Two vectors are linearly dependent if and only if they lie on a line through the origin.
a. true b. false

y=-1/2x-1 is equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3.

The slope of given line is 2

The slope of perpendicular line is -1/2

Now let us find the y intercept

1=-1/2(-4)+b

1=2+b

b=-1

Now the equation is y=-1/2x-1

Hence,  equation of the line that passes through (-4, 1) and is perpendicular to the line y = 2x + 3 is y=-1/2x-1.

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Answer: 59 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees so we subtract that by the values we already know the get the last angle.
180-31-90= 59 degrees

The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement is 0.45%.

The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement can be calculated as follows:

First, we calculate the probability of drawing an ace on the first draw. Since there are four aces in the deck and 52 cards in total, the probability of drawing an ace on the first draw is:

P(Ace on first draw) = 4/52 = 1/13

Next, we need to calculate the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw. Since there are now only three aces remaining in the deck and 51 cards in total, the probability of drawing an ace on the second draw is:

P(Ace on second draw given an ace on first draw) = 3/51

To calculate the probability of drawing two aces, we multiply the probability of drawing an ace on the first draw by the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw:

P(Drawing two aces) = P(Ace on first draw) x P(Ace on second draw given an ace on first draw)

P(Drawing two aces) = (1/13) x (3/51)

P(Drawing two aces) = 0.0045 or approximately 0.45%.

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Answer:

Step-by-step explanation:

1.To arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Therefore, there are 720 ways to arrange all 6 tables in a line.

2.To choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

C(6,4) = 6! / (4! x 2!) = (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1) = 15

Therefore, there are 15 ways to choose 4 out of the 6 tables.

There are 720 ways to arrange all 6 tables in a line.

And, there are 15 ways to choose 4 out of the 6 tables.

A combination is a technique to determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Given that;

Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom.

Now, After arrange all 6 tables in a line, we can use the factorial function which calculates the product of all positive integers up to a given number. We can write:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Hence, there are 720 ways to arrange all 6 tables in a line.

And, For choose 4 out of the 6 tables, we can use the combination function, which calculates the number of ways to choose k items out of n distinct items, without regard to their order. We can write:

⁶C₄ = 6! / (4! x 2!)

= (6 x 5 x 4 x 3) / (4 x 3 x 2 x 1)

= 15

Thus, there are 15 ways to choose 4 out of the 6 tables.

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Answer:

36

Step-by-step explanation:

Given:

1/6 of the marbles are red

1/3 of the marbles are blue

There are 18 green marbles in the jar

We can set up the following equations based on the given information:

Number of red marbles = 1/6 * x

Number of blue marbles = 1/3 * x

Number of green marbles = 18

Since the total number of marbles in the jar is "x", we can write the equation for the sum of all the marbles as:

(Number of red marbles) + (Number of blue marbles) + (Number of green marbles) = x

Substituting the values from the given information:

1/6 * x + 1/3 * x + 18 = x

Multiplying through by 6 to eliminate the fraction:

x/6 + 2x/6 + 18 = 6x/6

x + 2x + 108 = 6x

Combining like terms:

3x + 108 = 6x

Subtracting 3x from both sides of the equation:

3x + 108 - 3x = 6x - 3x

108 = 3x

Dividing both sides by 3 to solve for x:

108/3 = 3x/3

36 = x

The value of x that makes the equation true is 8

A linear equation is a type of equation that the highest power of it's variable is 1. Example of linear equation include, x+2 =y, x+7/2 =15.

The graph of a linear equation is a straight line and it is represented in form of y = mx+b. Where m is the slope and b is the y intercept.

Solving x-7 = (3/4)x -5

collecting like terms

x-(3/4)x = 7-5

x/4 = 2

x = 8

therefore the value of x that will make the equation x-7 = (3/4)x -5 true is 8.

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The null hypothesis is that the population mean weekly sales are $9820. The alternate hypothesis is that they are greater than $9820. The calculated t-value is 7.45, which is greater than the critical value of 1.677. Therefore, we reject the null hypothesis and conclude that the population mean weekly sales are higher than $9820.

To test whether the population mean weekly sales have increased after advertising, we can use a one-sample t-test.

The null hypothesis is that the population mean weekly sales have not increased, which means the population mean is still $9820:

H0: μ = $9820

The alternative hypothesis is that the population mean weekly sales have increased, which means the population mean is greater than $9820:

Ha: μ > $9820

The significance level is 0.05, so we need to calculate the critical value of t for a one-tailed test with 49 degrees of freedom (n-1), which is 1.677.

