Gandalf the Grey started in the Forest of Mirkwood at a point P with coordinates (3, 0) and arrived in the Iron Hills at the point Q with coordinates (5, 5). If he began walking in the direction of the vector v - 3i + 2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn?

Answer: There are 1,816,214,400 ways for arrangements.

Step-by-step explanation:

Since we have given that

"REPRESENTATION"

Here, number of letters = 14

There are 2 R's, 3 E's, 2 T's, 2 N's

So, number of permutations would be

[tex]\dfrac{14!}{2!\times 3!\times 2!\times 2!}\\\\=1,816,214,400[/tex]

Hence, there are 1,816,214,400 ways for arrangements.

Answer:

The tower deviates [tex]64^\circ36'[/tex] from the vertical.

Step-by-step explanation:

Having 3 point of our new plane we can construct vectors on the plane by substacting 2 of them:

[tex]v_1=(0,3,2)-(0,0,0)\\v_2=(1,3,0)-(0,0,0)[/tex]

These vectors are on the plane, so a cross product between them will give us a vector perpendicular to the plane:

[tex](0,3,2)\times(1,3,0)=\left[\begin{array}{ccc}i&j&k\\0&3&2\\1&3&0\end{array}\right] =(-6,2,-3)[/tex]

Asuming that the aliens used our conventions, the original plane was perpendicular to the z axis, so that a perpendicular vector to that plane was

(0,0,1)

We know that a dot product between 2 vectors |V.W| = |V| |W| cos(α), where α is the angle between them. If we use the vector perpendicular to this plane, and the one perpendicular to the original plane, α will represent the deviation angle of our new plane.

[tex]\|(-6,2,-3)\|=7\\\|(0,0,1)\|=1[/tex]

[tex](-6,2,-3)\odot(0,0,1)= 7 cos(\alpha )\\\\ -3=7 cos(\alpha ) \\ \alpha=arc\ cos \frac{-3}{7} =115.37 ^\circ\\[/tex]

Since this angle is greater than 90 degrees it means that the vector we calculated as perpendicular to the plane points towards negative z (this can be seen by the -3 z component)

To fix this we can calculate a new perpendicular vector, or simply compare ir with the vector (0,0,-1). The latter is easier:

[tex](-6,2,-3)\odot(0,0,-1)= 7 cos(\alpha )\\\\ 3=7 cos(\alpha ) \\ \alpha=arc\ cos \frac{3}{7} =64.6^\circ =64^\circ36'[/tex]

Answer:

No , any two quadrilaterals may not be similar if  their corresponding angles are congruent.

Step-by-step explanation:

We need to check that whether two quadrilaterals are similar if

their corresponding angles are congruent.

A  quadrilateral is a polygon having two sides .

Two figures are said to be similar if they have same shape .

Two angles are said to be congruent if they have same measure .

Consider two quadrilaterals :  rectangle and square

Each angle of square and rectangle is equal to [tex]90^{\circ}[/tex] . So, their corresponding angles are congruent .

But square and rectangle are not similar as they have different shape .

Answer: 120000 W and 0.12 MW

Step-by-step explanation:

The expression 120 kW uses a metric prefix "k" (kilo) which is the same as multiply by 1000. So you can replace k by 1000 to convert the expression to the unit W.

120 kW= 120(1000) W= 120000 W.

To convert 120kW to MW, where the prefix M (mega) is equivalent to 1000000, you can use a conversion factor like (1 MW / 1000 kW) and multiply the expression by it.

Notice that (1 MW / 1000 kW) = 1, so the expression remains unaltered.

Then,

120 kW (1 MW / 1000 kW) = 0.12 MW

Answer:

a) [tex]y(t) = y_{0}e^{4t} + 2[/tex]. It does not have a steady state

b) [tex]y(t) = y_{0}e^{-4t} + 2[/tex]. It has a steady state.

