A golfer rides in a golf cart at an average speed of 3.10 m/s for 28.0 s. She then gets out of the cart and starts walking at an average speed of 1.30 m/s. For how long (in seconds) must she walk: if her average speed for the entire trip, riding and walking, is 1.80 m/s?

Answer:

The root of the equation [tex]x^3-0.2589x^{2}+0.02262x-0.001122=0[/tex] is x ≈ 0.162035

Step-by-step explanation:

To find the roots of the equation [tex]x^3-0.2589x^{2}+0.02262x-0.001122=0[/tex] you can use the Newton-Raphson method.

It is a way to find a good approximation for the root of a real-valued function f(x) = 0. The method starts with a function f(x) defined over the real numbers, the function derivative f', and an initial guess [tex]x_{0}[/tex] for a root of the function. It uses the idea that a continuous and differentiable function can be approximated by a straight line tangent to it.

This is the expression that we need to use

[tex]x_{n+1}=x_{n} -\frac{f(x_{n})}{f(x_{n})'}[/tex]

For the information given:

[tex]f(x) = x^3-0.2589x^{2}+0.02262x-0.001122=0\\f(x)'=3x^2-0.5178x+0.02262[/tex]

For the initial value [tex]x_{0}[/tex] you can choose [tex]x_{0}=0[/tex] although you can choose any value that you want.

So for approximation [tex]x_{1}[/tex]

[tex]x_{1}=x_{0}-\frac{f(x_{0})}{f(x_{0})'} \\x_{1}=0-\frac{0^3-0.2589\cdot0^2+0.02262\cdot 0-0.001122}{3\cdot 0^2-0.5178\cdot 0+0.02262} \\x_{1}=0.0496021[/tex]

Next, with [tex]x_{1}=0.0496021[/tex] you put it into the equation

[tex]f(0.0496021)=(0.0496021)^3-0.2589\cdot (0.0496021)^2+0.02262\cdot 0.0496021-0.001122 = -0.0005150[/tex], you can see that this value is close to 0 but we need to refine our solution.

For approximation [tex]x_{2}[/tex]

[tex]x_{2}=x_{1}-\frac{f(x_{1})}{f(x_{1})'} \\x_{1}=0-\frac{0.0496021^3-0.2589\cdot 0.0496021^2+0.02262\cdot 0.0496021-0.001122}{3\cdot 0.0496021^2-0.5178\cdot 0.0496021+0.02262} \\x_{1}=0.168883[/tex]

Again we put [tex]x_{2}=0.168883[/tex] into the equation

[tex]f(0.168883)=(0.168883)^3-0.2589\cdot (0.168883)^2+0.02262\cdot 0.168883-0.001122=0.0001307[/tex] this value is close to 0 but again we need to refine our solution.

We can summarize this process in the following table.

The approximation [tex]x_{5}[/tex] gives you the root of the equation.

When you plot the equation you find that only have one real root and is approximate to the value found.

Answer: [tex]\sqrt{14}[/tex]

Step-by-step explanation:

The given notation is not clear enough, but I will asume that the question is: "Wich is the vector lenght of the vector [tex](2,3,1)[/tex] in a 3 dimensional euclidean space"

Vector lenght of a vector [tex](a,b,c)[/tex] is given by the next formula:

║[tex](a,b,c)[/tex]║=[tex]\sqrt{a^2+b^2+c^2}[/tex]

In this case we have a=2, b=3 and c=1. We should substitute these values in the formula given before to obtain:

║[tex](2,3,1)[/tex]║=[tex]\sqrt{2^2+3^2+1^2}=\sqrt{14}=3.74165[/tex]

Wich is the answer to the problem.  

The probability that a randomly selected bacterium that's currently alive will still be alive after one week is 1/3. The calculation is done by dividing the number of bacteria that can stay alive for at least 30 days by the total number of bacteria that are currently alive.

The question pertains to the concept of probability in mathematics and it's asking for the likelihood that a randomly chosen bacteria from a test tube would still be alive after one week. Given that 15 bacteria are alive (5 will stay alive for at least 30 days, and 10 will die on the second day), and you have chosen a bacterium that is currently alive. After one week (7 days), only the 5 that can stay alive for at least 30 days will still be alive.

As a result, the probability that the chosen bacterium will still be alive after one week can be calculated by dividing the number of bacteria that can stay alive for at least 30 days (5) by the total number of currently alive bacteria (15).