To calculate the test statistic, we can use the formula:

t = (X - μ) / (s / √n)

Where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Given that the sample mean is X = $10960, the hypothesized population mean is μ = $9820, the sample size is n = 50, and the population standard deviation is θ = $1580, we can calculate the sample standard deviation:

s = θ / √n = $1580 / √50 = $223.61

Now we can calculate the test statistic:

t = (X - μ) / (s / √n) = ($10960 - $9820) / ($223.61 / √50) = 7.45

Since the calculated t-value (7.45) is greater than the critical t-value (1.677), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population mean weekly sales have increased after advertising.

Therefore, we can infer that the advertising campaign in the local newspaper has been effective in increasing the sales of the electronics store.

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--The given question is incomplete, the complete question is given

"  a small electronics store has begun to advertise in the local newspaper. before advertising, the long term average weekly sales $9820. a random of 50 weeks while the newspaper ads were running gave a sample mean weekly sale of x = $10960. Does this indicate that the population mean weekly sales is now more than $9820? test at the 5% level of significance. Assume theta = $1580.

A. state the null and alternate hypothesis.

B. Compute the   or t va;ue of the sample test statistic.

C. Find the critical value(s).

D. based on the answers to a-c, what is your conclusion?"--

The equation in standard form is (x- (-12))² + (y - 0)²  = (√164)²

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

Using the completing square method on the given equation:

24x + y² = -x² + 20

x²+ 24x + y² = 20

[x² + 24x + (12)²] + [y² + 0x + (0)²] = 20 + (12)²

(x + 12)² + (y + 0)² = 164

(x - (-12))² + (y - 0)² = 164

(x- (-12))² + (y-0)²  = (√164)²

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By quadratic formula the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9 since it has solutions x=3 and x=9 which are also solutions to X² − 12x + 49 = 22

The quadratic equation ax² + bx + c = 0 can be resolved using the quadratic formula.

that uses the constants (a, b, c) and the numerical coefficients.

When factoring cannot be utilized to solve the quadratic expressions, this approach of solving a quadratic equation is typically used.

x = √(b² - 4ac) / (-b √(b²) / (2a)

We must solve each of the preceding equations to determine which one has the same solution(s) as X²- 12x + 49 = 22 in order to determine which equation has the same solution(s) as X²- 12x + 49 = 22.

Let's start by figuring out X²- 12x + 49 = 22:

X² − 12x + 49 = 22

X² − 12x + 27 = 0

The quadratic formula can then be used to find the value of x:

x = √(b² - 4ac) / (-b√(b²) / (2a)

where a=1; b=-12; and c=27.

x = (-(-12) ±√((-12)² - 4(1)(27))) / (2(1))

x = (12 ±√(144 - 108)) / 2

x = (12 √(36))/ 2

x = (12 6) / 2

x = 6,3

So x = 6,3 is the answer to the equation X²- 12x + 49 = 22.

Let's now resolve each of the provided equations:

M. (x − 6)² = 9 (x -6)² -9=0

(x-6+3)(x-6-3)=0

(x-3)(x-9)=0, where x=3 or x=9

P. (x − 7)² = 22 (x-7)²-22=0

(x-7+√(22))=0

(x=7+√(22))

or (x=7-√(22))

R. (x + 7)² = 4.7 (x+7)²-4.7=0

(x+7+√(4.7))(x+7-√(4.7))=0

No effective remedies

S. (x − 12)²= −27 (x-12)²+27=0

No effective remedies

Therefore, the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9

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yes very cool math problem

Answer:

N'(2, 3)

Step-by-step explanation:

my trick is counting how many spaces away it is from the axis it's being reflected over. So for this one N was at (2, -3) so I counted upwards 3 spaces from the 2 and i got to (2,3). i hope that makes sense the way i explained it.

hope this helps ;)

Answer:

  see attached

Step-by-step explanation:

You want the image of point N(2, -3) after reflection in the y-axis, plotted on the graph.

A line of reflection is the perpendicular bisector of the segment between a point and its image. That is, the image point is as far from the line as the original point, but on the opposite side of it.

The attached figure shows the location of image point N'(-2, -3).

__

Additional comment

The coordinate transformation for reflection in the y-axis just changes the sign of the x-coordinate. That puts the image point as far to the left as the original is to the right:

  (x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis

By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.

The CDF function of a Normal distribution is calculated by translating the random variable to the Normal Standard, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the normal standard. The Normal Standard, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).

Let x1, x2, .... be the scores on the test.

