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]
TDaP is a booster shot that prevents Diphtheria, Tetanus, and Pertussis in adults and adolescents. It should be administered every 8 years for it to remain effective. A random sample of 550 people living in a town that experienced a pertussis outbreak this year were divided into two groups. Group 1 was made up of 145 individuals who had not had the TDaP booster in the past 8 years, and Group 2 consisted of 355 individuals who had. In Group 1, 18 individuals caught pertussis during the outbreak, and in Group 2, 13 individuals caught pertussis. Is there evidence to suggest that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were? Test at the 0.05 level of significance. Enter the p-value - round to 5 decimal places.
Answer:
Yes. There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
P-value = 0.00013.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.05.
The sample 1 (Group 1), of size n1=145 has a proportion of p1=0.124.
[tex]p_1=X_1/n_1=18/145=0.124[/tex]
The sample 2 (Group 2), of size n2=355 has a proportion of p2=0.037.
[tex]p_2=X_2/n_2=13/355=0.037[/tex]
The difference between proportions is (p1-p2)=0.088.
[tex]p_d=p_1-p_2=0.124-0.037=0.088[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{18+13.135}{145+355}=\dfrac{31}{500}=0.062[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.062*0.938}{145}+\dfrac{0.062*0.938}{355}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0.001}=0.024[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.088-0}{0.024}=\dfrac{0.088}{0.024}=3.68[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=P(z>3.68)=0.00013[/tex]
As the P-value (0.00013) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of individuals who caught pertussis and were not up to date on their booster shot is higher than those that were.
An artist bought 5 yards of rope. Which of the following is equivalent to 5 yards?
A. 3 feet
B. 15 feet
C. 60 feet
D. 180 feet
The 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.
Given information:
An artist bought 5 yards of rope.
We know that one yard is equal to 3 feet.
So, here it is required to find the equivalent of 5 yards in the form of feet.
The value of 5 yards in the form of feet can be calculated as,
[tex]5\times 3=15\rm\;feet[/tex]
Therefore, the 5 yards rope of the artist is equivalent to 15 feet of the rope and the option B is correct.
For more details, refer to the link:
https://brainly.com/question/22316471
pleaseee answer this exponentt! 4ba^-4
Answer:
the answer would be (4b)/(a^4)
Step-by-step explanation:
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix A. Group of answer choices A. The Determinant cannot be found for a matrix with these dimensions B. 11 C. 7 D. 23
Answer: d) 23
Step-by-step explanation:
Consider matrix [tex]\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]. The determinant is: ad - bc
In the matrix given, a = 5, b = -1, c = 3, d = 4
det A = ad - bc
= 5(4) - 3(-1)
= 20 - (-3)
= 20 + 3
= 23
Please answer this math quesiton im desperate !! tysm!! will give brainliest!!
Answer: i am pretty sure it is C dont get your hopes up but
Step-by-step explanation:
from what i see if you take the y=3 over 2 and make that a decimal you can now take y = that number and make a line and so on then after that step you want to now take your final answer which is x and subtract it by 3 i MIGHT be wrong but i tried.
Answer:
The Answer is C I hope this helped
Step-by-step explanation:
I did it on my quiz!
The owner of a rental company rents bicycles and tricycles and keeps inventory by counting seats and wheels. One day, he counts 25 seats and 60 wheels. The equation representing the total number of seats is b + t = 25, where b is the number of bicycles and t is the number of tricycles. Which equation represents the number of wheels?
Answer:
2b + 3t = 60
Step-by-step explanation:
2b is the number of wheels on a bicycle
3t is the number of wheels on a tricycle
and 60 is the total number of wheels
The width of the pond shown is x ft. What is the value of x.
Answer:
Width (x) = 160ft
See explanation below
Step-by-step explanation:
The information given is incomplete as we are not told if the shape of the pond. This is about determining the surface area of a water body.
Looking at the question, we can tell we are to find the width of a pond whose shape wasn't given.
Assuming the shape of the pond is either a rectangular or square pond, let's consider the following question:
The acreage of a rectangular pond is 1.54 acres and the length is 420ft. The width of the pond shown is x ft. What is the value of x.
