Kluber lives 450 miles away from an amusement park. He is taking his family to an amusement park, leaving his house and traveling at an average speed of at least 65 miles per hour to the park but at most 80 miles per hour. Create a system of linear constraints that model the distance he is away from the park, d, after t hours. Then evaluate the inequality for t=3 and interpret the answer within the context of the scenario.

Answer:

to find surface area of cylinder

A=2πrh+2πr²

Step-by-step explanation:

Answer:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    7/n-(8/7)=0

Step by step solution :

STEP 1:

           8

Simplify   —

           7

The equation at the end of step

1:

 7    8

 — -  —  = 0

 n    7

STEP 2:

           7

Simplify   —

           n

The equation at the end of step

2:

 7    8

 — -  —  = 0

 n    7

STEP 3:

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       n

     The right denominator is :       7

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

7 0 1 1

Product of all

Prime Factors  1 7 7

                 Number of times each Algebraic Factor

           appears in the factorization of:

   Algebraic    

   Factor      Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

n  1 0 1

     Least Common Multiple:

     7n

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Denominator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 7

  Right_M = L.C.M / R_Deno = n

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction, multiply the numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      7 • 7

  ——————————————————  =   —————

        L.C.M              7n  

  R. Mult. • R. Num.      8 • n

  ——————————————————  =   —————

        L.C.M              7n  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

7 • 7 - (8 • n)     49 - 8n

———————————————  =  ———————

      7n              7n  

The equation at the end of step

3

:

 49 - 8n

 ———————  = 0

   7n  

STEP

4

:

When a fraction equals zero :

4.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now, to get rid of the denominator, Tiger multiplies both sides of the equation by the denominator.

Here's how:

 49-8n

 ————— • 7n = 0 • 7n

  7n  

Now, on the left-hand side, the  7n  cancels out the denominator, while, on the right-hand side, zero times anything is still zero.

The equation now takes the shape :

  49-8n  = 0

Solving a Single Variable Equation:

4.2      Solve  :    -8n+49 = 0

Subtract  49  from both sides of the equation :

                     -8n = -49

Multiply both sides of the equation by (-1) :  8n = 49

Divide both sides of the equation by 8:

                    n = 49/8 = 6.125

One solution was found :

n = 49/8 = 6.125

Step-by-step explanation:

hope this helps...

The solution of equation \((7^2)^4=n^8\) is n = 7

"It is a mathematical statement which consists of variables and constants, and some algebraic operations."

"It is a mathematical statement which consists of equal symbol between two mathematical statements."

For given question,

We have been given an equation \((7^2)^4=n^8\)

Consider an algebraic expression on the left side of the above equation.

\((7^2)^4\)

Using the properties of exponents we can write it as,

\((7^2)^4\\=7^{(2\times 4)}\\=7^8\)

So, given equation becomes,

\(7^8=n^8\)

Since power is same, base of above exponents is equal.

⇒ n = 7

Therefore, the solution of equation \((7^2)^4=n^8\) is n = 7

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The statement which is true is D. 65% of the seventh-grade students prefer the water park.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

A : Total number of students = 120

Number of students who prefer amusement park = 14 + 16 = 30

Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%

B : Total number of eighth grade students = 80

Number of eighth grade students who prefer amusement park = 16

Percentage = 16 / 80 = 0.2 = 20%

C : Total number of students = 120

Number of students who prefer water park = 26 + 64 = 90

Percentage = 90 / 120 = 0.75 = 75%

D : Total number of seventh grade students = 40

Number of seventh grade students who prefer water park = 26

Percentage = 26 / 40 = 0.65 = 65%

Hence the option D is the correct percentage.

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Answer: 60

Step-by-step explanation:

This is done by multiplying length x width x height (6x2x5)

Answer:

No

Step-by-step explanation:

The tangent line must form a right angle with the radius

No, 4 5 6 isn't a right triangle

Answer:

Line m is not a tangent line to circle B.

Step-by-step explanation:

The tangent line to a circle is always perpendicular to the radius.

The line segment measuring 4 units is the radius of Circle B, therefore if line m is a tangent line to the circle, the angle between this segment and the segment measuring 5 units will be a right angle (90°).

We can use Pythagoras' Theorem to check if the triangle is a right triangle.

