Answer:
this is an equation of closure property of rational numbers under addition
Step-by-step explanation:
this is the meaning of it
for every a and b belongs to q then a+b belongs to q
find m∠H
What does m∠H happened to equal
Answer:
[tex]m\angle H = 30^o[/tex]
Step-by-step explanation:
Given
See attachment
Required
Find [tex]m\angle H[/tex]
To calculate [tex]m\angle H[/tex], we make use of:
[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
So, we have:
[tex]\cos(H) = \frac{GH}{HI}[/tex]
This gives:
[tex]\cos(H) = \frac{10\sqrt3}{20}[/tex]
[tex]\cos(H) = \frac{\sqrt3}{2}[/tex]
Take arccos of both sides
[tex]m\angle H = cos^{-1}(\frac{\sqrt3}{2})[/tex]
[tex]m\angle H = 30^o[/tex]
Suppose f"(x) = -9 sin(3x) and f'(0) = -4, and f(0) = -2
Find f(pi/4)
Answer:
9sin (3)and f,(0)=4,AND f(0)=2
Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form
Answer:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]
Step-by-step explanation:
Hi there!
Slope-intercept form: [tex]y=mx+b[/tex] where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of y when x is 0)
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (15,2.2) and (5,1.6):
[tex]m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}[/tex]
Therefore, the slope of the line is [tex]\frac{\displaystyle 3}{\displaystyle 50}[/tex]. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]
Plug in a given point and solve for b:
[tex]1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b[/tex]
Therefore, the y-intercept is [tex]\frac{\displaystyle 13}{\displaystyle 10}[/tex]. Plug this back into [tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+b[/tex]:
[tex]y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}[/tex]
I hope this helps!
Based on the graph, what is one solution to the equation f(x) = g(x)?
x= -4
x = 2.5
x= -5.1
x = 2.75
Answer:
x= -5.1
Step-by-step explanation:
The solution to f(x) = g(x) is where to two graphs intersect
The graphs meet at
about x=2 and x = -5
The best answer listed is x = -5.1
Answer:
x = −5.1
Step-by-step explanation:
I took the practice test
The minimum number of parallel faces that a prism should have is
Answer:
The minimum number of parallel faces that a prism should have is three pairs
Answer:
The minimum number of parallel faces that a prism should have is three faces
Type the correct answer in each box. Use numerals instead of words.
What is the equation of the quadratic function shown in the graph?
Answer:
y - 8 = -2(x + 1)^2
Step-by-step explanation:
The vertex of this parabola is (-1, 8). It opens downward, so the x^2 term has a negative coefficient. The zeros are (-3, 0) and (1, 0), and the y-intercept is (0, 7).
Through the vertex form of the equation of a parabola we get:
y - (8) = a(x - (-1)) + 7, or
y - 8 = a(x + 1)^2. Find coefficient a by substituting the coordinates (-3, 0) in this equation:
0 - 8 = a(-3 + 1)^2, or
-8 = a(-2)^2, or a = -2
The desired equation is
y - 8 = -2(x + 1)^2
A scientist runs an experiment involving a culture of bacteria. She notices that the mass of the bacteria in the culture increases exponentially with the mass increasing by 249% per week. What is the 1-week growth factor for the mass of the bacteria
9514 1404 393
Answer:
3.49
Step-by-step explanation:
The growth factor is one more than the growth rate:
growth factor = 1 + growth rate
= 1 + 249% = 1 +2.49
growth factor = 3.49
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.
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
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
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:
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]
Which set of angles are supplementary
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)
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
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.
Toyotas manufactured in the 1990s have a mean lifetime of 22.6 years, with a standard deviation of 3.1 years. The distribution of their lifetimes is not assumed to be symmetric. Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least 95% of the Toyotas
Answer:
The answer is "8.74 and 36.46 years"
Step-by-step explanation:
Mean (life-time)=22.6 years
standard deviation= 3.1 years
We must find out how many standard deviations are 95% of the data.
[tex]1 - \frac{1}{k^2} = 0.95\\\\1 - 0.95 = \frac{1}{k^2}\\\\\frac{1}{k^2} = 0.05\\\\\frac{1}{0.05} =k^2\\\\k^2 = 20\\\\ k = 4.47[/tex]
Calculating the lower limit and upper limit:
[tex]Lower\ limit = 22.6 - 4.47(3.1) = 22.6 - 13.86 = 8.74\\\\Upper\ limit = 22.6 + 4.47(3.1) = 22.6 + 13.86 = 36.46[/tex]
Limit is 8.74 years to 36.46 years
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
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.
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
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]
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]
calculate the total surface area of a cuboid with the following dimensions. 4m by 6m by 8m
Answer:
V = 192 m^3
Step-by-step explanation:
The volume of a cuboid is given by
V = l*w*h
V = 4m * 6m *8m
V = 192 m^3
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:
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.
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
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%
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!
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).