Probablitiy = number of favourable outcomes / Total number of outcomes
Therefore, the probability that it will still be alive after one week is 5 / 15 = 1/3.

Therefore, the answer is (a) 1/3.

https://brainly.com/question/32117953

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Answer:

Step-by-step explanation:

Given is a phrase

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times."

This implies instead of attempting so many things without depth one thing indepth training is very much good and feared by others.

This applies to knowledge and also the subject Mathematics

Instead of practising many sums without getting answers, learning one concept and trying to get the difficult problem will help go a long way in learning.

In depth learning helps to master other allied concepts also very easily and this helps extending to other topics

Answer:

a) The distance of the light's base from the bottom of the building is approximately: 5.2 ft

b) The length of the beam is approximately: 10.4 ft

Step-by-step explanation:

First, we have to recognize that we may draw a right triangle to picture our problem. Then, in order to find out the distance of the light's base from the bottom of the building, we need to use the tangent trigonometric function:

tan(angle) = opposite side / adjacent side

We know the angle and the opposite side and we want to find the adjacent side:

adjacent side = opposite side / tan(angle) = 9 ft / tan(60°) = 9 ft / = 9 ft / 1.73 = 5.2 ft

In order to find the length of the light  beam, we use Pythagoras Theorem:

leg1²+leg2² = hyp²

Since the length of the beam corresponds to the hypotenuse and since we already know the length of the two legs, it is just a matter of substituting the values:

hyp = square_root(leg1²+leg2²) = square_root(9² + 5.2²) ft = square_root(108.4) ft = 10.4 ft

Answer:

(a) r = 57.628

    θ = 51.34°

(b) r = 0.711

    θ = 38.65°

Step-by-step explanation:

(a) Let's assume

 z = (5 + 4)(4 +5j)

    = 9 x (4+5j)

    = 36 + 45j

magnitude of z can be given by

[tex]\left | z \right |\ =\ r\ =\sqrt{36^2+45^2}[/tex]

               => r =57.628

angle of z can be given by,

     [tex]tan\theta\ =\ \dfrac{45}{36}[/tex]

[tex]=>\ tan\theta=\ \dfrac{5}{4}[/tex]

[tex]=>\ \theta\ =\ tan^{-1}\dfrac{5}{4}[/tex]

              θ = 51.34°        

(b) Let's assume

[tex]z =\ \dfrac{(5 +4j)}{5+4}[/tex]

    [tex]=\ \dfrac{(5+4j)}{9}[/tex]

    [tex]=\ \dfrac{5}{9}+\dfrac{4i}{9}[/tex]

magnitude of z can be given by

[tex]\left | z \right |=\ r=\sqrt{(\dfrac{5}{9})^2+(\dfrac{4}{9})^2}[/tex]

             [tex]=> r =\dfrac{\sqrt{41}}{9}[/tex]

              => r = 0.711

angle of z can be given by,

[tex]\ tan\theta\ =\ \dfrac{\dfrac{4}{9}}{\dfrac{5}{9}}[/tex]

[tex]=>\ tan\theta=\ \dfrac{4}{5}[/tex]

[tex]=>\ \theta\ =\ tan^{-1}\dfrac{4}{5}[/tex]

                => θ = 38.65°        

Answer:

5%.

Step-by-step explanation:

We have been given that a pharmacist attempts to weigh 120 mg of codeine sulfate on a balance with a sensitivity requirement of 6 mg.

To find the maximum potential error, we need to figure out 6 mg is what percentage of 120 mg.

[tex]\text{The maximum potential error}=\frac{6}{120}\times 100\%[/tex]

[tex]\text{The maximum potential error}=0.05\times 100\%[/tex]

[tex]\text{The maximum potential error}=5\%[/tex]

Therefore, the maximum potential error is 5%.

Answer:

B. It is greater than the median.

Step-by-step explanation:

If n is an odd, prime integer and 10<n<19, then the true statements about the mean of all possible values of n are:

B. It is greater than the median.

Here, n can be 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18.

But as n is odd , it can be 11, 13, 15 and 17.

And also it is given that n is prime, so we will cancel out 15.

Now we are left with 11, 13 and 17.

Their mean is = [tex]\frac{11+13+17}{3}[/tex] = 13.66

Median is 13, that is smaller than 13.66.

