Answer:
A) The range for the month of October is 6.
C) 35 summarizes the data with a single number.
E) 16 describes how the values vary with a single number.
Step-by-step explanation:
Week 1 | 40 Week 1 | 32
Week 2 | 34 Week 2 | 30
Week 3 | 36 Week 3 | 40
Week 4 | 40 Week 4 | 24
The ordered data can be written out as follows :
October :
34, 36, 40, 40
November :
24, 30, 32, 40
Whole data:
24, 30, 32, 34, 36, 40, 40, 40
Range = maximum - minimum :
October range = 40 - 34 = 6
Summarizing the fat with a single number :
Take the median of the whole data :
1/2(n+1)th term
1/2(9) = 4.5 th term
(34 + 36) /2 = 35
Median for October :
(36 + 40) / 2 = 38
Variation of all values :
Take the range :
40 - 24 = 16
Suppose that the middle 68% of speeding ticket fines on a highway fall between 93.18 and 118. Give an approximate estimate of the standard deviation of the speeding ticket fines. Assume the fine amount has a normal distribution
Answer:
The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
Middle 68% of speeding ticket fines on a highway fall between 93.18 and 118.
This means that 93.18 is one standard deviation below the mean and 118 is one standard deviation above the mean. That is, the difference between 118 and 93.18 is worth two standard deviations. So
[tex]2s = 118 - 93.18[/tex]
[tex]s = \frac{(118 - 93.18)}{2}[/tex]
[tex]s = 12.41[/tex]
The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.
Write the equation of the lines which have the following parameters. Write the equation in slope intercept form.
1. slope = 3; y-intercept = 5
2. slope = 2/5; y-intercept =-10
3. slope = -3/2; y-intercept = -2
4. slope = 18; y-intercept = 0
5. slope = -3.253; y-intercept =-14.159
6. Challenge problem: x-intercept = -2; y-intercept = 6
Answer:
Step-by-step explanation:
Slope intercept form is :
y = mx + b
where m is the slope and b is the y-intercept.
So, given slope and y-intercept, all you have to do is plug in slope for m and y-intercept for b.
1.) y = 3x + 5
2.) y = 2/5x - 10
3.) y = -3/2x - 2
4.) y = 18x
5.) y = -3.253x - 14.159
For question 6, you need to calculate the slope given the two points then plug in the slope and y-intercept to get the equation.
So to find slope, you use the equation below:
slope = (y2 - y1) / (x2 - x1) = (6-0) / (0 - -2) = (6) / (2) =3
6.) y = 3x + 6
The following measurements (in picocuries per liter) were recorded by a set of carbon dioxide detectors installed in a manufacturing facility: 799.2,784.3,803.8,806.8,780.5,794.8 Using these measurements, construct a 95% confidence interval for the mean level of carbon dioxide present in the facility. Assume the population is approximately normal. Step 3 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
(783.806 ; 805.994)
Step-by-step explanation:
Given the sample :
X : 799.2,784.3,803.8,806.8,780.5,794.8
Sample size, n = 6
Sample mean, xbar = Σx / n = 794.9
Sample standard deviation, s = 10.574 ( calculator)
Tcritical at 95%, df = 6 - 1 = 5 equals 2.57
Confidence interval :
Xbar ± standard error
Standard Error = Tcritical * s/√n
Standard error = 2.57 * 10.574/√6 = 11.094
Lower boundary = (794.9 - 11.094) = 783.806
Upper boundary = (794.9 + 11.094) = 805.994
(783.806 ; 805.994)
What equation can I use to solve for x?
What equation can I use to solve for y?
Answer:
125+9x-8=180
6x+13+6y+29=180
Step-by-step explanation:
What is the y-intercept for f(x) = x2 - 4x +6 ?