Pythagoras’ Theorem:  \(a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Therefore, the legs are the line segments measuring 4 and 5, and the hypotenuse is the line segment measuring 6 units.

Substituting the values for the legs into the formula:

\(\implies 4^2+5^2=c^2\)

\(\implies 16+25=c^2\)

\(\implies 41=c^2\)

\(\implies c=\sqrt{41}\)

Therefore, as the hypotenuse of the triangle is not √41, the triangle is not a right triangle, and therefore line m is not a tangent line to circle B.

Answer:

5/6 or 83.333333333333333

Step-by-step explanation:

Highway equivalent fuel efficiency rate in miles per gal = 67.27 mile / gal

City Equivalent fuel efficiency rate in miles per gal= 51.93 mile / gal

From unit conversions, we know that:

1 mile = 1.61 km

1 gal = 3.8 L

Thus, converting the fuel efficiency rates:

Highway rate = (28.5 km/L) * (1 mile / 1.61 km) * (3.8 L / 1 gal)

Highway equivalent fuel efficiency rate in miles per gal = 67.27 mile / gal

Rate for the city = (22.0 km/L) * (1 mile / 1.61 km) * (3.8 L / 1 gal)

City Equivalent fuel efficiency rate in miles per gal= 51.93 mile / gal

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Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

The domain of the step function f(x) = [2x] - 1, where [2x] represents the greatest integer less than or equal to 2x, can be determined by considering the restrictions on the input values.

In this case, the step function is defined for all real numbers. However, the greatest integer function imposes a restriction. Since the greatest integer function only outputs integers, the input values (2x) must be such that they produce integer outputs.

For any real number x, the greatest integer less than or equal to 2x will always be an integer. Therefore, the domain of the function f(x) = [2x] - 1 is:

Domain: {x | x is a real number}

Option D, "{x | x is a real number}" accurately represents the domain of the function.

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Answer:

5x−3=13−3x

x=2

positve 2

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

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

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

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

E

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 0) and (x₂. y₂ ) = (8, 2) ← 2 points on the line

m = \(\frac{2-0}{8-0}\) = \(\frac{2}{8}\) = \(\frac{1}{4}\)

y = \(\frac{1}{4}\) x → E

Answer:

y=1/4x

Step-by-step explanation:

because its the answer

The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

Given that,

In a survey, it was discovered that 68% of women and 78% of men preferred computer-assisted education to lectures, respectively. Each sample contained 100 people that were chosen at random.

We have to calculate the 95% confidence range for the difference between the two proportions.

We know that,

The 95% confidence interval for difference between two population proportions is given as follows :

\(((\bar p_{1} -\bar p_{2})\)±\(Z_{0.05/2}\sqrt{\frac{PQ}{n_{1} } +\frac{PQ}{n_{2} }} })\)

Here,

p₁ is 0.78

p₂ is 0.68

n₁ is 100

n₂ is 100

Z is 1.96

P is 0.73

Q is 0.27

So,

((0.78-0.68)±\(1.96\sqrt{\frac{(0.73)(0.27)}{100 } +\frac{(0.73)(0.27)}{100 }} })\)

(0.10±0.122)

(0.10-0.122,0.10+0.122)

(-0.022,0.222)

Therefore, The 95% confidence interval for the difference between the two population proportions is -0.022 < p₁ - p₂ < 0.222.

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The numbers arranged in ascending order are:

-5, -√3, √3

What is the ascending order?

"Ascending order" refers to the arrangement of a set of numbers or values from the smallest to the largest.

The given numbers are -5, √3, and -√3.

To arrange these numbers in ascending order, we can start by comparing -5 and √3. Since -5 is a negative number and √3 is a positive number, we know that √3 is greater than -5.

Next, we can compare √3 and -√3. Since √3 is a positive number and -√3 is a negative number, we know that √3 is greater than -√3.

Therefore, the numbers arranged in ascending order are:

-5, -√3, √3

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Complete question:

"Arrange the following numbers in ascending order: -5, -√3, √3."

Slamming on the brake applies an impulsive force over a period of time

What is an Impulse?

Impulse can be defined as a force felt or applied on a body over a period of time, when an impulse is applied on a body it produces a change in linear momentum.

Impulse is represented by the symbol J and the unit for measuring impulse is in Newton-seconds or kg m/s.

