Find f ( - 3 ) for the function below.

{ ( - 3, 2 ), ( - 1, 0 ), ( 1, 1 ), ( 3, - 3 ) }

The gun will need to turn at a rate of approximately 0.32 radians per second to accurately track the aircraft.

To determine the rate at which the gun needs to turn to track the aircraft, we can use the concept of angular velocity. Angular velocity is defined as the rate of change of the angle with respect to time.

In this scenario, the gun needs to track the aircraft, which is moving in a straight-line path directly overhead. The gun needs to match the angular position of the aircraft to ensure accurate tracking.

The angle between the gun and the vertical axis can be calculated using trigonometry. We can use the fact that the elevation of the aircraft from the ground remains constant at 160 ft.

The tangent of the angle between the gun and the vertical axis is given by the ratio of the vertical displacement (160 ft) to the horizontal displacement (the distance covered by the aircraft per unit time, which is 500 ft/s).

Tangent of the angle = vertical displacement / horizontal displacement

Tangent of the angle = 160 ft / 500 ft/s

Using inverse tangent (arctan) function, we can find the angle in radians:

Angle = arctan(160/500) ≈ 0.3198 radians

Since the gun needs to track the aircraft as it moves, it needs to turn at the same angular velocity as the aircraft. Therefore, the gun needs to turn at a rate of approximately 0.32 radians per second to accurately track the aircraft.

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Answer:

Step-by-step explanation:

Let's say Jeff ordered x tacos and y burritos.

From the problem, we know that:

- The calorie count of one taco is 150 calories

- The calorie count of one burrito is 380 calories

- Jeff ordered a total of 11 items

- Jeff consumed a total of 3030 calories

We can use the information given to form a system of equations:

x + y = 11 (Jeff ordered a total of 11 items)

150x + 380y = 3030 (Jeff consumed a total of 3030 calories)

To solve this system, we can use substitution.

Rearranging the first equation, we get:

x = 11 - y

Substituting this value of x into the second equation, we get:

150(11 - y) + 380y = 3030

Expanding and simplifying:

1650 - 150y + 380y = 3030

230y = 1380

y = 6

So Jeff ordered 6 burritos.

Substituting this value of y back into the first equation, we get:

x + 6 = 11

x = 5

So Jeff ordered 5 tacos.

Therefore, Jeff ordered 5 tacos and 6 burritos.

Based on the information given the length of one side of the hot tub is 4. 8 ft. So the correct option is B.

The complete question is given as:-

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the centre of dilation. Square A B C D is dilated to create square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Length: Using this formula

Length=B prime C prime length/Scale factor

Where:

B prime C prime length=24 feet

Scale Factor=5

Let plug in the formula

Length=24ft/5

Length=4.8ft

In conclusion, the length of one side of the hot tub is 4. 8 ft.

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Answer:

60000

Step-by-step explanation:

Answer:

60,000

Step-by-step explanation:

2 times 30,000 is 60,000

The alternative hypothesis states that the difference is greater than zero.

What Are Tails in a Hypothesis Test?

First, we need to cover some background material to understand the tails in a test. Typically, hypothesis tests take all of the sample data and convert it to a single value, which is known as a test statistic. You’re probably already familiar with some test statistics.

For example, t-tests calculate t-values. F-tests, such as ANOVA, generate F-values. The chi-square test of independence and some distribution tests produce chi-square values. All of these values are test statistics.

Keep in mind that this t-distribution assumes that the null hypothesis is correct for the population. Consequently, the peak (most likely value) of the distribution occurs at t=0, which represents the null hypothesis in a t-test. Typically, the null hypothesis states that there is no effect. As t-values move further away from zero, it represents larger effect sizes. When the null hypothesis is true for the population, obtaining samples that exhibit a large apparent effect becomes less likely, which is why the probabilities taper off for t-values further from zero.

Hence the answer is the alternative hypothesis states that the difference is greater than zero.

