Answer:
-7. negative
Step-by-step explanation:
49 + -56
49 - 56
-7
In 1960, there were approximately 3,000 million people living on earth. In 1999, the population of earth was approximately 6,000 million people. What was the approximate rate of increase, in millions of people, each year between these two years?
Answer:
76.9 million people per year
Step-by-step explanation:
The increase was 3,000 million people in 39 years, so the number per year was ...
3000/39 ≈ 76.9 . . . . million people per year
Compute the quadratic form xTAx for A = [3 2 0, 2 2 1, 0 1 0].
A. x = [x1 x2 x3].
B. x = [-2 -1 5].
C. x = [1/2 1/2 1/2].
Answer:
(a)[tex]x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]
(b) 12
(c)[tex]2\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right][/tex]
We are to compute the quadratic form [tex]x^TAx[/tex] for A.
Part A
[tex]x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]
[tex]x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right][/tex]
[tex]= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right][/tex]
[tex]= x_1(3x_1+2x_2+0x_3)+x_2(2x_1+2x_2+1x_3)+x_3(0x_1+1x_2+0x_3)\\= x_1(3x_1+2x_2)+x_2(2x_1+2x_2+x_3)+x_3(x_2)[/tex]
[tex]= 3x_1^2+2x_1x_2+2x_1x_2+2x_2^2+x_2x_3+x_2x_3\\\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3[/tex]
Part B
[tex]x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12[/tex]
Part C
[tex]x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}[/tex]
The improper fraction 37/6 can be changed to the mixed number
Answer: 6 1/6
Step-by-step explanation:
6 can go into 37 6 times
6x6=36
with 1 left over
The fraction 37/6 can be changed to the mixed number as 6 1/6 if the fraction is 37/6.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fraction is:
= 37/6
We can write the above number as:
= (36 + 1)/6
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 36/6 + 1/6
= 6 + 1/6
Or
= 6 1/6 (mixed fraction)
Thus, the fraction 37/6 can be changed to the mixed number as 6 1/6 if the fraction is 37/6.
Learn more about the fraction here:
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POSSIBLE POINTS
A toy box contains 12 colored toys and 12 white toys. If you pick out 3 toys at random, what is the probability that they will all be white?
Answer:
12white
12 coloured
12-12=0
if the degree of the monomial 3x^2y^az^a is 10 then what is a
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
i did it on edge
On June 18, Smith Technologies issued a $75,000, 6%. 180-day note payable to Johnson Company. What is
the due date of the note? 15
a. December 16
b. December 17
Answer:
a. December 16
Step-by-step explanation:
18 June + 180 days = 15 December
Since 2 options given,
a. December 16 is the answer
if k (x) = 5x - 6, which expression is equivalent to (k + k) (4)
Answer:
28
Step-by-step explanation:
[tex]k(x) = 5x -6\\\therefore k(4) = 5\times 4 -6\\\therefore k(4) = 20 -6\\\therefore k(4) = 14\\\\\because (k+k)(4) = k(4) + k(4)\\\therefore (k+k)(4)= 14+14\\\huge\red{\boxed{\therefore (k+k)(4) = 28}}[/tex]
According to Nielsen//NetRatings, the average visitor to the American Greetings Website spends 11.85 minutes at the site. Assuming this finding to be based on a random sample of 20 visitors to the site, a POPULATION standard deviation of 3.0 minutes, and a population of visiting times that is approximately normally distributed, a 99% confidence interval for the population mean is closest to:________.
Answer:
The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{3}{\sqrt{20}} = 1.73[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 11.85 - 1.73 = 10.12 minutes
The upper end of the interval is the sample mean added to M. So it is 11.85 + 1.73 = 13.58 minutes
The 99% confidence interval for the population mean is between 10.12 minutes and 13.58 minutes.
