Can anyone help please ??

Answer:

23

Step-by-step explanation:

The given vectors are:(5,2), (-2,11), (7,-3), and (-8,-14).

The direction angle of a vector is the angle between the vector and the positive x-axis measured counterclockwise. Therefore, the direction angle of vector v = (x,y) is given by θ = tan⁻¹(y/x).a. For vector (5,2), direction angle is given by:θ = tan⁻¹(2/5) = 21.801 degrees (rounded to 3 decimal places)b.

For vector (-2,11), direction angle is given by:θ = tan⁻¹(11/-2) = 101.31 degrees (rounded to 3 decimal places)c. For vector (7,-3), direction angle is given by:θ = tan⁻¹(-3/7) = -23.198 degrees (rounded to 3 decimal places)Note that the direction angle here is negative because the vector points towards the negative x-axis.d.

For vector (-8,-14), direction angle is given by:θ = tan⁻¹(-14/-8) = 60.26 degrees (rounded to 3 decimal places)

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56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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The exact height of the right triangle, with an angle measuring 30 degrees adjacent to a base of 18, is approximately 10.392 units.

To find the exact height of a right triangle with an angle measuring 30 degrees adjacent to a base of 18, we can use the trigonometric relationship of a right triangle.

In a right triangle, the side opposite the 30-degree angle is called the height. The side adjacent to the 30-degree angle is called the base.

Given that the base is 18, we can use the trigonometric function tangent (tan) to calculate the height.

Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side.

tan(30 degrees) = height / base

tan(30 degrees) = height / 18

To find the height, we rearrange the equation:

height = tan(30 degrees) * 18

Using a scientific calculator or reference table, we can determine the value of tan(30 degrees) to be approximately 0.57735.

height = 0.57735 * 18

height ≈ 10.392

Therefore, the exact height of the right triangle, with an angle measuring 30 degrees adjacent to a base of 18, is approximately 10.392 units.

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To find the points of discontinuity for the rational function y = (x - 8)/(x^2 + 6x - 7), we need to identify the values of x that make the denominator zero, as division by zero is undefined.

Setting the denominator equal to zero:

x^2 + 6x - 7 = 0

Factoring the quadratic equation:

(x + 7)(x - 1) = 0

This gives us two solutions: x = -7 and x = 1.

Therefore, the points of discontinuity for the rational function are x = -7 and x = 1.

To describe the vertical asymptotes and holes, we need to examine the behavior of the function around these points.

For x = -7:

When x approaches -7 from the left side, the function approaches negative infinity.

When x approaches -7 from the right side, the function approaches positive infinity.

This indicates a vertical asymptote at x = -7.

For x = 1:

When x approaches 1 from the left side, the function approaches negative infinity.

When x approaches 1 from the right side, the function approaches positive infinity.

This also indicates a vertical asymptote at x = 1.

Based on this analysis, there are two vertical asymptotes at x = -7 and x = 1. There are no holes in the graph.

Regarding the rational function y = (-4x^6 + 6x + 3)/(8x^6 + 9x + 3), to find the horizontal asymptote, we examine the degrees of the numerator and denominator polynomials.

Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Therefore, the rational function y = (-4x^6 + 6x + 3)/(8x^6 + 9x + 3) does not have a horizontal asymptote.

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Using Euclid's theorem for the right triangle AD  is ≈ 2.67

DB = 4 and DC = 6 , We need to find AD

Using Euclid's theorem for the right triangle

∴ DB² = AD * DC

∴ 4² = AD * 6

∴ 6 AD = 16

∴ AD = 16/6 = 8/3 ≈ 2.67

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The graph of Y > -2x + 4 can be drawn by plotting points on a coordinate plane and connecting them with a dashed line. The dashed line should be above the line Y=-2x+4.

A sample graph is shown below:

[Graph of Y > -2x + 4]

(0,4), (1,1), (2,-2), (3,-5), (4,-8)

To graph Y > -2x + 4, you need to plot points on a coordinate plane. Start by finding the intersection point of the line Y=-2x+4 and the x-axis, which will be (0,4). From there, you can calculate the coordinates of the other points by substituting x values into the equation and solving for y. For example, when x=1, y=-2x+4=-2+4=2, so the point (1,2) would be plotted. Then, plot the other points (2,-2), (3,-5), and (4,-8). Finally, connect the points with a dashed line to represent Y > -2x+4.

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The solution set of the inequality 3x-2 < 2-2x is:

(4/5, ∞)

To find this we need to isolate the variable in the inequality.

