answer this for me please

Mae's walking speed is 10 miles per hour. This is calculated by considering the given information.

Let's assume Mae's walking speed is represented by the variable "x" (in miles per hour). According to the given information, her jogging speed would then be "x + 12.5" miles per hour.

To calculate Mae's exercise time, we can use the formula: time = distance / speed.

Mae jogs 27 miles at a speed of "x + 12.5" miles per hour, so her jogging time can be calculated as:

jogging time = 27 / (x + 12.5)

Mae walks an additional 3 miles at a speed of "x" miles per hour, so her walking time can be calculated as:

walking time = 3 / x

The total exercise time is given as 3 hours. Therefore, we can set up the equation:

jogging time + walking time = 3

Substituting the calculated values, we get:

27 / (x + 12.5) + 3 / x = 3

To solve this equation, we can start by multiplying all terms by x(x + 12.5) to eliminate the denominators:

27x + 27 * 12.5 + 3(x + 12.5) = 3x(x + 12.5)

Simplifying the equation:

\(27x + 337.5 + 3x + 37.5 = 3x^2 + 37.5x\)

Combining like terms:

\(30x + 375 = 3x^2 + 37.5x\)

Rearranging the terms to set the equation equal to zero:

\(3x^2 + 7.5x - 375 = 0\)

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(\(b^2\) - 4ac)) / (2a)

In this case, a = 3, b = 7.5, and c = -375. Substituting these values into the quadratic formula:

x = (-7.5 ± √(\(7.5^2\) - 4 * 3 * -375)) / (2 * 3)

x = (-7.5 ± √(56.25 + 4500)) / 6

x = (-7.5 ± √(4556.25)) / 6

Calculating the square root:

x = (-7.5 ± 67.5) / 6

Simplifying further:

x = (60 / 6) or x = (-75 / 6)

Since Mae's walking speed cannot be negative, the solution is x = 10.

Therefore, Mae's walking speed is 10 miles per hour.

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The complete question is:

For exercise, Mae jogs 27 miles then walks an additional 3 miles to cool down. If her jogging speed is 12.5 miles per hour faster than her walking speed and her total exercise time is 3 hours, what is her walking speed? The athlete's walking speed is

To solve the trigonometric equation 2cos2x=cosx on the interval 0 to 2π, we can use some basic trigonometric identities and algebraic manipulations. The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3

First, we can simplify the equation by moving all the terms to one side:
2cos2x - cosx = 0
Next, we can use the double angle formula for cosine to express cos2x in terms of cosx:
2cos^2x - cosx = 0
Then, we can factor out the common factor of cosx:
cosx(2cosx - 1) = 0
This equation is satisfied when either cosx = 0 or 2cosx - 1 = 0. Solving for cosx in the second equation, we get:
2cosx - 1 = 0
2cosx = 1
cosx = 1/2

Therefore, the solutions to the original equation 2cos2x = cosx on the interval 0 to 2π are the values of x for which either cosx = 0 or cosx = 1/2. Using the unit circle or a calculator, we can find the values of x that satisfy these conditions:
cosx = 0 when x = π/2 and x = 3π/2
cosx = 1/2 when x = π/3 and x = 5π/3
Thus, the solutions to the equation 2cos2x = cosx on the interval 0 to 2π are x = π/2, π/3, 3π/2, and 5π/3.
Hi! I'd be happy to help you find the solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π.
Step 1: Rearrange the equation to create a quadratic equation.
Subtract cos(x) from both sides:
2cos^2(x) - cos(x) = 0
Step 2: Factor out cos(x).
cos(x)(2cos(x) - 1) = 0
Step 3: Solve for x.

Set each factor equal to zero:
a) cos(x) = 0
b) 2cos(x) - 1 = 0
Step 4: Find the solutions for each equation within the interval 0 to 2π.
a) cos(x) = 0
x = π/2, 3π/2
b) 2cos(x) - 1 = 0
cos(x) = 1/2
x = π/3, 5π/3
Step 5: Combine the solutions.
The solutions to the trigonometric equation 2cos^2(x) = cos(x) on the interval 0 to 2π are x = π/2, 3π/2, π/3, and 5π/3.

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Answer: Slope=−

2.000

1.600

​

=−0.800

x−intercept=

4

12

​

=3

y−intercept=

5

12

​

=2.40000

Step-by-step explanation:

The term "normally distributed error term with mean of zero" refers to the residual errors in a statistical model that follow a normal distribution with an average (mean) value of zero.

In statistics, when we use a model to represent data, there is often some variability or discrepancy between the predicted values of the model and the actual observed values. This discrepancy is captured by the error term, which represents the unexplained variation in the data.