Answer:
6
Step-by-step explanation:
the constant is the y-intercept
(I’ll give points + brainalist for the correct answer with an explanation)
Answer:
b
Step-by-step explanation:
divide 1/4 by 20
Find the area of the figure 2m 3m 6m 3m
Identify like Terms
8x2 yx3 9x2 y2 5y
25x to the 2nd power minus 49
Answer:
(5x+7) (5x-7)
Step-by-step explanation:
you can look up the answer on symbolab if needed
the width of a rectangle is 7 cm less than twice its length. its area is 30 square cm. find the dimensions
Answer:
l = 6 cm
w = 5 cm
Step-by-step explanation:
l(2l - 7) = 30
2l^2 - 7l - 30
(2l + 5)(l - 6)
l = 6
2(6) - 7 = 5
If the standard deviation of a data set were originally 4, and if each value in
the data set were multiplied by 1.75, what would be the standard deviation of
the resulting data?
A. 3
B. 4
c. 7
D. 1
Please help
Answer:
it's a.
Step-by-step explanation:
you have to find the mean
Someone walked%s the length of this room
then walked backward 4 the length of this
room before walking forward / the length
of the room and hiding the key there. How
far across the room (as a fraction) is the
key? Use a "/" as a fraction bar in your
answer.
Answer:
E-e-e-e-et-t-t-o.... B-b-b-b-b-baka h-h-huh... g-g-g-g-g-g-gOmensas-s-s-sai S-senpai...
Step-by-step explanation:
uHM yeah
Help me!! Thank you for the help!!
Answer:
D. 0.34
Step-by-step explanation:
0.24²+0.31²=x² then you find the square root
Answer:
the answer is 0.28, Because of SEGEMENT FH IS HALF OF FG BECAUSE ITS A RIGHT ANGLE.
Match each equation on the left with the number and type of its solutions on the right.
Answer:
Step-by-step explanation:
1). Given equation is,
2x² - 3x = 6
2x² - 3x - 6 = 0
To find the solutions of the equation we will use quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a, b and c in the formula,
a = 2, b = -3 and c = -6
x = [tex]\frac{3\pm\sqrt{(-3)^2-4(2)(-6)}}{2(2)}[/tex]
x = [tex]\frac{3\pm\sqrt{9+48}}{4}[/tex]
x = [tex]\frac{3\pm\sqrt{57}}{4}[/tex]
x = [tex]\frac{3+\sqrt{57}}{4},\frac{3-\sqrt{57}}{4}[/tex]
Therefore, there are two real solutions.
2). Given equation is,
x² + 1 = 2x
x² - 2x + 1 = 0
(x - 1)² = 0
x = 1
Therefore, there is one real solution of the equation.
3). 2x² + 3x + 2 = 0
By applying quadratic formula,
x = [tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
x = [tex]\frac{-3\pm\sqrt{3^2-4(2)(2)}}{2(2)}[/tex]
x = [tex]\frac{-3\pm\sqrt{9-16}}{4}[/tex]
x = [tex]\frac{-3\pm i\sqrt{7}}{4}[/tex]
x = [tex]\frac{-3+ i\sqrt{7}}{4},\frac{-3- i\sqrt{7}}{4}[/tex]
Therefore, there are two complex (non real) solutions.
Question #3 show steps or how you know
Answer: Choice D)
(-1.5, -1) and (0, 1)
=============================================================
Explanation:
Exponents can be a bit clunky if you have too many of them, and if they're nested like this. Writing something like e^(x^2) may seem confusing if you aren't careful. I'm going to use a different notation approach. I'll use "exp" notation instead.
So instead of writing something like e^(x^2), I'll write exp(x^2).
The given derivative is
f ' (x) = exp(x^4-2x^2+1) - 2
and this only applies when -1.5 < x < 1.5
Apply the derivative to both sides and we'll find the second derivative
f ' (x) = exp(x^4-2x^2+1) - 2
f '' (x) = d/dx[ exp(x^4-2x^2+1) - 2 ]
f '' (x) = exp(x^4-2x^2+1)*d/dx[ x^4-2x^2+1 ]
f '' (x) = exp(x^4-2x^2+1)*(4x^3-4x)
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
From here, we need to find the roots of f '' (x).
Set f '' (x) equal to zero and solve to get...
f '' (x) = 0
(4x^3-4x)*exp(x^4-2x^2+1) = 0
4x^3-4x = 0 ..... or .... exp(x^4-2x^2+1) = 0
4x(x^2-1) = 0
4x(x+1)(x-1) = 0
4x = 0 or x+1 = 0 or x-1 = 0
x = 0 or x = -1 or x = 1
Those are the three roots. We ignore the equation exp(x^4-2x^2+1) = 0 because it doesn't have any real number solutions.
