
D - 4
Answer:
Option D RX=4 units
Step-by-step explanation:
we know that
In the right triangle RTS
The cosine of angle TRS is equal to
cos(TRS)=RT/RS
substitute
cos(TRS)=6/9 -----> equation A
In the right triangle RTX
The cosine of angle TRX is equal to
cos(TRX)=RX/RT
substitute
cos(TRX)=RX/6 -----> equation B
∠TRS=∠TRX -----> is the same angle
Match equation A and equation B
6/9=RX/6
RX=6*6/9=4 units
wingspans of adult herons have approximate normal distribution with mean 125cm and a standard deviation 12cm. what proportion of herons have wingspan of excatly 140cm?
Answer:
[tex]P (X = 140) = 0[/tex]
Step-by-step explanation:
We know that the heron wingspan follow a normal distribution with an mean of 125 cm.
In this case we seek to find
[tex]P (X = 140)[/tex]
If X is a random variable that represents the length of the heron wingspan, then X follows a normal distribution and therefore is a continuous random variable.
Then by definition of continuous random variable we have to:
[tex]P (X = a) = 0[/tex] where a is a constant.
That is to say that only the ranges of values can have a different probability of zero. The probability that a continuous random variable is equal to some exact value is always zero.
Finally we can conclude that
[tex]P (X = 140) = 0[/tex]
To find the proportion of herons with a wingspan of exactly 140cm, calculate the z-score using the given mean and standard deviation. Use the z-score to find the area under the normal curve and determine the proportion. The resulting area is approximately 0.8944 or 89.44%.
Explanation:To find the proportion of herons with a wingspan of exactly 140cm, we need to calculate the z-score for 140cm using the formula:
z = (x - μ) / σ
where x is the value being analyzed, μ is the mean, and σ is the standard deviation. Plugging in the values:
z = (140 - 125) / 12 = 1.25
To find the proportion, we can use the z-table or calculator to find the area under the normal curve to the left of z = 1.25. The resulting area is approximately 0.8944 or 89.44%.
The A-1 Car Rental Agency charges $23 per day plus $.10 per mile. The EZ Rental Agency charges $30 per day and $.05 per mile. If x is miles and y is total cost, write the ordered pair (x,y) that shows at what point the two companies charge the same amount.
Answer:
(140, 37)
Step-by-step explanation:
If we are looking for the point where the 2 companies charge the same amount, we need to set the 2 cost function equal to each other and solve for the number of miles that makes the cost the same. The number of miles will also be the same at this cost. That means we need cost functions for each. x is the number of miles that is driven, our independent variable. If A-1 charges .10 per mile, the expression is .1x. If the flat fee is 23, regardless of how many miles you drive, you can expect to pay
y = .1x + 23
If EZ charges .05 per mile, the expression is .05x. If the flat fee is 30, regardless of how many miles you drive, you can expect to pay
y = .05x + 30
If we want to see where the cost functions are equal, we set the right sides of those equations equal to one another and solve for the number of miles that makes the cost the same.
.1x + 23 = .05x + 30 and
.05x = 7 so
x = 140 miles.
In order to find the cost we will pick one of the equations and sub in 140 for x and solve for y.
y = .1(140) + 23
y = 14 + 23
y = 37
The coordinate pair is (140 miles, $37)
This means that at 140 miles driven, the cost is $37 no matter which rental agency you choose.
What is the discontinuity of the function f(x) = the quantity of x squared minus 4 x minus 12, all over x plus 2?
A. (−6, 0)
B. (6, 0)
C. (−2, −8)
D. (2, −4)
Answer:
C. (-2, -8)
Step-by-step explanation:
The function reduces to ...
f(x) = (x^2 -4x -12)/(x +2) = (x -6)(x +2)/(x +2) = x -6 . . . . x ≠ -2
At x=-2, the function would evaluate to ...
f(-2) = -2 -6 = -8
but cannot, because there is a hole in the function definition at that point.
There is a hole at (-2, -8).
QUESTION IS GIVEN IN PICTURE NEED HELP!!!
Answer:
The slopes of f(x) and g(x) are the same.Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
========================================
We have:
[tex]f(x)=3x+6\to m_f=3[/tex]
From the table:
[tex](1,\ 3),\ (2,\ 6)\\\\m_g=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3[/tex]
[tex]m_f=m_g=3[/tex]
Answer:
1st one
Step-by-step explanation:
I really need help with this question!
Answer:
(s-6)/r
option D
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.
Now we are also given that (r,s) is on our line which means s=c(r)+6.
We need to solve this for c to put c in terms of r and s as desired.
s=cr+6
Subtract 6 on both sides:
s-6=cr
Divide both sides by r:
(s-6)/r=c
The slope in terms of r and s is:
(s-6)/r.
Spins a fair spinner numbered 1 - 5 and flips a fair coin. What is the probability of obtaining a factor of 15 and a tail?
Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.