Step-by-step explanation:

a) [tex]y' -4y = -8[/tex]

The first step is finding [tex]y_{n}(t)[/tex]. So:

[tex]y' - 4y = 0[/tex]

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

[tex]r - 4 = 0[/tex]

[tex]r = 4[/tex]

So:

[tex]y_{n}(t) = y_{0}e^{4t}[/tex]

Since this differential equation has a positive eigenvalue, it does not have a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

[tex]y_{p}(t) = C[/tex]

So

[tex](y_{p})' -4(y_{p}) = -8[/tex]

[tex](C)' - 4C = -8[/tex]

C is a constant, so (C)' = 0.

[tex]-4C = -8[/tex]

[tex]4C = 8[/tex]

[tex]C = 2[/tex]

The solution in the form is

[tex]y(t) = y_{n}(t) + y_{p}(t)[/tex]

[tex]y(t) = y_{0}e^{4t} + 2[/tex]

b) [tex]y' +4y = 8[/tex]

The first step is finding [tex]y_{n}(t)[/tex]. So:

[tex]y' + 4y = 0[/tex]

We have to find the eigenvalues of this differential equation, which are the roots of this equation:

[tex]r + 4 = [/tex]

[tex]r = -4[/tex]

So:

[tex]y_{n}(t) = y_{0}e^{-4t}[/tex]

Since this differential equation does not have a positive eigenvalue, it has a steady state.

Now as for the particular solution.

Since the differential equation is equaled to a constant, the particular solution is going to have the following format:

[tex]y_{p}(t) = C[/tex]

So

[tex](y_{p})' +4(y_{p}) = 8[/tex]

[tex](C)' + 4C = 8[/tex]

C is a constant, so (C)' = 0.

[tex]4C = 8[/tex]

[tex]C = 2[/tex]

The solution in the form is

[tex]y(t) = y_{n}(t) + y_{p}(t)[/tex]

[tex]y(t) = y_{0}e^{-4t} + 2[/tex]

Answer:

8%

Step-by-step explanation:

Motivation to learn represents a 40% of the learning acquired and its rated from 1 to 10. An increase from 7 to 9 represents an increase (of motivation to learn of 20%) But since this quality represent 40% of the total, the real increase in learning is 0.2*0.4=0.08 or 8%.

Answer:

There are two unknow values, your 8% which is the decrease and the main value which is "the sales last year".

It is correct, the number you gave as an answer $9798,91. Let's get the explanation by a rule of three.

Step-by-step explanation:

The 100 % was "the sales last year", the 8% are what the sales decreased but you don't have that number, you have the result in the substraction, $9015. So this are the step by step, hope you understand!

Answer:

[tex]0\le x\le 400[/tex]

x can take infinitely many values

Step-by-step explanation:

Vanessa walks from her house to a bus stop that is 400 yards away.

Let the variable x represent Vanessa's varying distance from her house (in yards). Then 400 - x yards is how far Vanessa is from the bus stop.

The variable x can take any value from 0 to 400 (0 when Vanessa is at home and 400 when Vanessa is at bus station), so

[tex]0\le x\le 400[/tex]

x can take infinitely many values, because there are infinitely many real numbers between 0 and 400.

Vanessa is 378 yards from the bus stop when she is 22 yards from her house and 236.6 yards away when she is 163.4 yards from her house. The variable x denoting Vanessa's distance from home assumes infinitely many values as she walks to the bus stop.

When Vanessa is 22 yards from her house, the distance remaining to reach the bus stop is simply the total distance to the bus stop minus her current position from the house. So, it's 400 yards - 22 yards = 378 yards. Similarly, if Vanessa is 163.4 yards from her house, the remaining distance to the bus stop is 400 yards - 163.4 yards = 236.6 yards.

As Vanessa walks from her house to the bus stop, variable x represents her varying distance from her house. The value of x starts at 0 when she is at her house and increases up to 400 yards as she reaches the bus stop. The variable x can assume infinitely many values, as it can represent any real number between 0 and 400, indicating her position at any given moment along her path.

Answer:

[tex]12.0\%=0.12[/tex]

Step-by-step explanation:

We have been given that your friend borrows $100 from you and promises to pay you back $109 in 8 months.