Find the intersection(s) of the line y = 2x - 3 with the circle whose center at origin, radius = 4
Answer:
[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]
And we got for the solution:
[tex] x_1= 2.885 , x_2 = -0.485[/tex]
And the value sof y are using the function y =2x-3:
[tex] y_1=2.77, y_2=-3.97[/tex]
Step-by-step explanation:
For this case we have this function given:
[tex] y = 2x-3[/tex] (1)
And the circle with center the origin and radius 4 is given by;
[tex] x^2 +y^2 = 16[/tex] (2)
We can solve fro y from the last equation and we got:
[tex] y = \pm \sqrt{16-x^2}[/tex] (3)
Now we can set equal equations (3) and (1) and we got:
[tex] 2x-3 = \sqrt{16-x^2}[/tex]
[tex] (2x-3)^2=16-x^2[/tex]
[tex] 4x^2 -12x +9 = 16-x^2[/tex]
[tex] 5x^2 -12x -7=0[/tex]
And using the quadratic equation we got:
[tex] x = \frac{12 \pm \sqrt{(-12)^2 -4(5)(-7)}}{2(5)}[/tex]
And we got for the solution:
[tex] x_1= 2.885 , x_2 = -0.485[/tex]
And the value sof y are using the function y =2x-3:
[tex] y_1=2.77, y_2=-3.97[/tex]
Factorize 225-49
[tex] {x}^{2} [/tex]
[tex]225-49x^2[/tex]
[tex]-49x^2+225[/tex]
[tex]=(7x+15)(-7x+15)[/tex]
Answer:
(15+7x)(15-7x)
Step-by-step explanation:
225-49 x² = 15² - (7x)² = (15+7x)(15-7x)
A bottle of water is supposed to have 12 ounces. The bottling company has determined that 98% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?
A. Zn=36, p=0.98, x=0
B. n=36, p=0.98, x=12
C. n=0, p=0.98, x=36
D. n=12, p=36, x=98
Answer:
B. n=36, p=0.98, x=12
Step-by-step explanation:
98% of bottles have the correct amount.
The probability is equal to 0.98
That is p = 0.98
A bottle of water is supposed to have 12 ounces.
That is the expected value is 12
X = 12
36 bottles has all bottles properly filled
The possible sample space is 36
N = 36
The mean percent of childhood asthma prevalence in 43 cities is 2.22% . A random sample of 30 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.5%? Interpret this probability. Assume that sigma equals 1.39%. nterpret this probability. Select the correct choice below and fill in the answer box to complete your choice. (Round to two decimal places as needed.) (A. What % of samples of 43 cities will have a mean childhood asthma prevalence greater than 2.5%? (B. What % of samples of 30 cities will have a mean childhood asthma prevalence greater than 2.22%? (C. What% of samples of 30 cities will have a mean childhood asthma prevalence greater than 2.5?
Answer:
C.
Step-by-step explanation:
Hello!
Given the variable:
X: childhood asthma prevalence
With mean μ= 2.22%
and standard deviation σ= 1.39%
You have to calculate the probability of the sample average of childhood asthma prevalence in a sample of n= 30 cities is greater than 2.5%
We don't know the distribution of the variable, but remember that thanks to the central limit theorem, since the n ≥ 30, we can approximate the sampling distribution to normal:
X[bar]≈N(μ;σ²/n)
And use the standard normal distribution to calculate the asked probability:
P(X[bar]>2.5)= 1 - P(X≤2.5)
Calculate the Z value for the given X[bar] value:
[tex]Z= \frac{X[bar]-Mu}{\frac{Sigma}{\sqrt{n} } } = \frac{2.5-2.22}{\frac{1.39}{\sqrt{30} } }= 1.10[/tex]
Using the Z-tables you have to look for the value of
P(Z≤1.10)= 0.86433
1 - 0.86433= 0.13567
Then P(X[bar]>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567
13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%
I hope this helps!
Consider the original parallelogram and its reduction.
A parallelogram with side length 18 millimeters. A parallelogram with side length 3 millimeters.
Figures not drawn to scale.