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Answer:

\(1 \frac{1}{4} \)

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

four centimeters

Therefore, the edge length of a cube whose volume is 64 cubic centimeters will be four centimeters.

Step-by-step explanation:

If 74 amplifiers are sampled, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

The question is asking for the probability that the mean of the sample would differ from the population mean by less than 2.8 watts. We are given that the mean output of the amplifier population is 321 watts with a variance of 144, and that 74 amplifiers are sampled.

To find the probability, we can use the standard deviation, which is the square root of the variance. Therefore, the standard deviation is √144 = 12 watts.

Since we are dealing with a sample mean, we can use the formula for the standard error of the mean, which is the standard deviation divided by the square root of the sample size. In this case, the sample size is 74.

The standard error of the mean is 12 / √74 ≈ 1.3922 watts.

To find the probability that the mean of the sample would differ from the population mean by less than 2.8 watts, we can use the standard normal distribution. We can calculate the z-score using the formula: (x - μ) / σ, where x is the difference in means (2.8 watts), μ is the population mean (321 watts), and σ is the standard error of the mean (1.3922 watts).

The z-score is (2.8 - 321) / 1.3922 ≈ -231.0971.

To find the probability, we need to find the area under the standard normal curve to the left of the z-score. Using a standard normal table or a calculator, the probability is essentially 0 (rounded to four decimal places).

Therefore, the probability that the mean of the sample would differ from the population mean by less than 2.8 watts is approximately 0.

Complete Question: The mean output of a certain type of amplifier is 321 watts with a variance of 144. If 74 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 2.8 watts? Round your answer to four decimal places.

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A moderately negative correlation between both of them variables is shown by the resultant correlation coefficient of -0.55.

We can construct a correlation matrix to determine the relationship between the number the group visits received and the fructosamine level. This indicates that the fructosamine level typically decreases as the amount of group visits increases.

This could imply that patients can keep better control of glucose, as seen by lower fructosamine levels, by participating in group visits and getting support or education about managing diabetes.

It's crucial to remember that a connection does not necessarily indicate a cause.

Further study is required to show a causal link between the fructosamine level and the number the group visits that participants attended. Overall, the moderately negative correlation points to some potential benefits of group visits for treating diabetes.

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Answer:

900 L

Step-by-step explanation:

after 10 hours : 10*10=100 liters

1000-100=900 liter

is the answer I recived

My work is below:

Next after 10 hours (10*10=100 liters )

1000-100=900 liter

Hope this helps you learn what to do in similar probles

If you like this question please mark brainest  

Answer:

(-2, 2)          

Step-by-step explanation:

x= -2  y= 2      

x and y-intercept :

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

Absolute min:

An absolute maximum point is a point where the function obtains its greatest possible value.

Absolute max :

An absolute minimum point is a point where the function obtains its least possible value.

Local Extrema (Local Maxima/Minima): The local maxima and minima on a graph refer to the maximum and minimum points of the graph over a specific interval of the graph as opposed to the entire graph, so there can be multiple local maxima and minima of a given graph.

When considering which points are the absolute maximum and the absolute minimum of a graph, we not only need to consider local extrema (a maximum/minimum of a graph on some interval that contains the point), but we also need to consider the endpoints (the furthest left/right points on our graph). By looking at the y-values for each of these points, we can identify the absolute maximum of the graph as the point with the highest y-value, and we can identify the absolute minimum as the point with the lowest y-value.

Step 1: Identify local maxima/minima, as well as the endpoints.

From this graph, we can see that our graph is on the interval

This means we have our endpoints at [-1,-1] , [4,1] ,

to consider. We also observe that we have one local minima and one local maxima in between these points on our interval. The estimated points are all shown in the image.

absolute minimum point : [-1,-1]

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The 95% confidence interval for the true population mean yield per plant based on the given data is estimated to be between 38.4 and 41.6 ounces. This means that we can be 95% confident that the true mean yield per plant falls within this range.

To construct the confidence interval, we can use the formula: Confidence interval = sample mean ± (critical value * standard error)In this case, the sample mean is 40 ounces per plant. The critical value can be obtained from the standard normal distribution for a 95% confidence level, which is approximately 1.96. The standard error can be calculated as the population standard deviation divided by the square root of the sample size, which in this case is 4.2 / √61.

Plugging in these values, we find that the confidence interval is 40 ± (1.96 * (4.2 / √61)), which simplifies to 38.4 to 41.6 ounces. This means that we can be 95% confident that the true mean yield per plant in the population lies within this interval.