We will use simple interest formula to solve our given problem.

[tex]A=P(1+rt)[/tex], where,

A = Amount after t years,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

Convert 8 months to year:

[tex]\frac{8}{12}\text{ year}=\frac{2}{3}\text{ year}[/tex]

[tex]108=100(1+r*\frac{2}{3})[/tex]

[tex]108=100+r*\frac{2}{3}\times 100[/tex]

[tex]108-100+r*\frac{200}{3}[/tex]

[tex]108-100=100-100+r*\frac{200}{3}[/tex]

[tex]8=r*\frac{200}{3}[/tex]

[tex]8\times \frac{3}{200}=r*\frac{200}{3}\times \frac{3}{200}[/tex]

[tex]\frac{24}{200}=r[/tex]

[tex]r=\frac{24}{200}[/tex]

[tex]r=0.12[/tex]

Convert to percent:

[tex]0.12\times 100\%=12\%[/tex]

Therefore, you are charging 12% APR to you friend.

Answer:

20%

Step-by-step explanation:

To find what percentage is $10 out of $50, we divide 10 by 50:

[tex] \frac{10}{50}=0.2[/tex]

If we want to get the result in percentage form, we simply multiply it by 100%:

[tex]0.2\cdot 100\%=20\%[/tex]

So a tip of $10 on a $50 bill is a tip of 20%.

Answer: P(3) is True

Step-by-step explanation:

The given statement is an inequality denoted as P(x). To find out which of the options is true you have to evaluate each given value of X in the inequality and perform the arithmetic operations, then you have to see if the expression makes sense.

For P(0): Replace X=0 in 2x+5>10

2(0)+5>10

0+5>10

5>10 is false because 5 is not greater than 10

For P(3): Replace X=3 in 2x+5>10

2(3)+5>10

6+5>10

11>10 is true because 11 is greater than 10

For P(2): Replace X=2 in 2x+5>10

2(2)+5>10

4+5>10

9>10 is false

For P(1): Replace X=1 in 2x+5>10

2(1)+5>10

2+5>10

7>10 is false

Answer:

This was an observational study.

Step-by-step explanation:

Given is that parents of children completed a questionnaire on the child’s light exposure both at present and before the age of 2 years.

This was an observational study since there is no treatment or control group.

We know that treatment, control groups or treatment groups are not specific to randomized control experiments.

The study where parents of pediatric ophthalmology patients completed questionnaires about light exposure is an observational study because data were collected without manipulating any variables.

The study described in which parents filled out questionnaires about their children's light exposure is an example of an observational study, not a controlled experiment. In an observational study, researchers collect data without manipulating any variables. In this case, the researchers gathered information on light exposure by asking parents to complete a questionnaire, but they did not control or alter the children's light exposure themselves.

Unlike in an observational study, a controlled experiment involves actively manipulating one variable (the independent variable) to determine if it causes a change in another variable (the dependent variable), often comparing against a control group in a systematic way. An example of a controlled experiment includes the trial of Jonas Salk's polio vaccine, in which one group received the vaccine and another group received a placebo.

The particular solution to the differential equation with the initial condition P(0) = 3000 is given by P = 3000e^((ln(2)/6)t), where P represents the population at time t. The growth rate is proportional to the population, and the constant of proportionality is ln(2)/6. This equation can be derived by solving the differential equation and using the initial condition.

In this problem, we are given that the population of a suburb grows at a rate proportional to the population. We are also given that the population doubles in size from 3000 to 6000 in a 6-month period. We need to find the particular solution to the differential equation with the initial condition P(0)=3000.

Let's denote the population at time t as P(t). Since the growth rate is proportional to the population, we can write the differential equation as dP/dt = kP, where k is the proportionality constant.

Integrating both sides of the equation, we get: ∫dP/P = ∫kdt. This gives us ln|P| = kt + C, where C is the constant of integration.