What is the scale factor?
One-sixth
One-third
3
6
Answer:
The answer is 1/6.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
OPTION A
Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 2t, 1 + 6t, 1 + 14t . Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) (x, y, z) = (smaller x-value) (x, y, z) = (larger x-value) Find the time(s) when the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t =
Answer:
A) points at which paths intersect : (1,1,1) ; (2,4,8)
B) DNE
Step-by-step explanation:
A) To find the points in which the particle paths intersect, it is necessary to find the values of t for which the three components of both vectors are equal:
[tex]t_1=1+2t_2\\\\t_1^2=1+6t_2\\\\t_1^3=1+14t_2[/tex]
you replace t1 from the first equation in the second equation:
[tex](1+2t_2)^2=1+6t_2\\\\1+4t_2+4t_2^2=1+6t_2\\\\4t_2^2-2t_2=0\\\\t_2(2t_2-1)=0\\\\t_2=0\\\\t_2=\frac{1}{2}[/tex]
Then, for t2 = 0 and t2=1/2 you obtain for t1:
[tex]t_1=1+2(0)=1\\\\t_1=1+2(\frac{1}{2})=2[/tex]
Hence, for t1=1 and t2=0 the paths intersect. Furthermore, for t1=2 and t2=1/2 the paths also intersect.
The points at which the paths intersect are:
[tex]r_1(1)=(1,1,1)=r_2(0)=(1,1,1)\\\\r_1(2)=(2,4,8)=r_2(\frac{1}{2})=(2,4,8)[/tex]
B) You have the following two trajectories of two independent particles:
[tex]r_1(t)=(t,t^2,t^3)\\\\r_2(t)=(1+2t,1+6t,1+14t)[/tex]
To find the time in which the particles collide, it is necessary that both particles are in the same position on the same time. That is, each component of the vectors must coincide:
[tex]t=1+2t\\\\t^2=1+6t\\\\t^3=1+14t[/tex]
From the first equation you have:
[tex]t=1+2t\\\\t=-1[/tex]
This values does not have a physical meaning, then, the particle do not collide
answer: DNE
Q 3.28: To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail. Indicate what percent of values must be chopped off from each tail for a 97% confidence level. A : We keep the middle 97% of values by chopping off 1.5% from each tail. B : We keep the middle 1.5% of values by chopping off 97% from each tail. C : We keep the middle 3% of values by chopping off 97% from each tail. D : We keep the middle 3% of values by chopping off 1.5% from each tail. E : We keep the middle 97% of values by chopping off 3% from each tail.
Answer:
A : We keep the middle 97% of values by chopping off 1.5% from each tail.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.97}{2} = 0.015[/tex]
This means that for a 97% confidence interval, 1.5% of each tail is removed, while the middle 97% of values are kept.
So the corect answer is:
A : We keep the middle 97% of values by chopping off 1.5% from each tail.
A number is randomly selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10).
What is the COMPLEMENT of selecting a number greater than 7?
Enter your answer as a FRACTION.
In this case, the complement would be selecting a number less than or equal to 7; the probability of this occurring is [tex]\boxed{\frac{7}{10}}.[/tex]
Answer:
it is 3/10
Step-by-step explanation:
1, 2, 3, 4, 5, and 6 are all LESS than 7. 8, 9, and 10 are all GREATER than 7, therefor, [tex]\frac{3}{10}[/tex] is the complement.Multiply 6.4 x 108 by 3.1 x 10-5 and leave the
answer in standard form.
Answer:
hope this.helps you
Find the gradient of the line 2y=-6x+1 =
Answer:
A line in form of y = ax + b has the gradient a.
2y = -6x + 1
<=> y = -3x + 1/2
=> The gradient of this line: g = -3
Hope this helps!
