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 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.
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]
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
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).
Using the Time Series Data for the US Nuclear Electric Power Production, calculate the exponential smoothing forecasts for 2005 through 2010 using alpha equals 0.2. Find the forecast error for each time period. If there is n
Answer:
????????????
I don't know
Simplify 7a – 11b + 4ab – 6a + 5b.
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
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.
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 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
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.
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....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 following images in width and circumference
Step-by-step explanation:
hey guys how do you put a picture like you did ?
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]
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]
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!
annual cost of 35,000 expected to save 40,000 during the first year how many months will the take to recover investment
Answer:
500000
Step-by-step explanation:
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.
Do number 7 plz finding QR
Answer:
QR = sqrt(147)
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
7^2 + QR^2 = 14^2
49 + QR^2 = 196
QR^2 = 196-49
QR^2 = 147
Taking the square root of each side
QR = sqrt(147)
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
Which number can be written on the line to make the inequality true?
3.91 < ___ < 4.23 < 4.44
a) 3.7
b) 3.9
c) 4.1
d) 4.3
Answer:
[tex]3.7[/tex]
Step-by-step explanation:
[tex]3.9 < 3.7[/tex]
Answer:
answer is A
3.7
Step-by-step explanation:
Perimeter (numerical)
Answer:
270 m
Step-by-step explanation:
Add up all the sides
P = 19 +18.8+18.8 +18.8+18.8+40.8+19+40.8+18.8+18.8+18.8+18.8
P = 270 m
Three ounces of cinnamon cost $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?
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
find the constant of variation k for the direct variation. 4x = -y
Answer:
k = - 4
Step-by-step explanation:
The equation representing direct variation is
y = kx ← k is the constant of variation
Given
4x = - y ( multiply both sides by - 1 )
- 4x = y , that is
y = - 4x ← in standard form
with k = - 4
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 sum of the digits of a two digit number is 5. If nine is subtracted from the number it will equal the reversed number. FIND THE EQUATION!! PLEASE!
Answer:
D
Step-by-step explanation:
Write the equation of a line in slope-intercept form that has a slope of 3/4 and passes through the point (-4, 1).
y equals 0.75 x plus 4
y equals 4 x plus 0.75
y equals minus 4 x plus 1
y equals 0.75 x plus 1
Answer:
y = 3/4 x + 4
y equals 0.75 x plus 4
Step-by-step explanation:
y = 3/4 x + b
1 = 3/4 (-4) + b
1 = -3 + b
b = 4
Answer:
A) y equals 0.75 x plus 4Step-by-step explanation:
Another way to solve this to use the point-slope form:
y - y₁ = m(x - x₁)Substitute the values of m, x₁, y₁ and convert this into slope-intercept form:
y - 1 = 3/4(x - (-4))y - 1 = 3/4x + 3y = 3/4x + 4y = 0.75x + 4Correct choice is A