Here we have:

3x - 2 < 2 - 2x

add 2x in both sides and add 2 in both sides, then we will get:

3x + 2x < 2 + 2

5x < 4

Now we can divide both sides by 5 to get:

x < 4/5

That is the inequality solved.

Then the solution set of the inequality is:

(4/5, ∞)

The set of all real numbers larger than 4/5.

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The test score is 91.5.

z-score:

A z-score is the number of standard deviations from the mean value of the reference population.

Here we have to find the test score.

Mean(μ) = 90

Standard deviation(б) = 15

z-score = 0.1

Formula for z-score:

z = X - μ / б

Now putting the values in the equation:

0.1 = X - 90 / 15

1.5 = X - 90

X = 91.5

Therefore the test score is 91.5.

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Answer: GRAPHED

Step-by-step explanation:

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Given:

Total syrup = 64 fluid ounces

Syrup used each day = \(3\dfrac{1}{5}\) fluid ounces

To find:

Whether there is enough syrup in the bottle for 25 days or not.

Solution:

According to the question,

Requirement of syrup for 1 day \(=3\dfrac{1}{5}\) fluid ounces

                                                   \(=\dfrac{3\times 5+1}{5}\) fluid ounces

                                                   \(=\dfrac{16}{5}\) fluid ounces

Requirement of syrup for 25 day \(=25\times \dfrac{16}{5}\) fluid ounces

                                                       \(=\dfrac{400}{5}\) fluid ounces

                                                       \(=80\) fluid ounces

Syrup required for 25 days is 80 fluid ounces which is greater than 64 fluid ounces.

Therefore,  64 fluid ounces of syrup is not enough for 25 days.

Answer:

13.5 pounds.

Step-by-step explanation:

9.18 divided by .68

= 13.5

Answer:

13.5

$0.68 times 13.5 = $9.18

a). The number of ways which the company can choose 4 workers from the list of employees is; 2,730 ways.

b). The number of ways the company can choose the workers if 2 labourers and 3 joiners are on holiday is; 700 ways.

It follows from the task content that the number of ways the company can choose 4 workers in each scenario be determined.

a). Since there are 3 labourers, 13 joiners, 10 electricians, and 7 plumbers.

The number of possible ways to choose 4 workers is; ³C₁ × ¹³C₁ × ¹⁰C₁ × ⁷C₁

= 3 × 13 × 10 × 7

= 2,730 ways.

b). Also, when 2 labourers and 3 joiners are absent, it follows that the selection space is now; 1 labourer, 10 joiners, 10 electricians and 7 plumbers.

The number of possible ways is therefore; ¹C₁ × ¹⁰C₁ × ¹⁰C₁ × ⁷C₁

= 1 × 10 × 10 × 7

= 700 ways.

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Answer:

35 hours

Step-by-step explanation:

9a+250=565

560-250=315

315÷9≡35

Answer: you forgot to put the quistion so nobody can really give you an answer

Step-by-step explanation:

A statistical approach to determine the exponent of the log-log representation of the learning curve is known as linear regression.

Linear regression is a statistical method used to model the relationship between two variables by fitting a linear equation to the observed data. In the context of the learning curve, the log-log representation is commonly used to analyze the relationship between the number of units produced (x-axis) and the corresponding time or cost (y-axis) on a logarithmic scale.

To determine the exponent of the log-log representation, you can follow these steps:

1. Collect data: Gather data on the number of units produced and the corresponding time or cost for each unit. Ensure that you have a sufficiently large sample size to make reliable inferences.

2. Transform the data: Take the logarithm (base 10 or natural logarithm) of both the x and y values to obtain the log-log representation. This transformation helps in linearizing the relationship between the variables.

3. Perform linear regression: Fit a linear regression model to the transformed data. The slope of the regression line represents the exponent of the log-log representation. It indicates how the y-variable changes with a one-unit increase in the x-variable on a logarithmic scale.

4. Interpret the results: The coefficient of the x-variable in the linear regression model corresponds to the exponent of the log-log representation. It provides insights into the rate of improvement or learning as the number of units produced increases.

By applying linear regression to the log-log representation of the learning curve, you can estimate the exponent and gain a better understanding of the learning process.

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The quantitative variables relating to TV shows are the number of commercials duration (in minutes) and the number of viewers.  The other variables mentioned in the options are categorical variables

The number of commercials duration (in minutes): This variable represents the length of time in minutes for commercials during a TV show. It can be measured and expressed as a numerical value.