Using the initial condition P(0) = 3000, we can substitute t = 0 and P = 3000 into the equation to get: ln|3000| = 0 + C. Solving for C, we find C = ln|3000|.

Substituting C = ln|3000| back into the equation, we have ln|P| = kt + ln|3000|. Simplifying, we get ln|P| - ln|3000| = kt.

Since ln|P| - ln|3000| = ln|(P/3000)|, we can write the equation as ln|(P/3000)| = kt.

Taking the exponential of both sides, we get |(P/3000)| = e^(kt).

Since the population cannot be negative, we can remove the absolute value sign and write the equation as (P/3000) = e^(kt).

Substituting the doubling in size from 3000 to 6000 in a 6-month period, we have (6000/3000) = e^(k(6)).

Simplifying, we get 2 = e^(6k).

Taking the natural logarithm of both sides, we have ln(2) = ln(e^(6k)).

Using the property ln(a^b) = bln(a), we can rewrite the equation as ln(2) = 6kln(e).

Since ln(e) = 1, we have ln(2) = 6k.

Solving for k, we get k = ln(2)/6.

Substituting k = ln(2)/6 back into the equation, we have (P/3000) = e^((ln(2)/6)t).

Multiplying both sides by 3000, we get P = 3000e^((ln(2)/6)t).

This is the particular solution to the differential equation with the initial condition P(0) = 3000.

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Step-by-step explanation:

First:

(Error/Total )x 100%

(0.49/23) x100%= 2.13%

Second:

(Absolute uncertainty/mean) x100%

(3/44)x100%= 6.81%

To calculate percent uncertainty, divide the uncertainty by the measured value and multiply by 100%. The percent uncertainty for the measuring tape is 0.0213%. The percent uncertainty for heartbeats (converted to per minute) is 6.82%.

The subject of this question is determining the percent uncertainty of measurements. Percent uncertainty is calculated by dividing the uncertainty by the measurement and multiplying by 100%.

1. For the measuring tape, the uncertainty is 0.49 cm which first needs to be converted to meters (0.0049 m) since the measurement is given in meters. The percent uncertainty of the measuring tape is therefore (0.0049 m / 23m) * 100% = 0.0213%, a small percentage reflecting a high level of accuracy.

2. For counting heartbeats, the uncertainty is 3 beats and the measurement is 44 beats. Since it's measured in 30 seconds, we should double it to get beats per minute. Therefore, the uncertainty becomes 6 beats and the measurement becomes 88 beats. The percent uncertainty is therefore (6 beats / 88 beats) * 100% = 6.82%, a more considerable uncertainty.

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Answer:

The negation will be : The shirt I am wearing to my interview is not orange.

Step-by-step explanation:

The negation of the statement means adding not, or nor to the statement.

The given statement is :

The shirt I’m wearing to my interview is orange.

The negation will be : The shirt I am wearing to my interview is not orange.

Answer:

0.2s is the time from the initial launch of the warhead to impact.

Step-by-step explanation:

This is a rule of three problem

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, our measures have a direct relationship.

The problem states that in a second, the warhead travels 489 meters. How long it takes to travel 100 meters? So

1s - 489m

xs - 100m

489x = 100

[tex]x = \frac{100}{489}[/tex]

x = 0.2s.

0.2s is the time from the initial launch of the warhead to impact.

Answer:

  67.73625

Step-by-step explanation:

The dot (scalar) product is also the sum of products of corresponding vector components.

~a • ~b = 9·2.97 +6.75·6.075 +0·0 = 27.73 +41.00625 = 67.73625

The scalar product or dot product of two vectors, ~a and ~b, in Cartesian form is calculated by multiplying the matching components of the two vectors and then adding them. Performing these steps will give us 67.73625, which represents the magnitude of ~a with the magnitude of the projection of ~b onto the direction of ~a.