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Answer:

\(-\frac{5}{3}\) or \(-1.7\)

Step-by-step explanation:

The slope formula is: \(\frac{y2-y1}{x2-x1}\)

The two coordinates that are given: (2,-3) and (-1,2)

-

Now let us substitute:

\(m= \frac{2-(-3)}{-1-2}\)  = \(-\frac{5}{3}\)

Therefore, the slope is \(-\frac{5}{3}\) or \(-1.7 (rounded)\)

Answer:

$62,600

Step-by-step explanation:

Answer:

9,600

Step-by-step explanation:

Ok the mistake yall were doing was adding 9,600 with 53,000 when they were asking for the commission so basically plus it says "what is his commission this year?"

.8%

.8 x 100 = .008

1,200,000 x .008 = 9,600

Answer:

- 6.5555   - 19/3    - sqrt 38     6.23

Step-by-step explanation:

Applying the area of the parallelogram formula, it can be concluded that the area is 56 square units.

The area of the parallelogram is the magnitude of the cross-product of the adjacent edges (base and height).

Given information:

A parallelogram is made up of 4 vertices: A(−3, 0), B(−1, 6), C(8, 5), and D(6, −1).

So first we find the adjacent edges as follows:

AB = B - A

     = ( (-1-(-3)) , (6-0) )

     = (2,6)

AD = D - A

     = ((6-(-3)) , (-1-0))

     = (9,-1)

We want to find the area of the parallelogram, we do the following step:

\(AB x AD = \left[\begin{array}{ccc}i&j&k\\2&6&0\\9&-1&0\end{array}\right]\)

               = i(0 - 0) + j(0 - 0) + k(-2 - 54)

               = -56k

The area of the parallelogram = | AB x AD |

                                                  = √(-56)²

                                                  = 56 square unit

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e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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You can infer causality from a correlational result, but only when the r value is greater than:

C. 1

Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.

However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.

In addition, there are other factors that need to be considered when assessing causality from a correlational result.

For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.

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Answer:

Step-by-step explanation:

Answer:

To graph the solution to the inequality -1/2x+3/4>-2/3 on the number line, we need to solve for x first.

-1/2x+3/4>-2/3

-1/2x>-2/3-3/4

-1/2x>-17/12

x<17/12*2

x<17/6

The solution is x<17/6. To graph this on the number line, we draw an open circle at 17/6 and shade everything to the left of it since x is less than 17/6.

The dimensions of the rectangular plot of land can be either 11 meters by 13 meters or 13 meters by 11 meters.

Let's assume the length of the rectangular plot of land is L and the width is W.

We are given that the perimeter of the fence is 48 meters, which means the sum of all four sides of the rectangular plot is 48 meters.

Therefore, we can write the equation:

2L + 2W = 48

We are also given that the area of the land is 143 square meters, which can be expressed as:

L * W = 143

Now, we have a system of two equations with two variables. We can use substitution or elimination to solve for the dimensions of the field.

Let's use the elimination method to eliminate one variable:

From equation 1, we can rewrite it as L = 24 - W.

Substituting this value of L into equation 2, we get:

(24 - W) * W = 143

Expanding the equation, we have:

24W - W^2 = 143

Rearranging the equation, we get:

W^2 - 24W + 143 = 0

Factoring the quadratic equation, we find:

(W - 11)(W - 13) = 0

Setting each factor to zero, we have two possibilities:

W - 11 = 0 or W - 13 = 0

Solving these equations, we get:

W = 11 or W = 13

If W = 11, then from equation 1, we have L = 24 - 11 = 13.

If W = 13, then from equation 1, we have L = 24 - 13 = 11.

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For the weight of bags 402 grams filled with chocolate chips the required null hypothesis and alternative hypothesis  equal to  H0: μ = 402 and Ha: μ ≠ 402.

Weight of the bag filled with chocolate chips made by machine works = 402 grams

The null hypothesis for the bag filled with machine work representing the statement has no effect.

And it represents that the mean weight of the bag filled with chocolate chips is 402grams.