The number of viewers: This variable represents the count or quantity of people who watched a particular TV show. It can be measured and expressed as a numerical value.

In summary, the quantitative variables relating to TV shows are the number of commercials duration (in minutes) and the number of viewers. These variables involve numerical measurements that can be quantified.

The other variables mentioned in the options, such as being aired during "prime time," the type of show (reality, comedy, drama, etc.), and the format (standard or HD), are categorical variables. They represent different categories or characteristics rather than numerical measurements.

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The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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We need two things to write the recursive formula

\(a\) is the first value of this sequence. For this set of values, \(a = 1\), since \(1\) appears first.

\(d\), the common difference, is \(d = t_{3} - t_{2} = t_{2} - t_{1}\). Basically it's just the the higher term minus the previous terms. To solve for \(d\),

So regardless of what terms you choose, the common difference will be the same. Now the general formula for a recursive function is

where \(n\) is the \(nth\) term. Let's substitute for \(a\) and \(d\) in this formula.

\(t_{n} = 1 + (n - 1) \times -3\\t_{n} = 1 + -3(n - 1)\\t_{n} = 1 - 3(n - 1)\)

So the recursive formula is \(t_{n} = 1 - 3(n -1)\)

Answer:

3

Step-by-step explanation:

Remember BEDMAS!!

Brackets first:

(15) / (1+(2)^2)

Exponents next:

(15) / (1+4)

15 / 5 = 3

Hope that helps, feel free to ask questions

The answer is 3 use BODMAS, BEDMAS or PEDMAS

Answer: x=5 or 5 Tickets

Step-by-step explanation:

186x + 16 = 946

186x + 16 = 946

          -16      -16

186x  = 930

186x divided by 186x = 0

930 divided by 186x = 5

Therefore our answer is, x=5 or 5 Tickets

The speed of red light in a diamond, denoted as vred, is approximately equal to the speed of light in a vacuum, c, which is 2.998 × 10^8 m/s, rounded to four significant figures.

According to the principles of optics and the refractive index of a material, the speed of light in a medium is generally lower than its speed in a vacuum. The refractive index of a diamond is approximately 2.42.

To calculate the speed of red light in a diamond, we can use the formula vred = c / n, where c represents the speed of light in a vacuum and n represents the refractive index of the diamond.

Substituting the given values, we have vred = (2.998 × 10^8 m/s) / 2.42. Evaluating this expression yields a result of approximately 1.239 × 10^8 m/s.

Rounding this value to four significant figures, we obtain the speed of red light in a diamond, vred, as approximately 1.239 × 10^8 m/s.

Therefore, the speed of red light in a diamond, rounded to four significant figures, is approximately 1.239 × 10^8 m/s, which is slightly lower than the speed of light in a vacuum, c.

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Answer:

Ratio of male and female in the shop = 5 : 7

Step-by-step explanation:

Fraction of male = 5/12

Number of Male =5

Total people in the shop = 12

Number of Female = Total people in the shop - Number of Male

= 12 - 5

= 7

Number of Female = 7

Write the ratio of male and female in the shop

Ratio of male and female in the shop = 5 : 7

The correct notation for the mean of the y values is D)yÌ. The notation "yÌ" is commonly used to represent the mean or average of a set of y values. It is calculated by adding up all of the y values and dividing by the number of values in the set. For example, if we have the y values 2, 4, 6, and 8, the mean would be (2 + 4 + 6 + 8) / 4 = 5, so yÌ = 5. This notation is often used in statistics and data analysis to represent the central tendency of a set of data.

Graphically estimating the age of the fossil with 18% of the original carbon-14 content involves determining the number of half-lives that have passed.  Therefore, the fossil is estimated to be between 11400 and 17100 years old.

Since the half-life of carbon-14 is 5700 years, we can divide the remaining carbon-14 content (18%) by the initial amount (100%) to obtain 0.18. Taking the logarithm base 2 of 0.18 gives us approximately -2.5146.

In the graph, we can plot the ratio of remaining carbon-14 to the initial amount on the y-axis, and the number of half-lives on the x-axis. The value of -2.5146 lies between -2 and -3 on the x-axis, indicating that the fossil is between 2 and 3 half-lives old.

Since each half-life is 5700 years, multiplying the number of half-lives by the half-life period gives us the age estimate.

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Answer:172.5

Step-by-step explanation:Xoxo