In physics, the scalar product, also known as dot product, of two vectors like ~a = h9, 6.75, 0i and ~b = h2.97, 6.075, 0i can be determined using their magnitudes and the cosine of the angle between them. However, in the given question, the vectors are in Cartesian form (i,j,k coordinate system), and we can calculate their dot product directly. The dot product is calculated by multiplying the respective i, j, and k components of the two vectors and then adding them. Let's do this step by step:

This scalar product gives the product of the magnitude of ~a with the magnitude of the projection of ~b onto the direction of ~a.

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Answer:

11/4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12x+3−1=35

12x+3+−1=35

(12x)+(3+−1)=35(Combine Like Terms)

12x+2=35

12x+2=35

Step 2: Subtract 2 from both sides.

12x+2−2=35−2

12x=33

Step 3: Divide both sides by 12.

12x / 12 = 33 / 12x =

11 / 4

Answer:

The 5.5 would be called a parameter.

Step-by-step explanation:

A parameter in statistics is a data/number/quantity that gives you information about an entire population. Given that Dr. Johnson asked ALL of her students to respond the question and the median of 5.5 was based on ALL of her students, we can say that this number would be a parameter for the population (in this case, Dr. Johnson's class)

Answer: [tex]20.38\ cm^2[/tex]

Step-by-step explanation:

We know that the circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle .

Given : Circumference of circle = 16 cm

Then, [tex]16=2\pi r[/tex]

i.e [tex]r=\dfrac{16}{2\pi}=\dfrac{8}{\pi}[/tex]          (1)

We know that the area of circle is given by :-

[tex]A=\pi r^2[/tex]

i.e. [tex]A=\pi (\dfrac{8}{\pi})^2[/tex]                    [From (1)]

i.e. [tex]A=\pi (\dfrac{64}{\pi^2})[/tex]

i.e. [tex]A=\dfrac{64}{\pi}[/tex]

Put [tex]\pi=3.14[/tex]

[tex]A=\dfrac{64}{3.14}=20.3821656051approx20.38\ cm^2[/tex]

Hence, area of circle = [tex]20.38\ cm^2[/tex]

Answer:

(4.5, 4.7)

Step-by-step explanation:

Hi!

Lets call X to the consumption of milk per week among males over age 32. X has a normal distribution with mean μ and standard deviation σ.

[tex]X \sim N(\mu, \sigma)[/tex]

When you know the population standard deviation σ of X  ,  and the sample mean is [tex]\hat X[/tex], the  variable q has distribution N(0,1):

[tex]q = \frac{\hat X - \mu}{\sigma} \sim N(0,1)[/tex]

Then you have:

[tex]P(-k < q <k ) = P(\hat X -\frac{\sigma}{\sqrt{N} }<\mu<\hat X +\frac{\sigma}{\sqrt{N} })=C[/tex]

This defines a C - level confidence interval. For each C the value of k is well known. In this case C = 0.98, then k = 2.326

Then the confidence interval is:

[tex](4.6 - 2.326*\frac{0.8}{\sqrt{710}}, 4.6 + 2.326*\frac{0.8}{\sqrt{710}})\\ (4.5, 4.7)[/tex]

Answer:

p-value = 0.1277

Step-by-step explanation:

p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.

Firstly we find the mean and standard deviation of the given data set.

⇒ Mean = [tex]\frac{4.41 +4.37+ 4.33+ 4.35 +4.30 +4.39 +4.36+ 4.38+ 4.40+ 4.39}{10}[/tex]

⇒ Mean = 4.368

[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }[/tex]

where, [tex]\bar{x}[/tex] is mean of the distribution.

⇒ Standard Deviation = 0.034

Applying t- test:

Let out hypothesis is:

H₀: μ = 4.35

H₁: μ ≠ 4.35

Now,

Here, μ = Population Mean = 4.35

[tex]\bar{x}[/tex]= Sample Mean = 4.368

σ = Standard Deviation = 0.034

n = 10

[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]

Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.

Then the p-value at 99% level of significance.

⇒ p-value = 0.1277

To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We will calculate the t-value and the p-value and compare the p-value with the significance level of 0.01.