So, we can see that the mean is greater than median.

Answer:

Angle between the two vectors is 20.7718°.

Step-by-step explanation:

The given two vectors are x = (1,2,3,4) and y = (4,2,4,5)

Now the dot product between two vector is defined as

x.y = ║x║║y║cosθ

Now, x.y( dot product of x and y) = 1×4 + 2×2 + 3×4 + 4×5 = 40

║x║= [tex]\sqrt{1+4+9+16}[/tex] = [tex]\sqrt{30}[/tex]

║y║= [tex]\SQRT{16+4+16+25} = \sqrt{61}[/tex] '

Thus, we get

40 = [tex]\sqrt{30}[/tex]×[tex]\sqrt{61}[/tex]×Cos θ

Thus, Cos θ = [tex]\frac{40}{\sqrt{30}\sqrt{61}}[/tex]

Cos θ = 0.935

θ = [tex]Cos^{-1} (0.935)[/tex]

θ = 20.7718°

Answer:

The dimensions are 68 meters by 42 meters.

Step-by-step explanation:

Let the length be x

Let the width be y

Perimeter = 220 meter

So, [tex]2x+2y=220[/tex]

or [tex]x+y=110[/tex] or [tex]x=110-y[/tex]    ...........(1)

Area = 2856 square meter

So, [tex]xy=2856[/tex]     ............(2)

Substituting the value of x from (1) in (2)

[tex](110-y)y=2856[/tex]

=> [tex]110y-y^{2}=2856[/tex]

=> [tex]y^{2}-110y+2856=0[/tex]

Solving this equation, we get roots as y = 68 and y = 42

So, if we put y = 68, we get x = 42

If we put y = 42, we get x = 68

As length is longer than width, we will take length = 68 meters and width = 42 meters.

Hence, the dimensions are 68 meters by 42 meters.

Answer:

She have both activities again on 20th day from now.

Step-by-step explanation:

Given :Ronna has volleyball practice every 4 days

         Ronna also has violin lessons every 10 days.

To Find : When will she have both activities again on the same day?

Solution:

We will find the LCM of 4 and 10

2  |   4 ,10

2  |   2 , 5

5  |   1  , 5

   |   1  ,  1

So, [tex]LCM = 2\times 2 \times 5[/tex]

[tex]LCM =20[/tex]

Hence she have both activities again on 20th day from now.

Answer:

x=-5+2t, y=-6+3t, z=-6+9t

Step-by-step explanation:

We need to find parametric equations for the line through the point ( - 5, - 6, - 6) and perpendicular to the plane 2x + 3y + 9z = 17 .

If a line passes through a point [tex](x_1,y_1,z_1)[/tex] and perpendicular to the plane [tex]ax+by+cz=d[/tex], then the Cartesian form of line is

[tex]\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}[/tex]

and parametric equations are

[tex]x=x_1+at,y=y_1+bt,z=z_1+ct[/tex]

For the given information, [tex]x_1=-5,y_1=-6,z_1=-6,a=2,b=3,c=9[/tex]. So, the Cartesian form of line is

[tex]\frac{x+5}{2}=\frac{y+6}{3}=\frac{z+6}{9}[/tex]

Parametric equations of the line are

[tex]x=-5+2t[/tex]

[tex]y=-6+3t[/tex]

[tex]z=-6+9t[/tex]

Therefore the parametric equation for the line are x=-5+2t, y=-6+3t, z=-6+9t.

Final answer:

The parametric equations for the line are found using the point (-5, -6, -6) and the normal vector of the plane (2, 3, 9) as the direction vector, resulting in the equations x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Explanation:

To find a parametric equation for the line through the point (-5, -6, -6) and perpendicular to the plane 2x + 3y + 9z = 17, we use the fact that the normal vector of the plane (2, 3, 9) gives the direction of the line that is perpendicular to the plane. The general form of a parametric equation of a line is x = [tex]x_{0}[/tex] + at, y = [tex]y_{0}[/tex] + bt, and z = [tex]z_{0}[/tex] + ct, where [tex](x_{0},y_{0},z_{0})[/tex] is a point on the line and (a, b, c) is the direction vector of the line. In this case, the point given is (-5, -6, -6) and the direction vector is (2, 3, 9), so the parametric equations of the line are x = -5 + 2t, y = -6 + 3t, and z = -6 + 9t.