A normally distributed error term with a mean of zero means that, on average, the errors have no bias or systematic tendency to be positive or negative. This means that the model is not consistently overestimating or underestimating the true values.

To illustrate this concept, let's consider a simple example. Suppose we have a linear regression model that predicts the exam scores of students based on the number of hours they studied. The error term in this model represents the difference between the predicted scores and the actual scores.

If the error term is normally distributed with a mean of zero, it implies that, on average, the predicted scores will be equal to the actual scores. However, individual predictions may still deviate from the true values due to random fluctuations.

In practical terms, a normally distributed error term with a mean of zero is desirable because it indicates that the model is unbiased and does not systematically under- or over-predict the outcomes. This assumption is often made in statistical analyses to ensure the validity of the results and to make appropriate inferences.

In summary, a normally distributed error term with a mean of zero implies that the errors in a statistical model have no systematic bias and follow a normal distribution. This assumption is important in many statistical analyses and helps to ensure the accuracy and reliability of the model's predictions.

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All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

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The solution to the system of equations y = 1.5x - 4 and y = -x  is (1.6,-1.6)

The equations are given as: y = 1.5x - 4 & y = -x

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables

Substitute y = -x in the first equation

-x = 1.5x - 4

Collect like terms

-1.5x - x = -4

Any set of values of x1, x2, x2,…xn which simultaneously satisfies the system of linear equations given above is called a solution of the system. If the system of equations has one or more solutions, the equations are called consistent. Also, if the system of equations does not admit any solution, then the equations are called inconsistent.

This gives

-2.5x = -4

Divide both sides by -2.5

x = 1.6

Substitute x = 1.6 in y = -x

y = -1.6

Hence, the solution to the system of equations is (1.6,-1.6).

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Answer:

x=6y-18

Step-by-step explanation:

Answer:

Step-by-step explanation:

Which variable are you solving for?

The function is an exponential growth since it is increasing with time and k is positive

Given that at t =6, P = 167075

Then;

167075 =110.8e^6k

167075/110.8 = e^6k

1507.9 = e^6k

ln(1507.9) = 6k

k = ln(1507.9)/6

k = 1.2

Thus in the year 2020;

P = 110.8e^20(1.2)

P = 2.9 * 10^12

In the year 2025;

P = 110.8e^25(1.2)

P = 1.18 * 10^15

To reach 290,000

290,000 = 110.8e^1.2t

290000/110.8 = e^1.2t

2617.3 = e^1.2t

t = ln(2617.3 )/1.2

t = 7 years

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Answer:

-6x-6

Step-by-step explanation:

Just simplify; solamente simplifica la expression y al final añade los resultados.  

Answer:

1. 32

2. 100

3. 36

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

Answer:

32

100

36

Step-by-step explanation:

The probability that a single student randomly chosen from all those taking the test scores 23 or higher is approximately 0.3557 or 35.57%.

To find the probability that a single student randomly chosen from all those taking the test scores 23 or higher, we need to calculate the area under the normal distribution curve.

Given that the mean (μ) is 21.1 and the standard deviation (σ) is 5.1, we can use these values to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the given score, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that the score is 23 or higher, so we can calculate the z-score for x = 23:

z = (23 - 21.1) / 5.1

z ≈ 0.3725

Now, we need to find the area under the normal distribution curve to the right of this z-score. We can use a standard normal distribution table or a calculator to find this area.

Using either method, we find that the probability corresponding to a z-score of 0.3725 is approximately 0.3557. This represents the probability that a randomly chosen student scores 23 or higher on the ACT.

Therefore, the probability that a single student randomly chosen from all those taking the test scores 23 or higher is approximately 0.3557 or 35.57%.

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Answer:

B. \(x>-17.5\)

C. \(x\leq-30\)

Step-by-step explanation:

B.)

\(\frac{-8}{14}x+22>32\\-8x+308>448\\-8x>140\\x>-17.5\)

C.)

\(0.9x+12\leq-15\\0.9x\leq-27\\x\leq-30\)

Hope this helped!! <3

The slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

The slope of a line can be defined a number that describes the direction and steepness of the line.

It is also known as gradient

It is denoted by the letter 'm'

Thus, the slope of a line shows the distance of that line. This means it tells us how far the line moves each time you move over one unit on the x-axis for that line.

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Answer:

B : 68.5°F and 76.5°F

I think sorry if i am wrong.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Each term is 3 times the previous term:  

                                                                r = 3

The sum of the first nine terms in a sequence is 49,205:

                                                      \(S_n=a_1\cdot\dfrac{1-q^n}{1-q}\\\\\\49205=a_1\cdot\dfrac{1-3^9}{1-3}\\\\49205=a_1\cdot\dfrac{1-19683}{-2}\\\\49205=a_1\cdot9841\\\\a_1=5\)

What is the third term?