Null hypothesis for the given scenario is equal to ,

H0: μ = 436

The alternative hypotheses for the above scenario of the bag isn't filled with chocolate chips with weight 402grams.

They are either under filled or that is less than 402grams or overfilled that is above 402grams.

Alternative hypothesis for the given scenario is equal to,

Ha: μ ≠ 402

Statistics is the study of surveys and research of the given numerically data.

Two different kinds of hypotheses we have,

A null hypothesis is one that holds true for the given scenario.

And an alternate hypothesis is another.

The null hypothesis is a default condition to represents nothing is happening.

Possibility of  no relationship between two given measured groups.

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Answer:

6^2

Step-by-step explanation:

A perfect square has to be raised to an even power

The only one raised to an even power is

6^2

The stretch of an exponential decay function is y = 2(1/5)ˣ

From the question, we have the following parameters that can be used in our computation:

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

The required solution of the given simultaneous equations are x = 2, 3 and y = 3,9.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Now the given simultaneous equations are,

y = x^2    ...(i)

y = x + 6  .....(ii)

Equating (i) and (ii) we get,

x^2 = x + 6

or, x^2 - x - 6 = 0

Solving we get,

x^2 - 3x - 2x - 6 = 0

⇒ x(x - 3) -2(x - 3) = 0

⇒ (x - 2)(x - 3) = 0

So, x = 2, 3

Putting x = 2, 3 in equation (i) we get,

y = 2^2

⇒ y = 4

and,

y = 3^2

⇒ y = 9

Thus, y = 3,9

Thus the required solution of the given simultaneous equations are x = 2, 3 and y = 3,9.

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Answer: Yes, is the same ratio.

Explanation:

For the girls we have that out of the 30 that tried out for the team, 12 were selected. The ratio for the girls is:

(we simplify 12/30 by dividing the numerator and denominator by 6)

For the boys we have that out of the 40 that tried out for the team, 16 were selected. The ratio for the boys is:

(we simplify 16/40 by dividing the numerator and denominator by 8)

We can see that the ratio of the number of students on the team to the number of students trying out is the same for girls and boys.

Answer:

1: double a number

3: the product of 18 and a number subtracted from the square of another number

4: x+14

6: 7+11x

9: n raised to the power of three + 5

To find the slope of a scatter plot on a TI-84 calculator, you can use the linear regression function. This function calculates the slope and y-intercept of the line of best fit for the data points on the scatter plot.

To find the slope of a scatter plot on a TI-84 calculator, you first need to enter the data into a list. Once the data is entered, you can access the linear regression function by pressing the STAT button, then scrolling over to CALC, and selecting option 4: LinReg(ax+b).

After selecting this option, you will be prompted to enter the list names for the x-values and y-values, which correspond to the independent and dependent variables, respectively. Once you have entered the list names, press enter to calculate the linear regression. The calculator will display the slope and y-intercept of the line of best fit, as well as other statistics such as the correlation coefficient and coefficient of determination.

Therefore, to find the slope of a scatter plot on a TI-84 calculator, you can use the linear regression function to calculate the line of best fit and its slope.

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Answer:

Step-by-step explanation:

\(18-\sqrt{-25}=18-\sqrt{i^{2}*5^{2}}\\\\=18-5i\)

Answer: the answer is b

Step-by-step explanation:

The temperature when the plane reaches an altitude of 5,000 ft is 47.2.

Temperature is he degree of hotness and coldness in a body.

In this case, there is a 1.6 drop in temperature for every thousand feet that an airplane climbs into the sky.

The temperature at 5000 feet will be:

= 55.2 - 1.6(5000 / 1000)

= 55.2 - 1.6(5)

= 55.2 - 8

= 47.2

The temperature is 47.2

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Answer:

a) -1/3 b) 3 c) y=3x-10

Step-by-step explanation:

Product owners play a crucial role in supporting a continuous pipeline that enables automated deployments without the need for manual conformity steps. This ensures that stories that meet the necessary criteria can be automatically cleared for deployment.

