Subtract 28.9 – 9.25 =_____
Answer:
19.65
Step-by-step explanation:
28.9-9.25=19.65
Noise levels at 5 volcanoes were measured in decibels yielding the following data: 127,174,157,120,161 Construct the 98% confidence interval for the mean noise level at such locations. 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:
The critical value used is T = 3.747.
The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation.
Sample mean:
[tex]\overline{x} = \frac{127+174+157+120+161}{5} = 147.8[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(127-147.8)^2+(174-147.8)^2+(157-147.8)^2+(120-147.8)^2+(161-147.8)^2}{4}} = 23.188[/tex]
Confidence interval:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 5 - 1 = 4
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 4 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.747, which is the critical value used.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.747\frac{23.188}{\sqrt{5}} = 38.856[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 147.8 - 38.856 = 108.944
The upper end of the interval is the sample mean added to M. So it is 147.8 + 38.856 = 186.656.
The 98% confidence interval for the mean noise level at such locations is (108.944, 186.656).
8P + 2 > 3P - 15
solve for p
Answer: p >-17/5
Step-by-step explanation:
Answer:
P = [tex]\frac{-17}{5}[/tex]
Step-by-step explanation:
Substract 3P from both sides:
5P + 2 > - 15
Subtract 2 from both sides:
5P > -17
Divide both sides by 5:
P = [tex]\frac{-17}{5}[/tex]
12. What is the solution of the system of equations?
y = - 2x + 5
y = -2x + 20
no solution
(1,3)
infinitely many solutions
Answer:
no solutions
Step-by-step explanation:
y = - 2x + 5
y = -2x + 20
Set the two equations equal
- 2x + 5 = -2x + 20
Add 2x to each side
- 2x+2x + 5 = -2x+2x + 20
5 = 20
This is never true so there are no solutions
Answer:
no solution
Step-by-step explanation:
Hi there!
We are given this system of equations:
y=-2x+5
y=-2x+20
and we want to find the solution (the point in which the lines intersect)
There are 3 ways to solve a system, but let's use substitution in this case
Both equations are set to y, so they should be equal to each other via a property known as transitivity (if a=b and b=c, then a=c)
-2x+5=-2x+20 (the same as y=y)
Now let's solve for x
add 2x to both sides
5=20
In this case, we got an untrue statement. If this happens, then the lines won't intersect.
If they won't intersect, there's no solution
Hope this helps!
The population of your hometown can be modeled by the equation P equals 2538 left parenthesis 1.025 right parenthesis to the power of t where t represents the number of years since 2000. What was the population of your hometown in 2000? By what percent did the population increase each year?
Answer:
2538
2.5%
Step-by-step explanation:
The population equayio since year 2000 can be modeled mathematically as :
P = 2538(1.025)^t
This is an exponential growth function which is represented by the general formula :
y = a(b)^t
Where, a is the initial population ;
b = growth factor ; b = (1 + r) where r = growth rate
Comparing the equations, the population in year 2000 represents the initial population, a = 2538
The percentage Rate of increase in population is :
(1 + r) = 1.025
r = 1.025 - 1
r = 0.025 ; 0.025 * 100% = 2.5%
Simplify 7a – 11b + 4ab – 6a + 5b.
The theoretical mean of a distribution is also known as its ______________.
Answer:
skewness
Step-by-step explanation:
Average.
The average of a set of observations is the most important and useful measure of statistics and is a position measure, as it shows the positions of the numbers to which it refers. The average value is involved in several types of statistics and is examined in almost all statistical distributions. It is generally defined as the sum of the observations by their number. That is, it is the mathematical operation of finding the "mean distance" between two or more numbers.
Learn more about averages in https://brainly.com/question/22390452
There are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes. how many boxes are there all together?
Answer:
There are 51 boxes all together.
Step-by-step explanation:
Since there are three separate, equal-size boxes, and inside each box there are four separate small boxes, and inside each of the small boxes there are three even smaller boxes, to determine how many boxes are there all together, the following calculation must be done:
3 + 3 x 4 + 3 x 4 x 3 = X
3 + 12 + 36 = X
51 = X
Therefore, there are 51 boxes all together.