Answer: [tex]d) 2.0*10^2[/tex]kilo gram

Step-by-step explanation:  

To know the greatest mass we have to convert all these measurements to the same unit, the gram. For that we have to state the next units:

[tex]mili = 10^-^3\\micro = 10^-^6\\pico = 10^-^1^2\\kilo= 10^3[/tex]

Now we can convert the measurements to the same unit:

[tex]b)5.0*10^1^2*10^-^1^2gram=5.0gram\\d)2.0*10^2*10^3gram=2.0*10^5gram\\c)9.0*10^9*10^-^6gram=9.0*10^3gram\\a)2.0*10^6*10^-^3gram=2.0*10^3gram[/tex]

Comparating the values, we can see that the option d) is the greatest mass.

Answer:

The greatest mass among the following measurements is:

[tex]2*10^{2}kg = 200kg[/tex]

Step-by-step explanation:

I am going to convert each one of these measurements to kilogram, then the biggest value in kg is the greatest mass.

a) [tex]2*10^{6}mg[/tex]

Each kg has [tex]10^{6} kg[/tex].

So

1 kg - [tex]10^{6} kg[/tex]

x kg - [tex]2*10^{6}mg[/tex]

x = 2.

So

[tex]2*10^{6}mg = 2kg[/tex]

b)[tex]5*10^{12}pg[/tex]

Each kg has [tex]10^{15}pg[/tex].

So

1 kg - [tex]10^{15}pg[/tex]

x kg - [tex]5*10^{12}pg[/tex]

[tex]x = 5*10^{-3}kg[/tex]

This is a smaller mass than a)

c) [tex]9.0*10^{9} mcg[/tex]

Each kg has  [tex]10^{9}mcg[/tex].

So

1 kg - [tex]10^{9}mcg[/tex]

x kg - [tex]9*10^{9} mcg[/tex]

x = 9kg.

[tex]9.0*10^{9} mcg = 9kg[/tex]

For now, this is the greatest mass.

d) [tex]2*10^{2}kg = 200kg[/tex]

This is the greatest mass.

Answer:

(C) Of the lost items, 11% cost between $100 and $200

Step-by-step explanation:

On the Y-axis is represented the frequency of lost items found.

In this case in the form of a percentage.

On the X-axis is represented the range of prices

See picture attached.

So, this means that 11% of the found items have an estimated price between $100 and $200

Answer : (a) 5040  b) 720  c) 288

Step-to step explanation:-

Given : There are 3 Computer Science, 2 Mathematics, and 2 Sociology textbooks.

Total books = 7

a) The number of ways the books can be arranged in any order is given by :-

[tex]7!=7\times6\times5\times4\times3\times2=5040[/tex]

b) We consider all computer books as one thing, then, the total number of things to arrange = 1+2+2=5

Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-

[tex]3!\times5!\\\\=6\times120=720[/tex]

c) We consider all computer books as one thing and math book as one thing, then, the total number of things to arrange = 1+1+2=4

Now, the number of ways to arrange books such that Computer Science books must be together, but all other books can be arranged in any order:-

[tex]4!\times 3!\times2!=24\times6\times2=288[/tex]

Answer:

b) 15,90,24.133,20

c) New average = 19.4, New Median = 20

d) 8

e) 40%

f) Wednesday

Step-by-step explanation:

a)                    Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17    90

     Week 3      16      17    22     20   20

This is a 3×5 matrix where the rows gives us the weeks(Week 1, Week 2, Week 3) and the columns are the weekdays(Mon, Tue, Wed, Thu, Fri).

b)The shortest duration out of the data given for fifteen days is 15 minutes.

The longest duration is 90 minutes.

To calculate the average of given data, we use the following formula:

Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+90+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=24.133

Median = the value that divides the data into two equal parts]

Ascending order: 15,16,16,17,17,17,20,20,20,21,22,22,24,25,90

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

c)                   Mon  Tue  Wed  Thu  Fri    

     Week 1      17      16     20     24   22

     Week 2     15      21    25     17     19

     Week 3      16      17    22     20   20

New average = [tex]\frac{\text{Sum of new observations}}{\text{Total no of observations}}[/tex]

=[tex]\frac{17+16+20+24+22+15+21+25+17+19+16+17+22+20+20}{15}[/tex]

=[tex]\frac{362}{15}[/tex]

