find the equation of the line passing through the point (-2,5)(−2,5) that is perpendicular to the line 6x 2y

Answer:

\(c<-4\), \(h=78\)

Step-by-step explanation:

\(\frac{h}{6}=13\)

\(\frac{h}{6}*6=13*6\)   Multiplication property of equality.

\(h=78\)   Simplify

\(3c+5<-7\)

\(3c+5-5<-7-5\)   Subtraction property of inequalities

\(3c<-12\)   Simplify

\(3c\div 3<-12\div 3\)   Division property of inequalities

\(c<-4\)   Simplify

To find the limit of (x + x²)/(9 − 4x²) as x approaches infinity, we can first try to apply l'Hospital's Rule, which states that if the limit of the ratio of the derivatives exists, then it is equal to the original limit.

However, in this case, a more elementary method is available: dividing both the numerator and denominator by the highest power of x.

1. Divide both the numerator and denominator by x²: lim (x/x² + x²/x²) / (9/x² - 4x²/x²) x→[infinity]

2. Simplify the expressions: lim (1/x + 1) / (9/x² - 4) x→[infinity]

3. As x approaches infinity, the terms with x in the denominator will approach 0: lim (0 + 1) / (0 - 4) x→[infinity]

4. Simplify the expression: (1) / (-4) The limit of (x + x²)/(9 − 4x²) as x approaches infinity is -1/4.

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Answer:

Arc ABC = 250°

Step-by-step explanation:

m<AOB = 110° (given)

Based on the central angle theorem, central angle m<AOB equals the intercepted arc AB

Therefore,

m<AOB = measure of arc AB = 110°

Thus:

Arc ABC = 360° - arc AB (Full circle = 360°)

Arc ABC = 360° - 110°

Arc ABC = 250°

Let,

Number of Advance Tickets = a

Number of Same-Day tickets = s

Given,

Total 45 tickets sold

We can write

Also, each advance ticket cost $15 and same day tickets cost $20 for a total of $825. Thus, we can write:

We will multiply the first equation by - 15 and then add both equations. Then, solve for "s". The steps are shown below:

Now, we can use this value of "s" and put it into Equation 1 and find the value of "a". Shown below:

The function f(x) = √(x^2 - 9) is concave up on the intervals (-∞, -3) and (3, +∞), and concave down on the interval (-3, 3).

To determine the concavity of the function, we need to find the second derivative and analyze its sign. Let's differentiate f(x) twice:

f(x) = √(x^2 - 9)

f'(x) = (x) / √(x^2 - 9)

f''(x) = [√(x^2 - 9) - (x)(x) / (√(x^2 - 9))^3] / (x^2 - 9)

To find the intervals of concavity, we set f''(x) equal to zero and find the critical points:

[√(x^2 - 9) - (x)(x) / (√(x^2 - 9))^3] / (x^2 - 9) = 0

Simplifying, we get:

√(x^2 - 9) = (x)(x) / (√(x^2 - 9))^3

(x^2 - 9) = (x^2) / (x^2 - 9)

(x^2 - 9)(x^2 - 9) = x^2

Expanding and simplifying further:

x^4 - 18x^2 + 81 - x^2 = 0

x^4 - 19x^2 + 81 = 0

Using the quadratic formula, we solve for x^2:

x^2 = (19 ± √(19^2 - 4(1)(81))) / 2

x^2 = (19 ± √(361 - 324)) / 2

x^2 = (19 ± √37) / 2

Since x^2 cannot be negative, we discard the negative square root. Therefore, we have x^2 = (19 + √37) / 2.

Taking the square root, we find:

x = ±√((19 + √37) / 2)

From these results, we can determine the intervals where the function is concave up or concave down. By testing points within each interval, we find that the function is concave up on (-∞, -3) and (3, +∞), and concave down on (-3, 3).

To find the intervals where the function f(x) = √(x^2 - 9) is concave up or concave down, we need to examine the concavity of the function by analyzing its second derivative.

By taking the first derivative of f(x), we find f'(x) = (x) / √(x^2 - 9). Then, by differentiating f'(x), we obtain the second derivative f''(x) = [√(x^2 - 9) - (x)(x) / (√(x^2 - 9))^3] / (x^2 - 9).