A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of 187 cars owned by students had an average age of 7.9 years. A sample of 221 cars owned by faculty had an average age of 5.04 years. Assume that the population standard deviation for cars owned by students is 3.07 years, while the population standard deviation for cars owned by faculty is 2.53 years. Determine the 98% confidence interval for the difference between the true mean ages for cars owned by students and faculty. Step 3 of 3 : Construct the 98% confidence interval. Round your answers to two decimal places.
Answer:
Hence the confidence interval (2.2, 3.52).
Step-by-step explanation:
Hence,
The point estimate = [tex]\bar x_{1} - \bar x_{2}[/tex]
= 7.9 - 5.04
= 2.86
Given CI level is 0.98, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.326
Margin of Error
ME = tc x sp
ME = 2.326 \ 0.2817
ME = 0.6552
CI = ([tex]\bar x_{1} - \bar x_{2}[/tex] - tc x sp , [tex]\bar x_{1} - \bar x_{2}[/tex] + tc x sp)
CI = (7.9 - 5.04 - 2.326 x 0.2817 , 7.9 - 5.04 - 2.326 x 0.2817
CI = (2.2 , 3.52)
The table below shows the age of some participants in a quiz competition and the number of questions they could answer correctly: Age (years) (x) 15 21 17 22 16 19 18 Number of questions they could answer (y) 17 17 17 17 17 17 17 What is the correlation coefficient for the data, and what does it represent? (5 points) 0; it represents no correlation between x and y 1; it represents a linear positive correlation between x and y −1; it represents a linear negative correlation between x and y 1; it represents a linear negative correlation between x and y
Your answer is:
A) 0; it represents no correlation between x and y
keep dreaming
I’m so bad at this pls-
Answer:
[tex]5 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt[]{5} \times \sqrt{2} \\ = 5\sqrt{2} [/tex]
Hope it is helpful....find the radius of the circle
help is VERY appreciated!!
Answer:
17/16 =x
Step-by-step explanation:
The triangle is a right triangle so we can use Pythagorean theorem
a^2+b^2 = c^2
x^2 + 9^2 = (x+8)^2
FOIL
x^2+81=x^2+16x+64
Subtract x^2 from each side
81 = 16x+64
Subtract 64 from each side
81 -64 = 16x+64-64
17 =16x
Divide by 16
17/16 =x
If there is a die that has 12 sides, that are numbered 1 to 12, what is the probability that she will roll either a 3 or a 9
Answer:
2/12 = 1/6
Step-by-step explanation:
To find the probability of something with an equal chance of each outcome, we can apply the formula (number of favorable outcomes)/(number of total outcomes). Because there is an equal chance for each side of the die to be landed on, we can apply this.
On a 12 sided die, there are 12 sides. Two of those sides are 3 and 9. Therefore, there are two favorable outcomes (3 and 9). There are 12 sides to choose from, so there are 12 total outcomes, making the probability 2/12 = 1/6
If 1 kilogram (kg) is equal to about 2.2046 pounds (lbs.), what is the value of 1kg/2.2046lbs? What is the value of 2.2046lbs/1kg?
Step-by-step explanation:
The relation between kg and lbs is :
1 kg = 2.2046 lbs
We need to find the values of 1kg/2.2046lbs and 2.2046lbs/1kg.
So,
[tex]\dfrac{1\ kg}{2.2046\ lbs}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]
and
[tex]\dfrac{2.2046\ lbs}{1\ kg}=\dfrac{2.2046\ lbs}{2.2046\ lbs}\\\\=1[/tex]
Hence, this is the required solution.
Answer:
Both are same as 1.