:)
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
2y = - 6x + 1
Convert the equation into a slope-intercept form. Then we have
2y = - 6x + 1
y = - 3x + 1/3
The slope represents the gradient of the line. Then the gradient of the line will be - 3.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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Please Someone help do not understand it ASAP
Answer:
1a) 90 = 2y + 2(2x) 1b) 45 - 2x = y
Step-by-step explanation:
1a) 90 = 2y + 2(2x)
1b) 90 = 2y + 2(2x) Use the equation from above and multiply
90 = 2y + 4x
-4x - 4x Subtract 4x from both sides
90 - 4x = 2y Divide both sides by 2
45 - 2x = y
Twelve books cost £51.60. How many books would I get for £193.50?
Answer:
45 books
Step-by-step explanation:
12=51.60
how about 193.50
193.50 x 12=2322 / 51.60=45 books
Solution,
Books Price
12 51.60
X(suppose) 193.50
In case of Direct proportion,
12/X=51.60/193.50
or,51.60x=2322( cross multiplication)
or,X=2322/51.60
X=45
Hope it helps
Good luck on your assignment
17. El precio de los terrenos en Lima es proporcional al área e inversamente proporcional a su distancia con respecto al centro de la ciudad. Un empresario desea adquirir un terreno de 1200 m2 para instalar una pequeña planta procesadora que este localizada a una distancia máxima de 40 Km del centro de la ciudad. Si se sabe que un terreno de 900 m2 a 45 Km del centro de la ciudad cuesta S/ 250 000, ¿cuánto deberá pagar como mínimo dicho empresario para adquirir el terreno con las condiciones dadas?
Answer:
375000
Step-by-step explanation:
We have that in this case the following proportion would be fulfilled:
Price * Distance / area
Now, we have that for a distance of 45 km and an area of 900 m ^ 2 the price is 250,000, now for a distance of 40 km but with an area of 1,200 m ^ 2, how would the price be, we replace:
250000 * 45/900 = P * 40/1200
12500 * 1200/40 = P
P = 375000
Which means that for these conditions the price is 375000.
Anybody know how to do this, it's about angles.
Step-by-step explanation:
45°+90°+60°+X°=360° (being complete angle)
or,195°+X°=360°
or,X°=360°-195°
or,X°=165°
Therefore,valueof X is 165°.
Answer:
165
Step-by-step explanation:
The sum of angles at a point is always 360 degrees and you know all the angles apart from x. so 360-90-45-60=165.
Better notation would be 360 = x+45+60+90 and then you have to find out what x is by rearangin the equation.
The population standard deviation for the height of college football players is 2.7 inches. If we want to estimate a 95% confidence interval for the population mean height of these players with a 0.65 margin of error, how many randomly selected players must be surveyed? (Round up your answer to nearest whole number, do not include any decimals) Answer:
Answer:
n = 66 (to the nearest whole number)
66 randomly selected players must be surveyed
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
x+/-M.E
M.E = zr/√n
Making n the subject of formula;
n = (zr/M.E)^2 ........1
Given that;
Mean = x
Standard deviation r = 2.7 inches
Number of samples = n
Confidence interval = 95%
z(at 95% confidence) = 1.96
Margin of error M.E = 0.65 inches
Substituting the given values into equation 1;
n = (zr/M.E)^2
n = (1.96×2.7/0.65)^2
n = 66.28464852071
n = 66 (to the nearest whole number)
66 randomly selected players must be surveyed
Assume a 10-year period at 8% compounded continuously and find the following: (a) the present value; (b) the accumulated amount of money flow at t = 10.
f(t)= 400e^0.03t
Answer:
Step-by-step explanation:
Consider the function of the rate of flow of money in dollar per year is
[tex]f(t)= 400e^{0.03t}[/tex]
The objective is to find the present value of this income over 10 years period an assume an annual interest rate of 8% compounded continuously.