To determine the concavity, we need to find the values of x for which f''(x) equals zero or is undefined. Setting f''(x) equal to zero and solving for x, we find the critical points. Simplifying the equation leads to the quadratic equation x^4 - 19x^2 + 81 = 0. Solving this equation yields two positive values for x^2, which, when taking the square root

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Answer:

width = 4

Step-by-step explanation:

Let the length = x.

The width is x/6.

perimeter = x + x + x/6 + x/6

perimeter = 56

x + x + x/6 + x/6 = 56

2x + x/3 = 56

6x/3 + x/3 = 56

7x/3 = 56

Divide both sides by 7.

x/3 = 8

x = 24

The length is 24.

width = x/6 = 24/6 = 4

Check: 24 + 24 + 4 + 4 = 48 + 8 = 56

The perimeter does equal 56.

Answer: width = 4

The distribution that the residuals in our model to follow is equals to the normal probability distribution. So, option(a).

Because residuals are defined as the difference between any data point and the regression line, they are sometimes called "errors". An error in this context does not mean that there is anything wrong with the analysis. In other words, the residual is the error that is not described by the regression line. The residue(s) can also be expressed by "e". The formula is written as, Residual = Observed value – predicted value or

\(e = y – \hat y \).

In order to draw valid conclusions from your regression, the regression residuals should follow a normal distribution. The residuals are simply the error terms or differences between the observed value of the dependent variable and the predicted value. Therefore, the residuals should have a normal distribution.

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Complete question:

we desire the residuals in our model to have which probability distribution? select answer from the options below

a) normal

b) binomial

c) poisson

Answer: -4

......................

Answer:

y = 6 or y = 0

Step-by-step explanation:

              |-2y + 6| = 6

-2y + 6 = -6          -2y + 6 = 6

 -2y = -12                -2y = 0

    y = 6                      y = 0

Best of Luck!

Answer:

Step-by-step explanation:

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

     |-2y+6| = 6  

STEP

2

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |-2y+6|

For the Negative case we'll use -(-2y+6)  

For the Positive case we'll use (-2y+6)  

STEP

3

Solve the Negative Case

     -(-2y+6) = 6  

    Multiply

     2y-6 = 6  

    Rearrange and Add up

     2y = 12  

    Divide both sides by 2

     y = 6  

STEP

4

Solve the Positive Case

     (-2y+6) = 6  

    Rearrange and Add up

     -2y = 0  

    Divide both sides by 2

     -y = 0  

    Multiply both sides by (-1)

     y = 0  

    Which is the solution for the Positive Case

STEP

5

:

Wrap up the solution

y=6

y=0

Two solutions were found :

y=0

y=6

Answer:

-10

Step-by-step explanation:

Let x = number

10 less than a number is the same number doubled

x-10 = 2x

Subtract x from each side

x-10-x = 2x-x

-10 = x

The number is -10

Answer:

Part 1) Option A. f of x equals one half times x plus 16

Part 2) Option  A. x = 5

Part 3) Option C. x − 4y = −9

Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.

Step-by-step explanation:

Part 1)

Let

x -----> the number of months

y ----> vertical jump in inches

step 1

Find the slope

we have the points

(0,16) and (2,17)

The equation of the line in slope intercept form is

we have

-----> the point (0,16) is the y-intercept

substitute

convert to function notation

f(x)=y

Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?

step 1

Find the slope

we have the points

(5, 0) and (5, −2)

the slope is undefined

This is a vertical line (parallel to the y-axis)

therefore

The equation is

x=5

Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)

step 1

Find the slope

we have the points

(−1, 2) and (3, 1)

step 2

Find the equation of the line into point slope form

we have

substitute

Convert to standard form

Multiply by 4 both sides to remove the fraction

Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario

we know that

The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)

The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))

Let

x ----> the number of rides

y ----> the total cost in dollars

In this problem

The independent variable or input is the number of rides

The dependent variable or output is the total cost

-brainly user

Answer:

Your function would be y = 1/2x + 16.