Find attached the diagram used for solving the question.
Formula for calculating the acreage of
a Square or Rectangular Ponds is multiplying average length (in feet) times average width (in feet) and dividing the result by 43,560 to derive our answer in acres.
That is: Average Length (ft) × Average Width (ft) ÷ 43,560 = Acres
Since we have been given acreage and length, we would make width subject of formula.
Width = (Acreage × 43500)/length
Width (x) = (1.54 × 43,560)/420
=67082.4 ÷ 420 = 159.72
Width (x) = 160ft (nearest feet)
Find the number of unique permutations of the letters in the word: ONGOING
Answer:
The Number of unique permutation is 6,615Step-by-step explanation:
This particular permutation deals with words that have repeated letters.
Given word = "ONGOING"
the formula for the permutation is
[tex]= \frac{n!}{mA! mB!.....mZ!}[/tex]
where n is the amount of letters in the word, and m A , m B , ... , m Z are the occurrences of repeated letters in the word. Each m equals the amount of times the letter appears in the word.
So in the word "ONGOING"
n= 7
mO= 2
mN= 2
mG=2
[tex]permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}[/tex]
[tex]permutations= \frac{52920}{8} \\permutation = 6,615[/tex]
in a certain town there were 113 robberies last year this year the number of robberies has gone down 14% how many robberies were there this year to the nearest whole number
Answer:
99 robberies
Step-by-step explanation:
What you are basically doing is taking the discount.
1 + 14% = 1.14
113 / 1.14 = 99.12
What’s the correct answer for this question?
Answer:
PQ = 6
Step-by-step explanation:
Using tangent-secant theorem,
(PQ)² = (PR)(PS)
(PQ)² = (4)(9)
(PQ)² = 36
Taking square root on both sides, we get
PQ = 6
Solving Division Story Problems: Tutorial
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Geri ran in a marathon race. It took her 3 hours and 28 minutes to run
26 miles. how many minutes did it take her to run 1 mile if she ran at the
same rate for the whole race?
Answer the question below. Type your response in the
space provided.
(1 hour = 60 minutes)
Answer the question.
minutes
Clear
832 PM
O Type here to search
na do
Answer:
8 minutes
Step-by-step explanation:
Let t represent the time for one mile. We are told the ratio of minutes to miles is constant, so we have the proportion ...
time / distance = t/(1 mi) = (208 min)/(26 mi)
Multiplying both sides of the equation by (1 mi), we have ...
t = (208/26) min = 8 min
Geri's average pace was 8 minutes to run 1 mile.
35 games a different team has 50pts 14 games were draws how many games was lost
Answer:
9 losts
The team had 14 draws which is 14points. So you will substrate 14points from the total 50point, which will left with 36point.
The 36point constitutes 12 wins
Therefore 12wins + 14draws = 26 matches.
You then substrate 26 matches from the 35total matches to get your lose matches.
: 35 - 26 = 9
Therefore, there was 9 lost matches
a boy is standing on a pole of height 14.7m throws a stone upwards. it moves in a vertical line slightly away from the pole and falls on the ground. its equation of motion in meters and seconds is x=9.8t-4.9t^2. find time taken for upward and downward motions. also find the maximum height reached by the stone from the ground.
Answer:
The time taken for the upward motion is 1 second. The same time is taken for the downward motion
It reaches a maximum height of 4.9 meters.
Step-by-step explanation:
The equation of motion is:
[tex]x(t) = -4.9t^{2} + 9.8t[/tex]
Since the term which multiplies t squared is negative, the graph is concave down, that is, x increases until the vertex, where it reaches it's maximum height, then it decreases.
Vertex of a quadratic equation:
Quadratic equation in the format [tex]x(t) = at^{2} + bt + c[/tex]
The vertex is the point [tex](t_{v}, x(t_{v}))[/tex], in which
[tex]t_{v} = -\frac{b}{2a}[/tex]
In this question:
[tex]x(t) = -4.9t^{2} + 9.8t[/tex]
So [tex]a = -4.9, b = 9.8[/tex]
Vertex:
[tex]t_{v} = -\frac{9.8}{2*(-4.9)} = 1[/tex]
The time taken for the upward motion is 1 second.