The factors of 15 = [tex]1,\ 3,\ 5[/tex]
Then ,the probability of obtaining a factor of 15 is given by :-
[tex]P(A)=\dfrac{3}{5}[/tex]
The probability of getting a tail :-
[tex]P(B)=\dfrac{1}{2}[/tex]
Since both the events are independent , thus
The probability of obtaining a factor of 15 and a tail is given by :-
[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]
Hence, the required probability : [tex]\dfrac{3}{10}[/tex]
A research group wants to find the opinions’ of city residents on the construction of a new downtown parking garage. What is the population of the survey
downtown shoppers
downtown visitors
downtown workers
city residents
Answer:
downtown workers
Step-by-step explanation:
The research group should do the survey with downtown workers in order to find the opinions for the construction of a new downtown parking garage in downtown. Since the workers need to commute to downtown for work by various modes such as buses, private vehicles, bicycles, taxis, share vehicles, etc., therefore the the research group will get maximum useful information from the downtown workers for the construction of a new parking garage.
Thus, option "downtown workers" is correct.
The population of the survey would be the city residents.
Explanation:The population of the survey would be the city residents. The research group wants to find the opinions of the city residents on the construction of a new downtown parking garage. While downtown shoppers, visitors, and workers could provide valuable insights, the opinions of the city residents would be the most relevant and encompassing for understanding the overall impact of the new downtown parking garage.
Learn more about Population of the survey#SPJ12
Hello, this was one of the questions in a test and above the answer choices, I couldn't find what I found to be the result. I would appreciate it if you help me.
[tex](5ab)^{\tfrac{3}{2}}=\sqrt{(5ab)^3}=\sqrt{125a^2b^3}[/tex]
As a part of a project for his statistics class, Marcus wanted to find out the percentage of American households that still have a landline phone.
*There wasn’t a question for this so I thought I would post it. The answer is C. 463 households!*
How many households is 463 households
Answer:
C
Step-by-step explanation:
Just got it right.
HELPPPP!!!!
Which model does the graph represent?
Answer:
C. y = Ae^(-(x-b)²/c)
Step-by-step explanation:
A is a model of exponential growth.
B is a model of exponential decay.
D is a "logistic function" model of growth in an environment of limited resources. It produces an "S" shaped curve.
The given bell-shaped curve can be described by the function of C, which decays either side of an axis of symmetry.
The model that the graph represent is C that is y = Ae^(-(x-b)²/c).
A is an exponential growth model.
B is an exponential decay model.
D is a "logistic function" model of growth in a resource-constrained setting. It results in a "S" shaped curve.
The function of C, which decays either side of an axis of symmetry, can be used to describe the provided bell-shaped curve.
For such more question on graph
https://brainly.com/question/19040584
#SPJ2
f(x)=8−4x−x^3
g(x)=x^2+7x−9
Find f(x)+g(x).
Select one:
a. x^3+x^2+3x−1
b. −x^3+x+3x−1
c. −x^3+x^2+11x−9
d. 8x^2+3x−9x^3
Answer:
its answer is -x^3+x^2+3x-1
Step-by-step explanation:
f(x) +g(x)
= 8-4x-x^3+x^2+7x-9
= -x^3+x^2+3x-1
Answer:
The value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=8-4x-x^3[/tex]
[tex]g(x)=x^2+7x-9[/tex]
We have to find the value of f(x)+g(x).
[tex]f(x)+g(x)=(8-4x-x^3)+(x^2+7x-9)[/tex]
[tex]f(x)+g(x)=8-4x-x^3+x^2+7x-9[/tex]
On combining like terms we get
[tex]f(x)+g(x)=-x^3+x^2+(-4x+7x)+(8-9)[/tex]
On simplification we get
[tex]f(x)+g(x)=-x^3+x^2+3x-1[/tex]
Therefore the value of f(x)+g(x) is [tex]-x^3+x^2+3x-1[/tex].
Drag each label to the correct location on the chart.
Classify the expressions based on whether they represent real numbers or complex numbers.
The numbers are √(-5)^2, 400, -9+10i^2, 0+5i, i^8, √-16, -2+6i, and √10
Thank you!
Answer:
Step-by-step explanation:
Brandy watched a beetle and a spider on the sidewalk. The beetle crawled 2/5 of a yard and the spider crawled 3/20 of a yard. How much farther did the beetle crawl than the spider?
Answer:
¼ yd
Step-by-step explanation:
2/5 - 3/20
1. Find the lowest common denominator of the two fractions.
The LCD of 5 and 20 is 20.
2. Give the fractions the same LCD
2/5 - 3/20 = 8/20 - 3/20
3. Subtract the numerators
Keep the same denominator.
8/20 - 3/20 = 5/20
4. Simplify the fraction
5/20 = ¼
The beetle crawled ¼ yd further than the spider.
Which is the correct awnser ?
Answer:
△ABC ~ △DEF
Step-by-step explanation:
the AA (angle angle) postulate is a postulate that says two triangles can be similar if they have two congruent angles. using this postulate with how each triangle has a 90° angle and ∠F is congruent to ∠C, we can determine that △ABC ~ △DEF.
The correct answer is C. OBC DE because of the definition of similarity in terms of similarity transformations.
A similarity transformation is a transformation that maps a figure onto a similar figure. A similar figure is a figure that has the same shape as the original figure, but may be a different size and orientation.