=19.4

New Median

Ascending order: 15,16,16,17,17,17,19,20,20,20,21,22,22,24,25

Median = [tex](\frac{n+1}{2})\text{th term}[/tex] = 8th term = 20

d) In order to know how many times we commute for 20 minutes or more, we check the entries that are greater than or equal to 20 minutes. We have 8 such entries. Thus, 8 times the commute was 20 minutes or more longer.

e)  Percent of commutes less than 18 minutes = [tex]\frac{\text{Commutes that are less than 18 minutes}}{\text{Total number of commutes} }[/tex]× 100%

=[tex]\frac{6}{15}[/tex]×100% = 40%

f) Average  = [tex]\frac{\text{Sum of all observations}}{\text{Total no of observations}}[/tex]

Average time spent in commuting on Monday = 16

Average time spent in commuting on Tuesday = 18

Average time spent in commuting on Wednesday = 22.3

Average time spent in commuting on Thursday = 20.3

Average time spent in commuting on Friday= 20.3

On Wednesday, we spent the most on commute time.

Answer:

An irrational number can never be represented precisely in decimal form.

Step-by-step explanation:

A number can be precisely represented in decimal form if you can give a rule for the construction of its decimal part,

for example:

2.246973973973973... (an infinite tail of 973's repeated over and over)

7.35 (a tail of zeroes)

If this the case, then the number is a RATIONAL NUMBER, i.e, the QUOTIENT OF TWO INTEGERS.

Let's show this for the first example and then a way to show the general situation will arise naturally.

Suppose N = 2.246973973973...

You can always multiply by a suitable power of 10 until you get a number with only the repeated chain in the tail

for example:

1) [tex]N.10^3=2246.973973973...[/tex]

but also

2) [tex]N.10^6=2246973.973973...[/tex]

Subtracting 1) from 2) we get

[tex]N.10^6-N.10^3=2246973.973973973... - 2246.973973973...[/tex]

Now, the infinite tail disappears

[tex]N.10^6-N.10^3=2246973 - 2246=226747[/tex]

But  

[tex]N.10^6-N.10^3=N.(10^6-10^3)=N.(1000000-1000)=999000.N[/tex]

We have then

999000.N=226747

and

[tex]N=\frac{226747}{999000}[/tex]

We do not need to simplify this fraction, because we only wanted to show that N is a quotient of two integers.

We arrive then to the following conclusion:

If an irrational number could be represented precisely in decimal form, then it would have to be the quotient  of two integers, which is a contradiction.

So, an irrational number can never be represented precisely in decimal form.

Answer:

solved

Step-by-step explanation:

Calculating i found the value of [tex]\frac{1}{128}[/tex]= 0.0078125

a.therefore the approximate valve of  [tex]\frac{1}{128}[/tex] (correct to three       decimal places) = 0.008

b. there are three significant digits in my approximation.

c. the absolute error = | exact value- approximate value |

   =|0.0078125- 0.008|= |-0.0001875| = 0.0001875

d.relative error= [tex]\frac{ absolute\ error}{exact\ value}[/tex]

    = [tex]\frac{0.0001875}{0.0078125}[/tex]= 0.024

Answer: Probability of trucks having both defects is 4%.

Step-by-step explanation:

Since we have given that

Probability of trucks having defective brake linings only = 6%

Probability of trucks having defective steering only = 3%

Probability of trucks having neither defect = 87%

Probability of trucks having either defect - 100 - 87 = 13%

Let the probability of trucks having both defects be 'x'.

P(defective brake lining) = P(B) = 0.06+x

P(defective steering) = P(S) = 0.03+x

So, Probability of the trucks having both defects is given by

[tex]P(S\cup B)=P(S)+P(B)-P(S\cap B)\\\\0.13=0.03+x+0.06+x-x\\\\0.13-0.03-0.06=2x-x\\\\0.04=x[/tex]

So, Probability of trucks having both defects is 4%.

The percentage of trucks with both defects is 0%.

To solve this problem, we will use the principle of inclusion-exclusion. Let's assume that the percentage of trucks with both defects is x. The percentage of trucks with only defective steering is 3%, the percentage of trucks with only defective brake linings is 6%, and the percentage of trucks with neither defect is 87%. We want to find the percentage of trucks with both defects.