To test whether the special additive has increased the mean weight of the chickens, we can use a t-test. We can set up the null hypothesis as follows:

H0: μ = 4.35

And the alternative hypothesis as:

H1: μ > 4.35

We will calculate the t-value and the p-value.

t-value = (mean of the sample - mean of the population) / (standard deviation of the sample / sqrt(sample size))

p-value = P(T > t)

In this case, we have to compare the p-value with the significance level of 0.01.

If the p-value is less than 0.01, we reject the null hypothesis and conclude that the special additive has increased the mean weight of the chickens.

Answer:

x = 22

Step-by-step explanation:

9x = 99y

y = 2

9x = 99 * 2

99 * 2 = 198

9x = 198

---     ----

9        9

x = 22

Hey!

------------------------------------------------

Solution:

9x = 99y

~Substitute

9x = 99(2)

~Simplify

9x = 198

~Divide 9 to both sides

9x/9 = 198/9

~Simplify

x = 22

------------------------------------------------

Answer:

x = 22

------------------------------------------------

Hope This Helped! Good Luck!

In order to get the answer to this question you will have to use KCC (Keep, Change, Change) and then solve.

[tex]-1.8 - 3.9=[/tex]

Using KCC:

[tex]-1.8-3.9=-1.8+-3.9[/tex]

[tex]-1.8 + -3.9 = -5.7[/tex]

[tex]= -5.7[/tex]

Therefore your answer is option D "-5.7."

Hope this helps.

Answer:

D "-5.7."

Step-by-step explanation:

Answer:

The 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Step-by-step explanation:

The given sequence is

[tex]40,10, \frac{5}{2}, \frac{5}{8}, ....[/tex]

The given sequence is a geometric​ sequence because it have common ratio.

[tex]r=\frac{10}{40}=\frac{\frac{5}{2}}{10}=\frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}[/tex]

In the given sequence the first term of the sequence is 40.

[tex]a_1=40[/tex]

The nth term of a GP is

[tex]a_n=a_1r^{n-1}[/tex]

where, [tex]a_1[/tex] is first term and r is common ratio.

Substitute [tex]a_1=40[/tex] and [tex]r=\frac{1}{4}[/tex] in the above formula.

[tex]a_n=40(\frac{1}{4})^{n-1}[/tex]

Substitute n=10 , to find the 10th term.

[tex]a_{10}=40(\frac{1}{4})^{10-1}[/tex]

[tex]a_{10}=\frac{5}{32768}[/tex]

Therefore the 10th term of given sequence  is [tex]\frac{5}{32768}[/tex].

Answer:

C. Probability is 0.90, which is inconsistent with the Empirical Rule.

Step-by-step explanation:

We have been given that on average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 6.1 inches.

First of all, we will find z-score corresponding to 87.5 and 107.5 respectively as:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{87.5-97.5}{6.1}[/tex]

[tex]z=\frac{-10}{6.1}[/tex]

[tex]z=-1.6393[/tex]

[tex]z\approx-1.64[/tex]

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{107.5-97.5}{6.1}[/tex]

[tex]z=\frac{10}{6.1}[/tex]

[tex]z=1.6393[/tex]

[tex]z\approx 1.64[/tex]

Now, we need to find the probability [tex]P(-1.64<z<1.64)[/tex].

Using property [tex]P(a<z<b)=P(z<b)-P(z<a)[/tex], we will get:

[tex]P(-1.64<z<1.64)=P(z<1.64)-P(z<-1.64)[/tex]

From normal distribution table, we will get:

[tex]P(-1.64<z<1.64)=0.94950-0.05050 [/tex]

[tex]P(-1.64<z<1.64)=0.899[/tex]

[tex]P(-1.64<z<1.64)\approx 0.90[/tex]

Since the probability is 0.90, which is inconsistent with the Empirical Rule, therefore, option C is the correct choice.

Answer:

10.50x ≤ 205

The maximum number of tickets, x, would be 19.