A rigid transformation is a transformation that maps a figure onto a congruent figure. A congruent figure is a figure that has the same size and shape as the original figure.
Since a series of rigid transformations maps F onto C where F is congruent to C, then the rigid transformations must have preserved the shape and size of F. This means that the rigid transformations must have been similarity transformations.
Therefore, the statement "OBC DE because of the definition of similarity in terms of similarity transformations" is true.
For such more question on similarity
https://brainly.com/question/29789257
#SPJ2
A cylindrical pail that has the base area of 9 pi inches squared and a height of 10 inches. One friend bought a pyramid mold with a square base with edge length of 4 inches and height of 7 inches. The other friend bought a cone with a radius of 2.5 inches and the height of six inches. What is the volume of these three objects?
Answer:
cylinder — 90π in³pyramid — 37 1/3 in³cone — 12.5π in³Step-by-step explanation:
The volume of a cylinder is given by ...
V = Bh . . . . . where B is the base area and h is the height
The volume of a pyramid or cone is given by ...
V = (1/3)Bh . . . . . where B is the base area and h is the height
The area of a square of side length s is ...
A = s²
The area of a circle of radius r is ...
A = πr²
___
Using these formulas, the volumes of these objects are ...
cylinder: (9π in²)(10 in) = 90π in³
square pyramid: (1/3)(4 in)²(7 in) = 37 1/3 in³
cone: (1/3)(π(2.5 in)²)(6 in) = 12.5π in³ . . . . slightly larger than the pyramid
Answer:
12.5
Step-by-step explanation:
Because of Theorem 5.47 any function that is continuous on (0, 1) but unbounded cannot be uniformly continuous there. Give an example of a continuous function on (0, 1) that is bounded, but not uniformly continuous.
Answer:
[tex]f: (0,1) \to \mathbb{R}[/tex]
[tex]f(x) = \sin(1/x)[/tex]
Step-by-step explanation:
f is continuous because is the composition of two continuous functions:
[tex]g(x) = \sin(x)[/tex] (it is continuous in the real numbers)
[tex]h(x) = 1/x[/tex] (it is continuous in the domain (0,1))
It is bounded because [tex]-1 \leq \sin(\theta) \leq 1[/tex]
And it is not uniformly continuous because we can take [tex]\varepsilon = 1[/tex] in the definition. Let [tex] \delta > 0[/tex] we will prove that there exist a pair [tex]x,y\in \mathbb{R}[/tex] such that [tex]|x-y|< \delta[/tex] and [tex]|f(x) -f(y)|> \varepsilon = 1[/tex].
Now, by the archimedean property we know that there exists a natural number N such that
[tex] \frac{1}{N} < 2\pi \delta[/tex]
[tex]\Rightarrow \frac{1}{2\pi N} < \delta[/tex].
Let's take [tex]x = \frac{1}{2\pi N + \pi/2}[/tex] and [tex]y = \frac{1}{2\pi N + 3\pi/2}[/tex]. We can see that
[tex]|x-y| = \frac{1}{2\pi N + \pi/2}-\frac{1}{2\pi N + 3\pi/2}<\frac{1}{2\pi N} <\delta[/tex]
And also:
[tex]|f(x)- f(y)| = |f(2\pi N + \pi/2) - f(2\pi N + 3\pi/2)| = |1 - (-1)| = 2 > \varepsilon[/tex]
And we conclude the proof.
The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20.
True or false
Answer:
True
Step-by-step explanation:
The binomial distribution that has a probability of success equal to .20, would be left skewed for sample size of 20.
The given statement "The binomial distribution that has a probability of success equal to .20 would be left skewed for sample size 20" is false.
The statement is incorrect. The binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would not necessarily be left-skewed. The shape of the binomial distribution depends on the values of the probability of success and the sample size.
In general, for a binomial distribution with a small probability of success (such as 0.20) and a large sample size (such as 20), the distribution tends to approximate a normal distribution. As the sample size increases, the binomial distribution becomes more symmetric and bell-shaped.
Therefore, it is not accurate to claim that the binomial distribution with a probability of success equal to 0.20 and a sample size of 20 would be left-skewed.
To know more about binomial distribution:
https://brainly.com/question/33656163
#SPJ2
How do you solve for n^3 + 3n^2 + n - 33 = 0?
Answer:
one real root: n ≈ 2.38450287889
Step-by-step explanation:
My favorite solution method for higher-degree polynomials is to use a graphing calculator.
Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).
You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.
__
Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...
y = (n +2.692)² + 6.591
Hence, the complex roots will be near -2.692±i√6.591.
_____
There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...
n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889
Can someone help me with this math question WILL GIVE 20 POINTS. By the way it’s not 51.496
Below is the formula for the circumference of a circle
C = 2πr
This question gives us the diameter. To find the radius (r) you would divide the diameter by two like so...
16.4/ 2 = 8.2
Plug what you know into the formula and solve...
π = 3.14
r = 8.2
C = 2(3.14)(8.2)
C = 6.28(8.2)
C = 51.496
In the question it asks to round to the nearest tenth like so...
51.5
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Step-by-step explanation:
51.496 rounded to the nearest tenth is 51.5