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Answer:

1 one firs side second one second side 3rd one second side 4th one first one 5th one second  side 6th one first side

Step-by-step explanation:

Answer:

Step-by-step explanation:

First [formula] goes to first category

Second [formula] goes to second category

Third [statement] goes to first category

Fourth [formula] goes to first category

Fifth [statement] goes to second category

Sixth [formula] goes to second category

Probability of an event is the measure of the likelihood that the event will occur. It is a number between 0 and 1, where 0 means the event will not occur and 1 means the event will occur.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Probability is a measure of the likelihood or chance that a particular event will occur. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain or guaranteed event.

In probability theory, the probability of event A is denoted as P(A) and is calculated by dividing the number of favorable outcomes for event A by the total number of possible outcomes in the sample space.

The probability formula is:

P(A) = Number of favorable outcomes / Total number of possible outcomes

Probability can also be expressed as a fraction, decimal, or percentage.

For example, if you have a standard six-sided die and you want to calculate the probability of rolling a 4, there is only one favorable outcome (rolling a 4) out of six possible outcomes (numbers 1 to 6). Therefore, the probability of hitting a 4 is 1/6 or approximately 0.1667 (16.67%).

Probability allows us to quantify uncertainty and make predictions based on the likelihood of different outcomes. It is a fundamental concept in various fields such as mathematics, statistics, physics, economics, and more.

Answer:

35, 35, and 50

Step-by-step explanation:

50 + x + x = n

n ÷ 3 = 40

n = 40 x 3

n = 120

50 + 2x = n

50 + 2x = 120

2x = 120 - 50

2x = 70

2x/2 = 70/2

x = 35

To check:

35 + 35 + 50 = 120

120 ÷ 3 = 40

Hope this helps

Answer:

35

Step-by-step explanation:

let us take each boy's weight as x

therefore,

average = \(\frac{x+x+50}{3\\}\)

40 = \(\frac{x+x+50}{3\\}\)

40 x 3 = x + x + 50

120 - 50 = 2x

70 = 2x

2x = 70

x = \(\frac{70}{2}\)

x = 35

So weight of each boys is 35.

Answer:

-18+ 13

-6 + 1

-20 + 15

-7 + 2

Step-by-step explanation:

A cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7

When exponents, constants, and variables are joined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable).

According to the conjugate root theorem, irrational roots of P(x) = 0 with the formula (a + √b) occur in conjugate pairs if P(x) is a polynomials with rational coefficients. This means that (a - √b) is likewise a root if (a + √b) is an irrational root and (a and b) are rational.

In this case, a cubic polynomial with rational coefficients has the roots 2 + √7 and 3/8, so the one additional root is: 2 - √7

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The sum of the first three terms in the series is -557.921 and a bound for the error is approximately 865.474.

What is series?

In mathematics, a series is the sum of the terms of a sequence. It is represented by the sigma notation (∑), which indicates that a sequence of terms is being added together.

To calculate the sum of the series and find the bounds for the error, let's break down the problem step by step.

The series can be represented as:

\(\sum_{n=1}^{\infty} [(-1)^n * 400*n^{0.6}]\)

To find the sum of the first three terms, S3, we need to calculate the values for n = 1, 2, and 3 and then sum them up.

For n = 1:

\((-1)^1 * 400 * 1^{0.6\) = -400

For n = 2:

\((-1)^2 * 400 * 2^{0.6\) = 564.189...

For n = 3:

\((-1)^3 * 400 * 3^{0.6\) = -721.110...

Now, let's calculate the sum of the first three terms, S3:

S3 = -400 + 564.189 + (-721.110) = -557.921

The sum of the first three terms, S3, is approximately -557.921.

To find a bound for the error, we can use the Alternating Series Estimation Theorem. The theorem states that the error in approximating an alternating series is less than or equal to the absolute value of the next term.

In this case, the next term of the series would be for n = 4:

\((-1)^4 * 400 * 4^{0.6\) = 865.474...

The bound for the error is given by the absolute value of this term:

|Next Term| = |865.474...| ≈ 865.474

Therefore, a bound for the error is approximately 865.474.

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Step-by-step explanation:

3).20⁰

4).60⁰

180-70+70_180-140__20