Explanation:

Points: (0, 16); (2, 17)

Slope: m = (17 - 16) / (2 - 0) = 1/2

Slope intercept form: y = mx + b

So, if the slope equals 1/2 and the y-intercept is (0, 16), you would use substitution to get y = 1/2x + 16.

Therefore, your ending function is y = 1/2x + 16.

Answer:

The total grams of fat that were in both servings based on the information is 27.625 grams.

Step-by-step explanation:

From the information, Lara bought Philly soft pretzels. Each serving has 1.7 grams of fat. She ate 15 servings of the pretzels at lunch and 1.25 servings of the pretzels as a snack.

Therefore, the total grams will be:

Therefore, the total grams of fat that were in both servings based on the information is 27.625 grams.

= (15 × 1.7) + (1.25 × 1.7)

= 25.5 + 2.125

= 27.625 grams

The probability that two or less people will prefer travelling with brilliant taxis is 0.678

bt represnts brilliant taxis

tr represent taxi ride

P(bt) = 1/5

P(tr) = 4/5

Total number of people surveyed is n = 10

a) what is the probability that two or less people will prefer travelling with brilliant taxis

P(x<=2) = P(×=0) + P(×=1) + P(×=2)

Using Binomial probability

P(x<=x) = nCx(p)^x(q)^n-x

nCx = n!/(n-×)!(x!)

P(x<=2) = 10C0 (1/5)^0(4/5)^10 + 10C1 (1/5)^1(4/5)^9 + 10C2 (1/5)^2(4/5)^8

P(x<=2) = 1(1)(0.1074) +  10(0.2)(0.1342) + 45(0.04)(0.1677)

P(x<=2) = 0.1074 +  0.2684 + 0.3020

P(x<=2) = 0.6778

P(x<=2) = 0.678 ( 3d.p)

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The solutions to trigonometric equation tan³x + tan²x - 3tanx - 3 = 0 in the interval [0, 2π) are x = 0, x = π, and x = π/4. The function g(x) = 10x² + log(1 - 2x) does not have any real roots in interval [0, 2π).The given equation is tan³x + tan²x - 3tanx - 3 = 0. We can solve this equation by factoring.

Let's factor out the common factor of tanx: tanx(tan²x + tanx - 3) - 3 = 0. Now, let's factor the quadratic expression inside the parentheses: tanx(tanx - 1)(tanx + 3) - 3 = 0. We can now set each factor equal to zero and solve for x.

First, tanx = 0. In the interval [0,2π), the solutions for this equation are x = 0 and x = π. Next, tanx - 1 = 0. Solving this equation gives us tanx = 1. In the interval [0,2π), the solution for this equation is x = π/4.

Lastly, tanx + 3 = 0. Solving this equation gives us tanx = -3. However, there are no solutions for this equation in the interval [0,2π) because the tangent function is positive in the first and third quadrants.

Therefore, the solutions to the equation tan³x + tan²x - 3tanx - 3 = 0 in the interval [0,2π) are x = 0, x = π, and x = π/4. Moving on to the function g(x) = 10x² + log(1 - 2x), we can analyze its properties.

The function g(x) is a quadratic function with an additional logarithmic term. The quadratic term 10x² is always positive and opens upward, indicating a U-shaped graph. The logarithmic term log(1 - 2x) is defined for values of x where 1 - 2x > 0, which leads to the condition x < 1/2.

The function g(x) has no real roots because the quadratic term is always positive and the logarithmic term is negative for values of x in the interval [0, 1/2). Therefore, the function g(x) does not intersect the x-axis in the interval [0, 2π).

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Answer:

The rectangle is 3.5 yd x 4 yd

Step-by-step explanation:

Area = length x width = lw

l = length = 2w - 3

w = width

Area = 14(2w - 3)(w) = 14

2w² - 3w - 14 = 0

Use quadratic equation to find the 2 roots of w:  a = 2, b = -3, c = -14

w = 3.5, -2     disregard the negative root

width = 3.5 yd

length = 2(3.5) - 3 = 4 yd

The dimensions of the rectangle are approximately 2.23 yards by 1.46 yards.