---------------------
The three roots of x = 0 or x = -1 or x = 1 represent possible locations of points of inflection (POI). Recall that a POI is where the function changes concavity. To determine if we have a POI or not, we'll need to a sign test.
Draw out a number line. Plot -1, 0, and 1 in that order on it. Pick something to the left of -1 but larger than -1.5, lets say we pick x = -1.2. Plugging this into the second derivative function leads to...
f '' (x) = (4x^3-4x)*exp(x^4-2x^2+1)
f '' (-1.2) = (4(-1.2)^3-4(-1.2))*exp((-1.2)^4-2(-1.2)^2+1)
f '' (-1.2) = -2.563
That value is approximate. The actual value itself doesn't matter. What does matter is the sign of the result. The negative second derivative value tells us we have a concave down region. So we just found that f(x) is concave down for the interval -1.5 < x < -1, which converts to the interval notation (-1.5, -1)
Repeat the process for something between x = -1 and x = 0. I'll pick x = -0.5 and it leads to f '' (-0.5) = 2.63 approximately. The positive result tells us that we have a concave up region. Therefore, -1 < x < 0 is not part of the answer we're after.
Repeat for something between x = 0 and x = 1. I'll pick x = 0.5 and it produces f '' (0.5) = -2.63 approximately. So the region 0 < x < 1 is also concave down. Meaning that the interval notation (0,1) is also part of the answer.
So far we have the interval notation of (-1.5, -1) and (0,1) as part of our solution set.
Lastly, we need to check something to the right of x = 1, but smaller than 1.5; let's go for x = 1.2
You should find that f '' (1.2) = 2.563 which allows us to rule out the region on the interval 1 < x < 1.5
Overall, the final answer is (-1.5, -1) and (0, 1)
Is -2.4 and 1.5 repeating or terminating decimals?
Answer:
terminating decimals
Step-by-step explanation:
what is the answer to my math problem. Evaluate 32^1/5
the answer is 2
Solution:
32⅕
(2⁵)⅕
Answer is 2
Which of the following numbers makes the statement true? 3/8 > < 3/6
Answer:
2/5
Step-by-step explanation:
3/8 = 375/1000
1/2 = 500/1000
2/5 = 400/1000
The table of values represents a function f(x).
How much greater is the average rate of change over the interval [7, 9] than the interval [4, 6]?
Enter your answer in the box.
Answer:
It is 603 units greater
Step-by-step explanation:
Given
See attachment for table
Average rate of change over (a,b) is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]
For interval [7,9], we have:
[tex][a,b] = [7,9][/tex]
So, we have:
[tex]Rate = \frac{f(9) - f(7)}{9-7}[/tex]
[tex]Rate = \frac{f(9) - f(7)}{2}[/tex]
From the table:
[tex]f(9) = 3878[/tex]
[tex]f(7) = 1852[/tex]
So:
[tex]Rate = \frac{f(9) - f(7)}{2}[/tex]
[tex]Rate = \frac{3878 - 1852}{2}[/tex]
[tex]Rate = \frac{2026}{2}[/tex]
[tex]Rate = 1013\\[/tex]
For interval [4,6], we have:
[tex][a,b] = [4,6][/tex]
So, we have:
[tex]Rate = \frac{f(6) - f(4)}{6-4}[/tex]
[tex]Rate = \frac{f(6) - f(4)}{2}[/tex]
From the table:
[tex]f(6) = 1178[/tex]
[tex]f(4) = 358[/tex]
So:
[tex]Rate = \frac{f(6) - f(4)}{2}[/tex]
[tex]Rate = \frac{1178 - 358}{2}[/tex]
[tex]Rate = \frac{820}{2}[/tex]
[tex]Rate = 410[/tex]
Calculate the difference (d) to get how much greater their rate of change is:
[tex]d = 1013 - 410[/tex]
[tex]d = 603[/tex]
Answer:
603
Step-by-step explanation:
i took it
A survey found that 25% of people gave up their home phone years ago and only use a cell phone now. If 3,000 people said that they only use a cell phone now, how
many total people were surveyed?