                                     \(a_n=a_1\cdot q^{n-1}\\\\a_3=5\cdot3^8=32805\)

The solution to the initial value problem y'' - 4y = t^2 + 2e^t, y(0) = 0, y'(0) = 1 is given by the equation y(t) = (11/16)e^(2t) + (-19/16)e^(-2t) - 1/4 * t^2 - 3/8 * e

To solve the given initial value problem, we will follow the steps for solving a second-order linear homogeneous differential equation with constant coefficients.

The differential equation is:

y'' - 4y = t^2 + 2e^t

First, let's find the general solution of the homogeneous equation (setting the right-hand side to zero):

y'' - 4y = 0

The characteristic equation is obtained by substituting y = e^(rt) into the homogeneous equation:

r^2 - 4 = 0

Solving the characteristic equation, we find two distinct roots:

r1 = 2 and r2 = -2

The general solution of the homogeneous equation is then given by:

y_h(t) = c1e^(2t) + c2e^(-2t)

Next, we need to find a particular solution of the non-homogeneous equation (with the right-hand side):

y_p(t) = At^2 + Be^t

Taking the derivatives:

y_p'(t) = 2At + Be^t

y_p''(t) = 2A + Be^t

Substituting these derivatives into the non-homogeneous equation, we get:

2A + Be^t - 4(At^2 + Be^t) = t^2 + 2e^t

Matching the coefficients of the terms on both sides, we have:

-4A = 1 (coefficient of t^2)

2A - 4B = 2 (coefficient of e^t)

From the first equation, we find A = -1/4. Substituting this value into the second equation, we find B = -3/8.

Therefore, the particular solution is:

y_p(t) = -1/4 * t^2 - 3/8 * e^t

The general solution of the non-homogeneous equation is the sum of the general solution of the homogeneous equation and the particular solution:

y(t) = y_h(t) + y_p(t)

= c1e^(2t) + c2e^(-2t) - 1/4 * t^2 - 3/8 * e^t

To determine the values of c1 and c2, we can use the initial conditions:

y(0) = 0 and y'(0) = 1

Substituting these values into the equation, we get:

0 = c1 + c2 - 1/4 * 0^2 - 3/8 * e^0

0 = c1 + c2 - 3/8

1 = 2c1 - 2c2 + 1/2 * 0^2 + 3/8 * e^0

1 = 2c1 - 2c2 + 3/8

Solving this system of equations, we find c1 = 11/16 and c2 = -19/16.

Therefore, the solution to the initial value problem is:

y(t) = (11/16)e^(2t) + (-19/16)e^(-2t) - 1/4 * t^2 - 3/8 * e^t

In summary, the solution to the initial value problem y'' - 4y = t^2 + 2e^t, y(0) = 0, y'(0) = 1 is given by the equation:

y(t) = (11/16)e^(2t) + (-19/16)e^(-2t) - 1/4 * t^2 - 3/8 * e

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Answer:we are not your servers to that i should solve this problems

Step-by-step explanation:

Answer:

I have no idea? the first is 11 the second is 5 the three is 11 again the last 2 are 1

Step-by-step explanation:

Answer:

explain more

Step-by-step explanation:

On solving the provided question ,we can say that As a result, the pie chart's slice representing sleep has a 45 degree centre angle

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

We must first determine the percentage of the 24 hours that Burt slept in order to determine the size of the centre angle of the slice of the pie chart that represents sleep.

Burt slept for three hours out of a total of twenty-four, thus this is how much time he slept:

3/24 = 1/8

We need to multiply this ratio by 360 degrees (the total number of degrees in a circle) to determine the centre angle of the slice indicating sleep:

1/8 times 360 equals 45 degrees.

As a result, the pie chart's slice representing sleep has a 45 degree centre angle.

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The measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

To calculate the measure of the central angle representing sleep in the pie chart, we need to determine what fraction of the 24 hours Burt spent sleeping.

Burt slept for 3 hours out of 24, so the fraction of time he spent sleeping is:

3 / 24 = 1 / 8

To convert this fraction into an angle, we use the formula:

angle = fraction * 360 degrees

So, the central angle representing sleep in the pie chart would be:

angle = (1 / 8) * 360 degrees = 45 degrees

Therefore, the measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

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The dot represents the vertex, and the x represents the point where the parabola touches the x-axis. The parabola is symmetric about the vertical line x = h and does not cross the x-axis anywhere else.