Given that,
[tex]f(t)= 400e^{0.03t}[/tex]
r = 0.08, t = 10
if f(t) is the rate of continuously money flow at an interest rate r to T year,
the present value is,
[tex]P= \int\limits^T_0 {f}(t)e^{-rt} \, dt[/tex]
Now input the values to get
[tex]p=\int\limits^{10}_0 400e^{0.03t}*e^{-0.08t} dt[/tex]
[tex]=400\int\limits^{10}_0 e^{0.03t}*^{-0.08t} dt[/tex]
[tex]= 400\int\limits^{10}_0 e^{-0.05t} dt[/tex]
[tex]=400(-\frac{e^{-0.05t}}{0.05} )|_0^1^0[/tex]
[tex]=-\frac{400}{0.05} (e^{-0.05*10}-e^{-0.05*0})\\\\=-\frac{400}{0.05} (e^{-0.5}-e^{*0})\\\\=3147.75[/tex]
Therefore, the present value is $3147.75Baby talk: In a sample of 69 children, the mean age at which they first began to combine words was 16.44 months. with a standard deviation of 9.47 months. Part 1 out of 2 Construct a confidence interval for the mean age at which children first begin to combine words. Round the answers to two decimal places. A 98% confidence interval for the mean age is:__________
Answer:
A 98% confidence interval for the mean age is:
= ( 13.78, 19.10) months
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 16.44 months
Standard deviation r = 9.47 months
Number of samples n = 69
Confidence interval = 98%
z(at 98% confidence) = 2.33
Substituting the values we have;
16.44+/-2.33(9.47/√69)
16.44+/-2.33(1.140054028722)
16.44+/-2.656325886922
16.44+/-2.66
= ( 13.78, 19.10) months
Therefore, A 98% confidence interval for the mean age is:
= ( 13.78, 19.10) months
Question 7 (5 points)
Consider the function f(x) = f(x)=-x^4+ 9. Determine which of the following is its
graph, based on end behavior.
Answer:
.
Step-by-step explanation:
Calculate the perimeter of the following parallelogram:
10 in
4 in
3 in
Answer:
28
Step-by-step explanation:
10=x 4=y
P=2(x+y)
P=2(10+4)
P=2(14)
P=28
A 13-foot ladder leans against the side of a building, forming an angle with the ground. Given that the foot of the ladder is being pulled away from the building at the rate of 0.1 feet per second, what is the rate of change of when the top of the ladder is 12 feet above the ground
Step-by-step explanation:
We have [tex]\mathrm{dx} / \mathrm{dt}=0.1 \mathrm{ft} / \mathrm{sec},[/tex] and we want
dy/dt.
[tex]x[/tex] and [tex]y[/tex] are related by the Pythagorean Theorem [tex]x^{2}+y^{2}=(13 f t)^{2}[/tex]
Differentiate both sides of this equation with respect to [tex]t[/tex] to get [tex]2 x \frac{d x}{d t}+2 y \frac{d y}{d t}=0[/tex]
[tex]\frac{d y}{d t}=-\frac{x}{y} \frac{d x}{d t}[/tex]
When [tex]x=12 \mathrm{ft},[/tex]
we have,
[tex]y=\sqrt{(13 \mathrm{ft})^{2}-(12 \mathrm{ft})^{2}}=5 \mathrm{ft}[/tex]
therefore
[tex]\frac{d y}{d t}=-\frac{12f t}{5 f t} \cdot \frac{1 f}{\sec }=-\frac{12}{5} \frac{f t}{\sec }[/tex]
x/x+1-1/x-1+2x/x^2-1
Answer:
Input:
x/x + 1 - 1/x - 1 + 2×x/x^2 - 1
Result:
1/x
URGENT PLEASE ANSWER
inverse function
*see attachment*
Answer:
Horizontal shift to the RIGHT of one unit
Step-by-step explanation:
When looking at a square root equation, the transformation form is:
[tex]f(x) = a\sqrt{b(x-h)} +k[/tex]
'h' represents a horizontal shift of the graph. Therefore, in this instance:
[tex]f(x) = \sqrt{x-1}[/tex]
This means that there is a horizontal shift to the RIGHT of one unit.