We are assuming the width of rectangle to be "x" yards. Then, the length would be (2x - 3) yards, since it is 3 yards less than double the width. The formula for the area of a rectangle is A = l x w, so we can plug in the values we know:

14 = (2x - 3) x x

Expanding the brackets:

14 = 2x² - 3x

Put this equation=0:

2x² - 3x - 14 = 0

Using the quadratic formula:

x = (3 ± √(3² + 4 x 2 x 14)) / (2 x 2)

x = (3 ± √97) / 4

We can ignore the negative root, since the width cannot be negative. Therefore,

x ≈ 2.23

This is the width of the rectangle. To find the length, we can plug this value back into the expression we derived earlier:

length = 2x - 3

length ≈ 1.46

Therefore, the dimensions of the rectangle are approximately 2.23 yards by 1.46 yards

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Answer:

First image: (6, -1)

2nd image: y = 63

Explanation:

1)

2x + y = 11

1/2x - 5y = 8

y = -2x + 11

1/2x - 5(-2x + 11) = 8

1/2x + 10x - 55 = 8

10.5x - 55 = 8

10.5x = 63

x = 6

2x + y = 11

2(6) + y = 11

12 + y = 11

y = -1

(x , y) = (6, -1)

2)

1/4(8y - 4.8) = 2 (0.9y + 5.4) + 3/5

2y - 1.2 = 1.8y + 10.8 + 0.6

0.2y - 1.2 = 11.4

0.2y = 12.6

y = 63

Answer: = 16

Step-by-step explanation: Hope this help :D

Step-by-step explanation:

the bottom left is the right option.

just by saying "the temperature increases ..." the 2 options on the right are wrong. the line has to go up, not down.

the first graph (top left) increases too strongly, way more than just 4ft per hour.

Answer:

unlikely

Step-by-step explanation:

Answer:

-4 -5x

Step-by-step explanation:

4(1 – 3x) + 7x – 8.

Distribute

4 -12x +7x -8

Combine like terms

-4 -5x

Answer:

The simplified answer of this expression is -5x - 4

Step-by-step explanation:

4(1 - 3x) + 7x - 8

Distribute 4 to (1 - 3x)

4 - 12x + 7x - 8

Rearrange the terms so it'll be easier to combine them.

4 - 8 - 12x + 7x

Combine like terms.

-4 - 5x

Put the equation in standard form.

-5x - 4

Answer:

x either equals to 4 of 9 so you can write it like x=4, 9

Step-by-step explanation:

Start by simplifying each sides of the equation.

x^2-13x+36=0

Then factor the left side of the equation.

(x-4)(x-9)=0

Set factors equal to 0

x-4=0 or x-9=0

x=4 or x=9

Answer:

4, 9

Step-by-step explanation:

(x-4)(x-9)=0

x-4=0, x-9=0

x=0+4=4

x=0+9=9

The simplified expression of the expression given as (62)4 is 248

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

(62)4

Remove the bracket and rewrite the expression as a product expression

So, we have the following representation

(62)4 = 62 * 4

Evaluate the products

This gives

(62)4 = 248

The above expression cannot be further simplified

Hence, the solution is 248

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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The main impact of increasing the standard deviation from 3.1 to 5.8 leads to a wider confidence interval, from (9.38, 10.62) to (8.88, 11.12).

This is because the standard deviation is a measure of the spread of the data, and the wider the spread, the wider the confidence interval will be. Mathematically, this can be shown by the following calculation:

The confidence interval is usually given by the formula:

where x is the mean of the sample, z is the z-score representing the confidence level, sigma is the standard deviation, and n is the sample size.

In this case, let's assume that x = 10, z = 1.96 (95% confidence interval), and n = 10. Then, when the standard deviation is 3.1, the confidence interval is 10 +/- (1.96*3.1/sqrt(10)) = 10 +/- 0.62, or (9.38, 10.62).

However, when the standard deviation is increased to 5.8, the confidence interval becomes 10 +/- (1.96*5.8/sqrt(10)) = 10 +/- 1.12, or (8.88, 11.12).

Therefore, increasing the standard deviation from 3.1 to 5.8 leads to a wider confidence interval, from (9.38, 10.62) to (8.88, 11.12).

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Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.

This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.

Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.

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