[tex]x(t_{v}) = x(1) = 9.8*1 - 4.9*(1)^{2} = 4.9[/tex]
It reaches a maximum height of 4.9 meters.
Downward motion:
From the vertex to the ground.
The ground is t when x = 0. So
[tex]-4.9t^{2} + 9.8t = 0[/tex]
[tex]4.9t^{2} - 9.8t = 0[/tex]
[tex]4.9t(t - 2) = 0[/tex]
[tex]4.9t = 0[/tex]
[tex]t = 0[/tex]
Or
[tex]t - 2 = 0[/tex]
[tex]t = 2[/tex]
It reaches the ground when t = 2 seconds.
The downward motion started at the vertex, when t = 1.
So the duration of the downward motion is 2 - 1 = 1 second.
At a Psychology final exam, the scores are normally distributed with a mean 73 points and a standard deviation of 10.6 points. The lower 5% of the class will not get a passing grade. Find the score that separates the lower 5% of the class from the rest of the class. 58.0 56.6 55.6 57.2
Answer:
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 73, \sigma = 10.6[/tex]
Find the score that separates the lower 5% of the class from the rest of the class.
This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 73}{10.6}[/tex]
[tex]X - 73 = -1.645*10.6[/tex]
[tex]X = 55.6[/tex]
The score that separates the lower 5% of the class from the rest of the class is 55.6.
The lengths of two sides of a right triangle are given. Find the length of the third side. Round to the nearest tenth if
necessary.
legs: 18 in, and 17 in.
24.8 in.
a.
b.
5.9 in.
c. 27.7 in.
d. 19.5 in.
Answer:
A)24.8in
Step-by-step explanation:
17^2 + 18^2 =613
sq root of 613 = 24.758...
24.8in
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your answer to the nearest whole number.
Answer:
80 g
Step-by-step explanation:
mass of sanitizer = 400 g
percentage of alcohol = 24%
mass of alcohol in the sanitizer = 24% of 400 g = 0.24 x 400 = 96 g
this means that the mass of other chemicals = 400 - 96 = 304 g
If alcohol content is increased to 30% by removing more of the other chemicals, then mass of alcohol will still remain 96 g
this means that 96 g becomes 30% of the resulting hand sanitizer, we write mathematically as
96 g = 30% of y
where y is the new mass of the sanitizer
96 = 0.3y
y = 96/0.3 = 320 g
The remaining mass of other chemicals = 320 - 96 = 224 g
the total mass of other chemical lost is
304 - 224 = 80 g
What is the product
46 times 10 (the ten has a exponent number) and the exponent number is 2
Answer:
The answer is 4600. 10 with the exponent of 2 is 100, so 100 times 46 is 4600. Hope this helps;)
Step-by-step explanation:
The three sides of a right-angled triangle are x, x+1 and 5. Find x and the area, if the longest side is 5.
Answer:
x = 3
area = 6
Step-by-step explanation:
using phytagoras's. theorem
a² + b² = c² (with c is the longest one)
x² + (x+1)² = 5²
x² + x² + 2x + 1 = 25
2x² + 2x - 24 = 0 (divide all by 2)
x² + x -12 = 0 then factorize
(x-3)(x+4) = 0
we get x = 3 and x = -4. Take the positive one.
so now we have x = 3 then x + 1 must be 4.
the area is
A = ½ . 3 . 4 = 6
10. How many different combinations are there of the digits 46987?
25.
Look at this:
There are 5 digits in 46987.
There will be 5 combinations.
5 times 5 = 25.
You have your answer.
A total of 31 possible combinations are there for number 46987.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 5 - digit number 46987.
Assume that there are [y] possible combinations. For a [x] digit number, the total possible combinations are -
y = 2ˣ - 1
So, for [x] = 5, we will have -
y = 32 - 1
y = 31
Therefore, a total of 31 possible combinations are there for number 46987.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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Find the value of x that makes A || B.