According to the principle of inclusion-exclusion, the total percentage of trucks with at least one defect is given by:

Total = Percentage with defective steering + Percentage with defective brake linings - Percentage with both defects

Using the given percentages, we can set up the equation:

100% = 3% + 6% - x

Simplifying the equation, we get:

x = 9% - 100% = -91%

Since a negative percentage does not make sense in this context, there are no trucks with both defects.

Answer:

[tex]C^{102}_{100}=5151[/tex]

Step-by-step explanation:

Let's imagine the following situation, if we want to distribute 100 coins between three pirates we could represent this situation with a line arrangement. For example if we had7 coins and 3 pirates one possible distribution of coins would be given by  CC|CCCC|C, the C's represent coins and the bars the boundaries between two pirates, for the particular line arrangement shown, we have that pirate A has 2 coins, B has 4 coins and C has a single coin. Another possible arrangement is,

|CCC|CCCC, where pirate A has no coin, pirate B has 3 coins and C has 7 coins. If we take notice of the fact that the arrangement representing a distribution is composed of 9 elements, that is 7 C's and 2 | (bars), then a way to make an arrangement would be to fill 9 empty boxes with our available coins and bars in all the possible ways. This means that if we first choose to fill 7 out of 9 boxes with  coins then the number of possible combinations is [tex]C^{9}_7=\frac{9!}{7!(9-7)!}36[/tex]. In general if we want to distribute n elements in k boxes, where the boxes can either be filled with any number of elements (including 0 number of elements), we have that the number of possible distributions will be [tex]C^{n+k-1}_{n}=\frac{(n+k-1)!}{n!(k-1)!}[/[tex], where we used the fact that we need k-q bars to represent k boxes. Thus pirate A can choose from [tex]C^{102}_{100}=5151[/tex] possible divisions.

Bonus:

If every pirate wants to have the maximum number of coins possible without being executed, here's how pirate A has to divide the coins in order to keep the largest amount of coins.

We have to think backwards to figure this out. Imagine pirate A was executed and there are only two remaining players. Pirate B should propose to keep all the coins, pirate C could oppose but pirate B's vote would break the vote and keep all the loot. Pirate A, B and C are all aware of this, so pirate A should propose to keep 99 coins and give the remaining gold piece to pirate C, Pirate B will of course oppose the division, but pirate C should accept because if not he would get no coins. Thus the division would be.

A: 99 coins

B: 0 coins

C: 1 coins

The measure of angle ABC in the figure is 53 degrees.

Option D) 53° is the correct answer.

From the figure in the image;

Angle ABC and angle CBD are complementary angles, hence, their sum equals 180 degrees.

From the figure:

Angle ABC = ( 5x + 3 )

Angle CBD = ( 3x + 7 )

First, we solve for x:

Since the two angles are complementary:

Angle ABC + Angle CBD = 90

( 5x + 3 ) + ( 3x + 7 ) = 90

5x + 3x + 3 + 7 = 90

8x + 10 = 90

8x = 90 - 10

8x = 80

x = 80/8

x = 10

Now, we find the measure of angle ABC:

Angle ABC = ( 5x + 3 )

Plug in x = 10:

Angle ABC = 5(10) + 3

Angle ABC = 50 + 3

Angle ABC = 53°

Therefore, angle ABC measures 53 degrees.

The correct option is D) 53°

Answer:

True

Step-by-step explanation:

Let B={[tex]v_1, v_2,\cdots,v_k,0[/tex]} a set of vectors containing the zero vector.

B is linear dependent if exist scalars [tex]a_0,a_1, a_2,\cdots,a_k[/tex] not all zero such that [tex]a_0*0+a_1*v_1+\cdots+a_k*v_k=0[/tex].

Observe that if [tex]a_1=a_2=\cdots=a_k=0[/tex] and [tex]a_0=\lambda\neq 0[/tex] then

[tex]\lambda*0+0*v_1+\cdots+0*v_k=0[/tex].

Then B is linear dependent.

Final answer:

True, any set of vectors that contains the zero vector is linearly dependent because a nontrivial combination of the vectors (including the zero vector scaled by any scalar) can produce the null vector.