In modern software development practices, a continuous pipeline is often employed to streamline the process of delivering software updates. This pipeline includes various stages such as development, testing, and deployment. Product owners, as key stakeholders in the development process, contribute to the successful implementation of this pipeline.

By supporting a continuous pipeline, product owners enable the automation of deployments, eliminating the need for manual conformity steps. This means that once a story or feature has been developed and tested, it can be automatically cleared for deployment if it meets the necessary criteria. This automation significantly speeds up the release process, reduces the potential for human error, and allows for faster feedback and iteration cycles.

Product owners collaborate closely with the development team and stakeholders to define the criteria that determine when a story is ready for automatic deployment. These criteria may include passing all relevant tests, meeting user acceptance criteria, and fulfilling any necessary compliance or security requirements. By ensuring that these criteria are clearly defined and communicated, product owners help maintain the quality and reliability of the software being delivered.

In conclusion, product owners play a critical role in supporting a continuous pipeline that enables automated deployments without the need for manual conformity steps. Their involvement ensures that stories meeting the necessary criteria can be seamlessly cleared for deployment, promoting efficiency, reliability, and faster delivery of software updates.

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The equation is y+9=(1/5)(x-2).

It is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point. The three major forms of linear equations are point-slope form, standard form, and slope-intercept form. The equation of the slope form is y-y₁ = m(x - x₁)

The formula for the point-slope is,

y-y₁ = m(x - x₁)

y₁ is the y-coordinate of the point in the line, x₁ is the x-coordinate of the point in the line and m is the slope.

y₁ = -9

m = 1/5

x₁ = 2

Substituting the above values in the above equation, we get

y-(-9) = (1/5)(x-2)

By simplifying the above equation, we get

y+9 = (1/5)(x-2)

Therefore, the equation is y + 9 = (1/5)(x-2).

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The equation of the line from give points is y = 2/3x - 5/3.

According to the statement

We have given that the two points which are (-2,-3) and (4,1)

And we have to find the equation of a line that passes through the given points.

So,For this purpose,

First, we need to determine the slope of the line. The slope can be found by using the formula:

\(m = \frac{(y_2) -(y_1)}{(x_2) -(x_1)}\)

Where

m is the slope and

Substituting the values from the points in the problem gives:

m = 1 + 3 /4 + 2

m = 4/6

m = 2/3.

And then

Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:

\(y - (y_1) = m(x -x_1)\)

Put the values in it then

y - (-3) = 2/3 (x-(-2))

y +3 = 2/3 (x +2)

3y + 9 = 2x + 4

3y - 2x = 4 -9

3y -2x = -5

3y = 2x - 5

y = 2/3x - 5/3.

So, The equation of the line from give points is y = 2/3x - 5/3.

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Answer:

15

Step-by-step explanation:

Answer:

Can you show us the picture of the double number line?

Step-by-step explanation:

That would be helpful! :)

A line graph is best suited for showing changes in statistics over time or space.

Line graphs are commonly used to visualize trends, patterns, and fluctuations in data over a continuous or discrete period. The x-axis represents time or space, while the y-axis represents the corresponding statistic being measured. The line graph connects the data points, allowing for a clear representation of how the statistic changes over the given time or space interval.

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The distance covered is. 90 miles

Speed is the distance an object travels in a given time.

This is represented as

Speed = Distance ÷ Time

We can also use the speed formula to calculate the distance or time by substituting the known values in the formula for speed and further evaluating,

Distance = Speed × Time or,

Time = Distance/Speed

To find the distance covered, we find the total speed

= 5 + 10(twice as fast on the trip back)

= 15

Distance = speed x time

= 15mph x 6hours

= 90miles

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The values of the inverse functions are f-¹ (3) = -1 and f-¹ (8) = 7

From the question, we have the following parameters that can be used in our computation:

x   f(x)

-1   3

1     6

2    5

3    7

7   8

Using the above as a guide, we have the following:

f-¹ (x) means that we calculate the value of x from the table when y = x in the function notation

So, we have

f-¹ (3) = -1 and f-¹ (8) = 7

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