Answer:
x = 20
Step-by-step explanation:
3x - 10 = x + 30
2x = 40
x = 20
Which equation below represents the inverse function T(c)
Answer:
the answer is A
Step-by-step explanation:
Answer:
Correct answer is A
Step-by-step explanation:
Hope this helps you
Suppose that 75% of adult Americans agree that, while downloading music from the Internet and then selling it is piracy and should be prohibited, downloading for personal use is an innocent act and should not be prohibited.We will take a random sample of 30 American adults and ask them if they agree with the statement. Then the sampling distribution of the sample proportion of people who answer yes to the question is:
Answer:
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.75, n = 30[/tex]
So
[tex]\mu = 0.75, s = \sqrt{\frac{0.75*0.25}{30}} = 0.0791[/tex]
The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.
An aquarium 8 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use 9.8 m/s2 for g and the fact that the density of water is 1000 kg/m3.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter xi* as xi.)
Answer:
9800Joules
Step by step Explanations
Before we can set the integral up, let the upper half the aquarium be divided into horizontal slices for easy calculation
Then we will represent distance from the top of the tank as X and also
2 its thickness as ∆x
We will be working on the horizontal slices , since in the horizontal slices each drop of water in a given slice will be have the same distance from the top of the tank.
Given that An aquarium has;
Length = 8 m long,
Width = 1 m wide,
Dept =1 m deep
And ∆x m,
density of water is 1000 kg/m3
g = 9.8 m/s2
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Robert is 40 years older than Brittany. the sum of their ages is 82. find their ages.
Answer:
brittany is 42
Step-by-step explanation:
if he is 40 years older than her and the sum of there ages is 82
82-40 = 42
"Rebecca walks 100 feet in a straight line. She then turns 20 degrees to her left and walks another 100 feet, and then turns 20 degrees to her left again. She continues this pattern until she reaches the point where she started. How far did she walk
Answer:
1,800 ft
Step-by-step explanation:
Rebecca will walk in the pattern of a regular polygon with 'n' sides and internal angles of 160 degrees (180 at a straight line - 20 degrees from each turn).
The equation that describes the internal angle of a regular polygon is:
[tex]A = \frac{(n-2)*180}{n}[/tex]
For A = 160 degrees:
[tex]160n=(n-2)*180\\(180-160)n=360\\n=18\ sides[/tex]
If each side is 100 ft long, the total distance that Rebecca has walked is:
[tex]d = 18*100\\d=1,800\ ft[/tex]
She walked 1,800 ft.
Find the perimeter. Use 3.14 for pi. Round to the nearest tenth.
58 cm
O 22 cm
O 72 cm
O 44 cm
Answer:
22cm
See explanation below
Step by step explanation:
The question is incomplete without the diagram of the shape or its dimensions.
From the question, we are to determine the perimeter of the circle.
Let's consider the following question by determining the perimeter of a circle. If diameter is 7cm. Use pi as 3.14.
Perimeter of circle = circumference of circle
circumference of circle = 2πr
Radius = diameter/2 = (7/2)cm
circumference of circle = 2πr
= 2×π×(7/2) = (14/2)×3.14
= 7×3.14
=21.98cm
circumference of circle = 22cm (nearest tenth)
Perimeter of circle = 22cm
Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) x + y = 6 x − y = 2
Answer:
(4,2). DEPENDENT
Step-by-step explanation:
As each equation consist on two variable, both can be represented graphically on a cartesian plane. First, each expression is rewritten in explicit form:
[tex]y = 6 - x[/tex] (red line) and [tex]y = x - 2[/tex] (blue line)
By the resource of graphing software, the solution is (4,2). The representation is presented below as attachment. As solution exists, both expression are linearly DEPENDENT.
Which numbers belong to the solution set of the Inequality? x + 9 < 78
Answer: x<69
Step-by-step explanation:
For this problem, we solve is just as we would if it was an equal sign.
x+9<78 [subtract 9 on both sides]
x<69
If you roll two fair six-sided dice, what is the probability that at least one die shows a 3?
Answer:
3
Step-by-step explanation:
you are right
what’s the area of this triangle?
Answer:
hi there, the answer is
A=45 cm2
Step-by-step explanation:
A= 1/2 x 10 x 9
A=5 x 9
A=45 cm2