Explanation:

True. Any set of vectors containing the zero vector is linearly dependent. This is because the null vector, which has all components equal to zero (0î + 0ç + 0k) and therefore no length or direction, can always be represented as a linear combination of other vectors in the set by simply scaling it by any scalar. In more technical terms, for a set of vectors that includes the zero vector, you can find a nontrivial combination (not all scalars being zero) such that when these scalars are applied to their respective vectors, their sum equals the zero vector. This is the very definition of linear dependency. For instance, if you consider any scalar 'a' not equal to zero, a∗0 + 0∗0 + ... + 0∗0 = 0, which demonstrates linear dependence because not all the scalars are zero (namely 'a' is not).

Linear independence would require that the only way to represent the zero vector as a linear combination of the set of vectors is to have all scalars that multiply each vector in the combination be zero. Since the set includes the zero vector itself, this condition is violated, and the set is dependent.

Answer:

1536 tiles

Step-by-step explanation:

Given,

The length of kitchen = 10 ft,

Width of the kitchen = 8 ft,

∵ The shape of floor of kitchen must be rectangular,

Thus, the area of the kitchen = 10 × 8 = 80 square ft = 11520 in²

( Since, 1 square feet = 144 square inches )

Now, the length of a tile = 2.5 in and its width = 3 in,

So, the area of each tile = 2.5 × 3 = 7.5 in²,

Hence, the number of tiles needed = [tex]\frac{\text{Area of kitchen}}{\text{Area of each tile}}[/tex]

[tex]=\frac{11520}{7.5}[/tex]

= 1536

Approximately 1536 tiles are needed to cover a kitchen floor that is 10 feet by 8 feet using tiles that are 2.5 inches by 3 inches.

To determine how many tiles are needed to cover a kitchen floor that is 10 feet long and 8 feet wide with tiles that are 2.5 inches by 3 inches, we first need to convert the dimensions of the kitchen to inches because the tile dimensions are given in inches. There are 12 inches in a foot, so the kitchen is 120 inches long (10 feet × 12 inches/foot) and 96 inches wide (8 feet  × 12 inches/foot).

We now calculate the area of the kitchen floor: Area = Length ×  Width = 120 inches × 96 inches = 11520 square inches.

Next, we calculate the area of one tile: Tile Area = Length × Width = 2.5 inches × 3 inches = 7.5 square inches.

Now, to find the number of tiles needed, we divide the total area of the kitchen floor by the area of one tile: Number of Tiles = Kitchen Area / Tile Area = 11520 square inches / 7.5 square inches ≈ 1536 tiles.

Therefore, approximately 1536 tiles are needed for the kitchen.

Final answer:

To find the percentage of students who voted for the athlete, divide the number who voted for the athlete (25) by the total number of students (100), and multiply by 100%. Therefore, 25% of the students voted for the athlete.

Explanation:

To calculate the percentage of students who voted for the athlete, we divide the number of students who voted for the athlete by the total number of students who voted, and then multiply the result by 100 to convert it to a percentage.

Total number of students = 25 (voted for the athlete) + 75 (voted for the actor) = 100 students

Now, to find the percentage who voted for the athlete:

Percentage voting for the athlete = (Number of students voting for the athlete ÷ Total number of students) × 100%

Percentage voting for the athlete = (25 ÷ 100) × 100%

Percentage voting for the athlete = 0.25 × 100%

Percentage voting for the athlete = 25%

25% of the students voted for the athlete.

Answer with Step-by-step explanation:

We are given that sum of three vectors in [tex]R^3[/tex] is zero.

We have to tell and explain that if sum of three vectors in [tex]R^3[/tex] is zero then they must lie in the same plane or not.

We know that if three or more vectors lie in the same then they are coplanar.

If three vectors are co-planar then their scalar product is zero.

According to given condition

Let (x,0,0), (-x,0,0) and (0,0,0)

[tex]\vec{u}=x\hat{i}[/tex]

[tex]\vec{v}=-x\hat{i}[/tex]

[tex]\vec{w}=0[/tex]

Sum of three vectors=[tex](x-x+0)\hat{i}+(0+0+)\hat{j}+(0+0+0)\hat{k}=0[/tex]

[tex]u\cdot (v\times w)=\begin{vmatrix}x_1&y_1&z_1\\x_2&y_2&z_2\\x_3&y_3&z_3\end{vmatrix}[/tex]

[tex]u\cdot (v\times w)=\begin{vmatrix}x&0&0\\-x&0&0\\0&0&0\end{vmatrix}[/tex]

When all elements of one row or column are zero of square matrix A then det(A)=0

[tex]u\cdot (v\times w)=0[/tex]

Therefore, vectors u,v and w are co-planar.