Step-by-step explanation:
1 kg = 2.2046 lbs
So,
[tex]\frac{1 kg}{2.2046 lbs }=\frac{1 kg }{1 kg} = 1[/tex]
And
[tex]\frac{2.2046 lbs}{1 kg }=\frac{1 kg }{1 kg} = 1[/tex]
the diameter of a circle is 7 inches.find it's area to the nearest 10th
Answer: d=7 inches
r=7/2
r=3.5
A=πr²
A=3.14(3.5inch)²
A=3.14×12.25inch²
A=38.465inch²
A≈38.47inch²
sin x =.3 what is the cos x =?
Answer:
If you're asking what cosine 3 is it's 0.9999986292247
Step-by-step explanation:
I don't really understand the question
What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?
1
–1
i
–i
Answer:
Answer is -1
Step-by-step explanation:
i1 = i
i2 = -1
i3 = -i
i4 = 1
i0 × i1 × i2 × i3 × i4 = 1 × i × (- 1) × (- i) × 1 = i2 = - 1
Answer:the answer is -1
Step-by-step explanation:
find the x – intercepts of the graph of the function f(x) = x2 – 2x + 1
A) (1,0)
B) (-1,0)
C) (0,-1)
D) (0,1)
PLEASE HELP ME ITS URGENT , WILL MARK AS BRAINLIEST!!!
Answer:
[tex]\boxed{\sf A) ( 1,0) }[/tex]
Step-by-step explanation:
A quadratic function is given to us and we need to find the x Intercept of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = x^2 -2x + 1 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies x^2 -2x + 1 = 0 [/tex]
Split the middle term ,
[tex]\sf \implies x^2-x-x+1=0[/tex]
Take out common terms ,
[tex]\sf \implies x( x -1) -1( x -1) = 0[/tex]
Take out (x - 1 )as common ,
[tex]\sf \implies (x - 1 )(x-1) = 0[/tex]
Equate with 0 ,
[tex]\sf \implies x = 1,1 [/tex]
Therefore the root of the function is 1. Hence the x Intercept is (1,0)
Hence the x Intercept is (1,0) .
Step-by-step explanation:
x² - 2x + 1 = 0
x² - (x + x) + 1 = 0
x² - x - x + 1 = 0
x(x - 1) - 1(x - 1) = 0
(x - 1)(x - 1) = 0
x = 1
Hence,
Option A
The triangles below are similar (being similar means there is a proportional relationship between the measures of each of the sides). What is the length of ED? (HINT: You can solve this question by using the MATH Ratio Table)
=================================================
Work Shown:
ED/DF = AB/AC
x/24 = 12/16
16x = 24*12
16x = 288
x = 288/16
x = 18
------------
Explanation:
Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.
So for instance, another proportion you could solve is ED/AB = DF/AC.
The key is to keep up the same pattern when forming the ratios.
What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.
Which set of angles are supplementary
Which of the following
statements is true about
angle K?
K
R
a. Angle K is obtuse
b. angle K is acute
c. angle K is greater than
90
d. angle K is a right angle
Answer:
angle k is acute.
Step-by-step explanation:
it is less than 90 degrees
Answer:
a., b.
Step-by-step explanation:
Angle K looks like an acute angle with measure between 0 and 90 degrees.
Answer: a., b.
A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
Abebe babe
Answer:
It multiplies
Step-by-step explanation:
if the number of hours changes to example to 2 then you multiply 60 by 2 resulting in 120miles in 2 hours
Expresa de. Forma fraccionaria y decimal 7%
Answer:
7% = .07 = [tex]\frac{7}{100}[/tex]
Step-by-step explanation:
Select the correct answer.
Given the following formula, solve for a.
Answer: option C is correct
Step-by-step explanation:[tex]s=( \alpha +\beta +c)/2\\2s=\alpha +\beta +c\\2s-\beta -c=\alpha \\\alpha =2s-\beta -c[/tex]
A certain brand of coffee comes in two sizes. An 11.5-ounce package costs $.4.24 . A 27.8-ounce package costs $9.98.
Find the unit price for each size. Then state which size is the better buy based on the unit price.
Round your answers to the nearest cent.