A parabola is a type of curve that is defined by a specific mathematical equation, namely, the quadratic equation. It is a symmetrical curve that can be described as the shape of the graph of a quadratic function.

by the question.

If (h, k) is a zero of the function, then. \(f(h) = 0\). Substituting this into the equation for f(x), we get:

\(0 = a(h - h)^2\)

\(0 = 0\)

This is a true statement, which tells us that (h, k) is indeed a zero of the function.

Now, let's consider the graph of this function. Since the coefficient a is non-zero, the parabola will be facing either upwards or downwards. If a > 0, then the parabola will be facing upwards, and if a < 0, then the parabola will be facing downwards.

Since the vertex of the parabola is at (h, k), the axis of symmetry is the vertical line x = h. Therefore, the parabola is symmetric about this line.

Finally, since (h, k) is also a zero of the function, the parabola must cross the x-axis at x = h with a single point of tangency. This means that the parabola just touches the x-axis at this point and does not cross it.

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The system of linear equations has no solution. Then the number of the solution of the equations will be zero.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equations are given below.

y = 0 and y = - 7

The lines are parallel to each other. Then they will never intersect with each other.

The system of linear equations has no solution. Then the number of the solution of the equations will be zero.

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In order to maximize utility, Jade has to follow various steps such as assessing the weight of each exam, evaluating proficiency and difficulty, etc.

The factors that influence this decision include Jade's current knowledge and proficiency in each subject, the weight of each exam, and the time she has available for studying.

1. Assess weight of each exam: Determine the percentage or points allocated to the economics and astronomy exams. This information will help prioritize the subjects.
2. Evaluate proficiency and difficulty: Consider Jade's current knowledge and skills in economics and astronomy. If she is already proficient in one subject but struggling with the other, it may be wise to allocate more time to the challenging subject.
3. Allocate study time proportionately: Based on the weight of each exam, divide the total study time between economics and astronomy. For example, if the economics exam is worth 40% and the astronomy exam is worth 60%, Jade could spend 40% of her study time on economics and 60% on astronomy.
4. Consider the time available: Take into account Jade's schedule and other commitments. If she has limited study time available, she may need to allocate more time to the subject she finds most challenging or where she has lower proficiency
5. Regular practice and review: Regardless of the time allocation, it's crucial for Jade to engage in regular practice and review sessions for both subjects. This will help reinforce concepts and improve understanding.

It's important to note that these steps provide a general framework, but the specific allocation of study time may vary depending on individual circumstances. Jade should also consider her learning style and preferences when making a study plan

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Answer:

\(f(t) = 7.23( {1.0114}^{t} )\)

t = 0 represents January 1, 2014

(a)

\(f(6) = 7.23( {1.0114}^{6} ) = 7.739\)

The population of the world is expected to be about 7.739 billion people on January 1, 2020.

(b)

\(7.23( {1.0114}^{t} ) = 10\)

\(t = about \: 28.61 \: years\)

The population of the world is expected to be 10 billion people in about 28.61 years after January 1, 2014 (sometime in August 2042).

The bank she would suggest is Neighborhood Bank - 1.2 % interest, compounded weekly.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

A = P \((1 + r/n)^{nt\)

Given:

Gail has $5,500 that she wants to put in a new savings account.

Neighborhood Bank - 1.2% interest, compounded weekly

Beautiful Day Bank - 1.2% interest, compounded daily

Thus, $5,500 x 1.2% = $66

$66 a day times 360 days = $23,760

and, $23,760 times 20 = $475, 200.

and, $257,400 times 20 = $9504000

Hence, The bank she would suggest Gail pick is Neighborhood Bank - 0.65% interest, compounded weekly.

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Since the internal angle sum of a triangle is 180 degrees, and the angles are in ratio if 1:1:4, the angles with that's corresponding to the 1 will have value of 180/6=30 degrees.

The largest angle will have value 30*4=120 degrees.

This is an obtuse triangle because largest angle>90 degrees.

Answer:

212121.

Step-by-step explanation:

It is odd number so it ends in 1.

There are 3 2's and 3 1's which alternate.

Diivisible by 3 and 9

It is 212121.

The diagram shows a dot plot with a given data set

To estimate the mean, you add up the total score and dividde by the number of scores

The constant term for the expression 5g³ + 2 is 2.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the expression,

5g³ + 2,

a linear equation consists of three terms,

variables, coefficient of variables, and constant.

A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

Compared with the given expression,

g is the variable and 5 is the coefficient,

2 is the constant term.

Hence 2 is constant.

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Answer:

3.5%

Step-by-step explanation:

The value of the car decreased by 3.5%. Hope it helps!