X ~ N (82, 64)

P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)

Step-by-step explanation:

cores Distribution and Percentile

The scores on a test are normally distributed, with a mean of 82 and a standard deviation of 8. What percent of scores are less than 90? Explain

To find the percentage of scores that are less than 90 in a normally distributed test with a mean of 82 and a standard deviation of 8, we can use the cumulative distribution function (CDF) of the normal distribution.

The CDF of a normal distribution gives the probability that a random variable falls below a particular value. In this case, we want to find the probability that a score is less than 90.

The formula for the CDF of a normal distribution is:

CDF(x) = (1/2) * (1 + erf((x - μ) / (σ * sqrt(2))))

where erf is the error function, μ is the mean, σ is the standard deviation, and x is the value we want to find the cumulative probability for.

Plugging in the given values:

μ = 82

σ = 8

x = 90

We can calculate the cumulative probability using the formula:

CDF(90) = (1/2) * (1 + erf((90 - 82) / (8 * sqrt(2))))

Using a calculator or statistical software that provides the error function, we can find that erf(1.0) is approximately 0.6827.

Plugging this value back into the formula, we get:

CDF(90) = (1/2) * (1 + 0.6827) = 0.8414

So, the cumulative probability that a score is less than 90 is approximately 0.8414, or 84.14%.

Therefore, about 84.14% of the scores are less than 90 in this normally distributed test.

Answer: True

Step-by-step explanation:

Answer:

Step-by-step explanation:

330/2 = 165

330/3 = 110

330/5 = 66

330/6 = 55

330/10 = 33

330/11 = 30

the answer is true

The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is [tex]SE = \frac{σ }{\sqrt{n}}[/tex]

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

The angle of C is 161.4°.

Law of sines defines the ratio of sides of a triangle and their respective sine angles are equivalent to each other. The other names of the law of sines are sine law, sine rule and sine formula.

We have :

In the Triangle ABC,

Angle A is 9 º

Side of a is 44 m,

and side of b is 46 m

To find the angle of C

Now, use the law of sines to find angle B:

b/sin B  = a/sin A

Plug all the values in above formula :

=> 46/Sin B = 44/Sin 9°

=> 46 × Sin9°/ 44 = Sin B

Sin B = 0.164

[tex]B = Sin^-^10.164[/tex]

B = 9.555

Now, By angle sum of property of a triangle,

The sum of three angles of a triangle is 180°

So, Let's apply angle sum property to find angle C

=> ∠ A + ∠ B + ∠C = 180°

Put the value of B = 9.555 and angle A = 9°

=> 9° + 9.555 + ∠C = 180°

18.555 +∠C = 180°

∠C = 180°- 18.555

∠C = 161.4°

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The gross death rate is 8.38%.

What is a Rate?

A rate is a measure of the frequency of an event or occurrence in relation to a specific population or time period. Rates are often expressed in terms of units per time or per population, such as cases per 100,000 people or births per year.

The gross death rate is the number of deaths in a given time period divided by the total population or, in this case, the total number of discharges.

To calculate the gross death rate for City Hospital in June, we need to subtract the eight deaths that occurred within 48 hours of admission from the total number of deaths:

Total deaths = 49 - 8 = 41

Then, we divide the total number of deaths (41) by the total number of discharges (489) and multiply by 100 to get the rate per 100 discharges:

Gross death rate = (41 ÷ 489) x 100 = 8.38%

Therefore, the gross death rate for City Hospital in June is 8.38%.

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The width of the river is approximately 45m.

Let's say the illustration may be explained as follows:

The big right triangle is located inside the river, with its base extending down one of its sides and its height spanning its breadth.

The base of the little right triangle lies on the opposite bank of the river, outside of it.

Triangles don't cross over one another. Their bases' endpoints contact, as does the end of their hypotenuses.

Let's assume the two right triangles are similar (which means they have proportional sides).

H1/B1 = H2/ B2

which is H1/55 = 21.4/26

=21.4/26 x 55

= 45.27

It is the larger triangle is the width of the river

If the smaller triangle represents the land on one side of the river and the larger triangle includes both the land and the river, we need to find the width of the river by subtracting the base of the smaller triangle from the base of the larger triangle:

Width of the river = 55 - 26 = 29 meters

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The intercepts of the graph of y = x²- 25 are (-5, 0), (5, 0), and (0, -25).

Data can also be presented as a table. However, when the information is presented graphically, it is much easier to understand. There are many types of charts and each of them serves specific purposes in different fields.  