Hence, if the sum of three vectors in [tex]R^3[/tex] is zero then they must lie in the same plane.

If the sum of three vectors in three-dimensional space is zero, they typically lie in the same plane, forming a triangle with their magnitudes and directions. They must also be linearly dependent since their linear combination can produce the zero vector.

If the sum of three vectors is zero in R^3 (three-dimensional space), it is a common situation for these vectors to lie in the same plane. This condition implies that they can be represented as three sides of a triangle taken in sequence in terms of magnitude and direction. If we consider two vectors in sequence, such as AB and BC, the third vector must be the closing side CA, taken in the opposite direction, in order to satisfy the triangle law of vector addition. In this case, the sum of vectors AB + BC + CA equals zero.

Furthermore, vectors are homogeneous when added, which means that they must have the same nature and dimension. However, three vectors can still form a linearly dependent set in three-dimensional space even if they lie in the same plane. For instance, if we take vectors a, b, and c, and if a linear combination of these vectors yields the zero vector (i.e., if we can find scalar coefficients x, y, and z such that xa + yb + zc = 0), then these vectors are not linearly independent and must lie in the same plane.

Answer:

Multiplication is commutative.          

Step-by-step explanation:

Let n,m be two natural numbers.

We have to show that [tex]n\times m=m\times n[/tex]

We will prove this by induction

For n = 1, we have [tex]n\times 1 = 1\times n = n[/tex], which is true.

Let the given statement be true for n-1 natural numbers, that is,

[tex](n-1)\times m = m\times (n-1)[/tex]

Now, we have to show that it is true for n natural numbers.

[tex]nm = (n-1)m + m = m(n-1) + m[/tex]

which is equal to

[tex](m-1)(n-1) + (n-1) + m[/tex]

[tex]= (m-1)(n-1) + (m-1) + n[/tex]

[tex]= n(m-1) + n[/tex]

[tex]= (m-1)n + n[/tex]

[tex]= mn[/tex]

Hence, by principal of mathematical induction, the given statement is true for all natural numbers.

Answer:

5 = radius

Step-by-step explanation:

According to one of the Circle Equations, (X - H)² + (Y - K)² = R², you take the square root of your squared radius:

√25 = √R²

5 = R

* When we are talking about radii and diameters, we want the NON-NEGATIVE root.

I am joyous to assist you anytime.

To estimate the result of 542,817 - 27,398, we can round to the nearest ten thousand and perform the subtraction, yielding an estimation of 510,000.

The student wants to estimate the result of 542,817 - 27,398. One way of doing this is by rounding to the nearest ten thousand. In this case, 542,817 becomes 540,000 and 27,398 becomes 30,000.

Now, perform the calculation: 540,000 - 30,000 = 510,000. Hence, the estimated result of 542,817 - 27,398 is roughly 510,000.

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Answer:

229.17 kilo-calories

Step-by-step explanation:

We have been given that 240 ml of orange juice (1 cup) provides about 110 kcal.

First of all, we will divide 500 by 240 to find amount of cups in 500 ml.

[tex]\text{Number of cups}=\frac{500}{240}[/tex]

[tex]\text{Number of cups}=2.08333[/tex]

Now, we will multiply 2.08333 by 110 to find amount of k-cal in orange juice.

[tex]\text{Number of k-cal}=2.08333\times 110\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}=229.16666\text{ k-cal}[/tex]

[tex]\text{Number of k-cal}\approx 229.17\text{ k-cal}[/tex]

Therefore, there are approximately 229.17 kilo-calories in 500 ml of orange juice.

Final answer:

To find the number of kcalories in 500 ml of orange juice, set up a proportion using the known ratio of 240 ml to 110 kcal. Cross multiply and solve for the unknown value to find that there are approximately 229 kcalories in 500 ml of orange juice.

Explanation:

To calculate the number of kcalories in 500 ml of orange juice, we can use the ratio method. First, we know that 240 ml (1 cup) of orange juice provides 110 kcal. We can set up a proportion to find the number of kcalories in 500 ml of orange juice.

240 ml / 110 kcal = 500 ml / x kcal

Cross multiplying, we get 240x = 55000. Dividing both sides by 240, we find that x is approximately equal to 229.17. Therefore, there are about 229 kcalories in 500 ml of orange juice.