Answer:
12000
Step-by-step explanation:
25/100 = 3000/total people surveyed
total people surveyed = 3000×100 / 25
= 12000 people surveyed
Solve for all values of x by factoring.'
x2 + 10x + 21 = 0
Answer:
Step-by-step explanation:
2x+10x=12x
12x=-21
x=-1.75
Answer:
x=-7,-3
Step-by-step explanation:
x2+10x+21
(x+7)(x+3)
x=-7,-3
Devin has a rectangular vegetable garden. He planted tomatoes in section of the garden with an area of 6 square yards. There were 30 square yards remaining for Devin to plant zucchini. Let g represent the total area of the garden. Which equation models the problem? Solve the equation to find the total area of the garden. g =
Answer:
g=30y^2+6y^2
Step-by-step explanation:
30 years left after six were taken
3. Suppose that a parabola has
x-intercepts (-3,0) and (2,0) and goes
through the point (-1,12). Which
quadratic function represents the parabola
in factored form?
A
y=-(2 - 3)(x + 2)
B
y= -2(x − 3)(x + 2)
Y= -2(x+3)(2 – 2)
D.
y= (2 + 1)(x - 2)
Answer:
C. I used to not get this but now I do. hope I helped
The length of a rectangle is 5 more than the width. The area is 500 square feet. Find the length and width of the rectangle.
Answer:
length = 25ft, width = 20ft
Step-by-step explanation:
Let x= width, so length = x+5
Area = l x w so A = x(x+5)
Since the area is given as 500 sqft, your equation is x(x+5)=500.
Although the numbers are easy enough to factor in your head, mathematically the equation can be solved as a quadratic, as follows:
x^2 + 5x -500 = 0
Using either factoring or quadratic formula, x = 20 (the other value is negative). Therefore the width is 20ft and the length is 25ft.
PLS HELP 50 POINTS
A rectangular prism has a surface area of 8 square feet. A similar rectangular prism has a surface area of 200 square feet. How many times larger is the surface area of the larger prism?
25
625
10
5
Answer:
25
Step-by-step explanation:
20x8+5x8=200
20+5=25 the answer would be 25
This is a review of last lesson's concept You have 2 red marbles, 3 black marbles, and 2 blue marbles. You pick a marble, look at it, and replace it in the bag Then you pick a marble again. What is the probability of picking a red marble both times?
62. AAA+AA+A= 246 => A= ?
A.1 B.4 C. 2 D.5 E. 8
Answer:
C. 2
Step-by-step explanation:
222 + 22 + 2 = 246
So A = 2
Help 100 points to answer the page
Answer:
Use trigonometry
sine = opposite leg / hypotenusecosine = adjacent leg / hypotenusetangent = opposite leg / adjacent leg#123/x = sin 68x = 23 / sin 68x = 24.8Choice A
#221/x = tan 26x = 21/ tan 26x = 43.1Choice D
Note. All numbers below are rounded to the nearest tenth#312/x = sin 53x = 12 / sin 53x = 15.0#48/x = tan 34x = 8/tan 34x = 11.9#5x/ 12 = cos 26x = 12 cos 26 x = 10.8#6x / 13 = sin 34x = 13 sin 34x = 7.3#7x / 18 = sin 53x = 18 sin 53 x = 14.4#8x / 10 = tan 30x = 10 tan 30 x = 5.8#9cos X = 21/35 = 3/5#10tan X = 32/24 = 4/3Answer:
the person above me is correct i said that because i did the math and solved it
Step-by-step explanation:
Express 72km/h in meter per sec
Answer:
20meter per second is tw correct answer
20 m/s
Step-by-step explanation:
1km/h = 1000m/3600s = 5m/18s
⇒ 72 × 5 ÷ 18 = 20 (m/s)
12. If one line passes through the points
(-3,8) & (1,9), and a perpendicular line passes
through the point (-2,4), what is another point
that would lie on the 2nd line. Select all that apply.
A. (-1,0)
B. (2,5)
C. (5,2)
D. (-6,3)
E. (8,-3)
F. (-3,8)
9514 1404 393
Answer:
A, F
Step-by-step explanation:
Points A(-1, 0) and F(-3, 8) lie on the 2nd line. (Its equation is 4x+y=-4.)