Step-by-step explanation:

Given,

The cost of one ticket = $ 10.50,

The cost of x tickets = 10.50x dollars,

Since,  the total cost can not exceed  $ 205,

⇒ 10.50x ≤ 205

∵ 10.50 > 0 thus, when we multiply both sides by 1/10.50 the inequality sign will not change,

⇒ x ≤  [tex]\frac{205}{10.50}[/tex] ≈ 19.52

Hence, the maximum number of tickets would be 19.

Answer:

$482

Step-by-step explanation:

Data provided:

Total earning per week = $518

Medicare, federal withholding, state disability insurance, state withholding, union dues = $15

charitable contributions = $21

Now,

The total deductions = $15 + $21 = $36

also,

Net pay = Total income - Total deductions

thus,

Net pay = $518 - $36

or

Net Pat = $482

Answer: 3253

Step-by-step explanation:

Given : A test requires that you answer either part A or part B.

Part A consists of 7 true-false questions.

i.e.  there are 2 choices to answer each question.

Now, the number of ways to answer Part A : [tex]2^7=128[/tex]    (1)

Part B consists of 5 multiple-choice questions with one correct answer out of five.

i.e.  there are 5 choices to answer each question.

Now, the number of ways to answer Part B : [tex]5^5=3125[/tex]                           (2)

Now, the number of  different ways to completed answer sheets are possible=  [tex]128+3125=3253[/tex]          [Add (1) and (2) ]

The number of different completed answer sheets possible is 400,000.

To find the number of different completed answer sheets, we need to determine the number of ways to choose either part A or part B, and then calculate the number of possible combinations for each part.

For part A, since there are 7 true-false questions, each with 2 choices (true or false), there are 2^7 = 128 possible answer combinations.

For part B, since there are 5 multiple-choice questions, each with 5 choices, there are 5^5 = 3125 possible answer combinations.

To calculate the total number of different completed answer sheets, we multiply the number of choices for part A (128) by the number of choices for part B (3125), giving us a total of 128 * 3125 = 400,000 possible answer sheets.

Answer:

The angle between the lines [tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex] is [tex]\sqrt{\frac{6}{7}}[/tex]

Step-by-step explanation:

The equation of a line with direction vector [tex]\vec{d}=(l,m.n)[/tex] that passes through the point [tex](x_{1},y_{1},z_{1})[/tex] is given by the formula

[tex]\frac{x-x_{1}}{l}= \frac{y-x_{1}}{m}=\frac{z-z_{1}}{n},[/tex] where l,m, and n are non-zero real numbers.

This is called the symmetric equations of the line.

The angle between two lines [tex]\frac{x-x_{1}}{l_{1} }= \frac{y-y_{1}}{m_{1} }=\frac{z-z_{1}}{n_{1}}[/tex] and [tex]\frac{x-x_{2}}{l_{2} }= \frac{y-y_{2}}{m_{2} }=\frac{z-z_{2}}{n_{2}}[/tex] equal the angle subtended by direction vectors, [tex]d_{1}[/tex] and [tex]d_{2}[/tex] of the lines

[tex]cos (\theta)=\frac{\vec{d_{1}}\cdot\vec{d_{2}}}{|\vec{d_{1}}|\cdot|\vec{d_{2}}|}=\frac{l_{1} \cdot\l_{2}+m_{1} \cdot\ m_{2}+n_{1} \cdot\ n_{2}}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}} \cdot \sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}}[/tex]

Given that

[tex]\frac{x-1}{3}= \frac{y-0.5}{2}=\frac{z-0}{1}[/tex] and [tex]\frac{x-0}{1}= \frac{y-0}{1}=\frac{z-0}{1}[/tex]

[tex]l_{1}=3, m_{1}=2,n_{1}=1\\ l_{2}=1, m_{2}=1,n_{2}=1[/tex]

We can use the formula above to find the cosine of the angle between the lines

[tex]cos(\theta)=\frac{3 \cdot 1+2 \cdot 1 +1 \cdot 1}{\sqrt{3^{2}+2^{2}+1^{2}} \cdot \sqrt{1^{2}+1^{2}+1^{2}}} = \sqrt{\frac{6}{7}}[/tex]