Answer:
Small (11.5) is 37 cents per ounce.
Large (27.8) is 36 cents per ounce.
27.8 ounces is the better buy.
Here is a cube of side length 2.5 cm.
2.5 cm
Work out the surface area of this cube.
Answer:
2.5 x 2.5 = 6.25cm^2 (area of one side)
6.25 * 6 = 37.25cm^2 (area of all sides)
Step-by-step explanation:
y+2 2y2-y+3 y-2
In the equation
1,2 - 1
+
the value of a is:
„V+1
1 - ע
Answer:
The answer:
I think the choose (1) 1
Evaluate I=∫(sinx+9y)dx + (4x+y)dy for the nonclosed path ABCD in the figure.
Close the path by connecting D to A. Then by Green's theorem, the integral over the closed path ABCDA - which I'll just abbreviate C - is
[tex]\displaystyle \oint_C (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy \\\\ = \iint_{\mathrm{int}(C)}\frac{\partial(4x+y)}{\partial x} - \frac{\partial(\sin(x)+9y)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy[/tex]
(where int(C ) denotes the region interior to the path C )
The remaining double integral is -5 times the area of the trapezoid, which is
[tex]\displaystyle -5\iint_{\mathrm{int}(C)}\mathrm dx\,\mathrm dy = -\frac52\times(12+4)\times4=-160[/tex]
To get the line integral you want, just subtract the integral taken over the path DA. On this line segment, we have x = 0 and dx = 0, so this integral reduces to
[tex]\displaystyle\int_{DA}y\,\mathrm dy = \int_{12}^0y\,\mathrm dy = -\int_0^{12}y\,\mathrm dy = -72[/tex]
Then
[tex]\displaystyle \int_{ABCD} (\sin(x)+9y)\,\mathrm dx + (4x+y)\,\mathrm dy = -160 - (-72) = \boxed{-88}[/tex]
A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as P = 0.006A*2-0.02A + 120. Find the age of a man whose normal blood pressure measures 129 mmHg. Round your answer to the nearest year. The man would be ? years old.
Answer:
The man would be 40 years old.
Step-by-step explanation:
Blood pressure as function of age:
Is given by the following equation:
[tex]P = 0.006A^2 - 0.02A + 120[/tex]
Find the age of a man whose normal blood pressure measures 129 mmHg.
This is A for which P = 129. So
[tex]129 = 0.006A^2 - 0.02A + 120[/tex]
[tex]0.006A^2 - 0.02A - 9 = 0[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
Quadratic equation with [tex]a = 0.006, b = -0.02, C = -9[/tex]. So
[tex]\Delta = (-0.02)^2 - 4(0.006)(-9) = 0.2164[/tex]
[tex]A_{1} = \frac{-(-0.02) + \sqrt{0.2164}}{2*(0.006)} = 40.4[/tex]
[tex]A_{2} = \frac{-(-0.02) - \sqrt{0.2164}}{2*(0.006)} = -37.1[/tex]
Age has to be a positive number, so rounding to the nearest year:
The man would be 40 years old.
Norman and Suzanne own 35 shares of a fast food restaurant stock and 63 shares of a toy company stock. At the close of the markets on a particular day in 2004, their stock portfolio consisting of these two stocks was worth $1596.00. The closing price of the fast food restaurant stock was $19 more per share than the closing price of the toy company stock on that day. What was the closing price of each stock on that day? The price per share of the fast food restaurant stock is
Answer:
closing price of the fast food stock was $997.50
closing price of the toy company stock was $598.50
the price per fast food share was $28.50
Step-by-step explanation:
x = price per share fast food
y = price per share toy company
35x + 63y = 1596
x = y + 19
=>
35(y+19) + 63y = 1596
35y + 665 + 63y = 1596
98y + 665 = 1596
98y = 931
y = $9.50
=>
x = 9.5 + 19 = $28.50
the value of the whole fast food stock was
35x = 35×28.5 = $997.50
the cake if the whole toy company stock was
63y = 63×9.5 = $598.50