To find the x-intercepts of the graph, we need to set y = 0 and solve for x:

0 = x²- 25

Adding 25 to both sides gives:

25 = x²

Taking the square root of both sides gives us:

x = ±5

So the x-intercepts are (-5, 0) and (5, 0).  To find the y-intercept, we need to set x = 0 and solve for y:

y = 0²-25

y = -25

So the y-intercept is (0, -25).  

Therefore, the intercepts of the graph of y = x² - 25 are (-5, 0), (5, 0), and (0, -25).

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The volume of the cone is 1960.64 cubic yards.

We have,

The formula for the volume of a cone is:

V = (1/3)πr²h

where π is approximately 3.14, r is the radius, and h is the height.

Substituting the given values, we get:

V = (1/3) x 3.14 x 12² x 13

V = (1/3) x 3.14 x 144 x 13

V = 1/3 x 3.14 x 1872

V = 1960.64

Rounding to the nearest hundredth, we get:

V = 1960.64

Therefore,

The volume of the cone is 1960.64 cubic yards.

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Therefore, the maximum displacement of the particle is 4 units, and it occurs at time t = 1.

To find the maximum displacement, we need to first determine the particle's velocity and acceleration.

The velocity of the particle is given by the derivative of its position function:

[tex]v(t) = y'(t) = 3t^2 - 12t + 9[/tex]

The acceleration of the particle is given by the derivative of its velocity function: a(t) = v'(t) = 6t - 12

Now, to find the maximum displacement, we need to find the time at which the particle comes to rest.

This occurs when its velocity is zero:

[tex]3t^2 - 12t + 9 = 0[/tex]

Simplifying this equation, we get:

[tex]t^2 - 4t + 3 = 0[/tex]

This quadratic equation factors as:

(t - 1)(t - 3) = 0

So the particle comes to rest at t = 1 or t = 3.

Next, we need to determine whether the particle is at a maximum or minimum at each of these times.

To do this, we look at the sign of the acceleration:

When t = 1, a(1) = 6(1) - 12 = -6, which is negative.

Therefore, the particle is at a maximum at t = 1.

When t = 3, a(3) = 6(3) - 12 = 6, which is positive.

Therefore, the particle is at a minimum at t = 3.

Finally, we need to find the displacement of the particle at each of these times:

[tex]y(1) = 1^3 - 6(1)^2 + 9(1) = 4[/tex]

[tex]y(3) = 3^3 - 6(3)^2 + 9(3) = 0.[/tex]

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The statement "System analysts define an object's attributes during the systems design process" is true because  defining object attributes is an essential part of the systems design process to ensure that the system meets the desired functional requirements.

In systems design, objects are used to represent real-world entities that are relevant to the system being developed. These objects have attributes that describe their characteristics or properties, which are used to identify and manipulate them within the system. System analysts define these attributes during the systems design process to ensure that the system meets the desired functional requirements.

For example, in a library system, a book object may have attributes such as title, author, publisher, and ISBN. Defining these attributes helps ensure that the system can properly manage and retrieve books as needed. Object-oriented design is a popular approach to systems design that relies heavily on defining objects and their attributes.

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l'exercice 3 est la boisson d'Andres. Je suis désolé si cela ne ressemble pas vraiment à un français parfait, je parle anglais et j'utilise Translate. passe une bonne journée!

The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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Answer:

First, we can multiply both sides of the equation by the absolute value of x plus 8, to get rid of the fraction:

52 = 4(|x| + 8)

Now we can solve for the absolute value of x:

| x | + 8 = 13

| x | = 5

This means that x could be either positive 5 or negative 5. Therefore, the possible values of x are {-5, 5}.

So the answer is option D: {-5, 5}.

Answer:

2/3 pizza is left!

Step-by-step explanation:

You take 1/3 from a whole pizza (3/3), leaving 2/3 for ur 2 buddies :D

If a taxi company charges ​f(x)=2. 20+0. 6[4x] dollars, the cost of a 2.7-mile trip is $8.68.

To find the cost of a 2.7-mile trip using the given function f(x) = 2.20 + 0.6[4x], we substitute x = 2.7 in the function.

f(2.7) = 2.20 + 0.6[4(2.7)]

f(2.7) = 2.20 + 0.6[10.8]

f(2.7) = 2.20 + 6.48

f(2.7) = 8.68

The function f(x) = 2.20 + 0.6[4x] represents the cost of a taxi ride based on the distance traveled. The first term 2.20 represents the base fare, which is added to the cost regardless of the distance.

The second term 0.6[4x] represents the variable cost, which is calculated by multiplying the distance traveled by 4 and then by 0.6. This function helps the customers to calculate their fare in advance and plan their expenses accordingly.

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