Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (412) i+(21+3)j + (51³) k. t=to=5 What is the standard parameterization for the tangent line? X = y = Z = (Type expressions using t as the variable.)

Total distance travelled by lisa before falling off is 56.52 m

The circumference of a circle is the straight-line distance around it. In other words, if you open a circle and draw a straight line, the length of that line will be the perimeter. The perimeter is the total distance around the circle. Then find the perimeter using the formula C = 2πr.

Given,

Unicycle wheel diameter = 0.6 m

Unicycle wheel radius = 0.3 m

Number of revolutions before falling = 32

Circumference (C) = 2 x Pi x Radius

= 2 × π × r

= 2 × 3.14 × 0.3

= 1.884 m

Distance travelled by lisa = 30 × 1.884

= 56.52 m

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This will give you the MSE value for the new model, which excludes the statistically insignificant independent variable.

To run the regression model in RStudio and calculate the Mean Squared Error (MSE), we need to perform the following steps:

1. Import the data into RStudio. Let's assume the data is stored in a data frame called "data".

```R

data <- data.frame(

 Graduate = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10),

 StartingSalary = c(40, 46, 54, 39, 37, 38, 48, 52, 60, 34),

 GPA = c(3.2, 3.5, 3.6, 2.8, 2.9, 3.0, 3.4, 3.7, 3.9, 2.8),

 Activities = c(4, 5, 2, 4, 3, 4, 5, 6, 6, 1)

)

```

2. Run the regression model using the lm() function in R. We will use the StartingSalary as the dependent variable and GPA and Activities as independent variables.

```R

model <- lm(StartingSalary ~ GPA + Activities, data = data)

```

3. Calculate the Mean Squared Error (MSE) of the model. The MSE is obtained by dividing the sum of squared residuals by the number of observations.

```R

mse <- sum(model$residuals^2) / length(model$residuals)

mse

```

This will give you the MSE value of the model.

To run the regression model again without including the statistically insignificant independent variable, you would need to determine which variable is statistically insignificant. You can do this by examining the p-values of the coefficients in the model summary.

```R

summary(model)

```

Look for the p-values associated with each coefficient. If a p-value is greater than the desired significance level (e.g., 0.05), it indicates that the corresponding independent variable is not statistically significant.

Suppose, for example, the Activities variable is found to be statistically insignificant. In that case, you can run the regression model again without including it and calculate the MSE for this new model.

```R

new_model <- lm(StartingSalary ~ GPA, data = data)

mse_new <- sum(new_model$residuals^2) / length(new_model$residuals)

mse_new

```This will give you the MSE value for the new model, which excludes the statistically insignificant independent variable.

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Answer:

x = 2

Step-by-step explanation:

distribute -2 first

-2 + 8x = 3x + 8

-2 + 5x = 8

5x = 10

x = 2

Answer: 30 6/29

Step-by-step explanation: 6132 \ 203 is 30 and 42/203. 42/203 simplified is 6/29

Answer:

225

Step-by-step explanation:

the person chages 40 per hour with a one time service charge of 65. our equation is 40h+65 where h equal hours. the person spend 4 hour so the equation is (40x4)+65. 40x4 is 160. 160 + 65 is 225

Answer:

The value of p(-a) must be 0

There is an x intercept of the function at (-a,0)

Step-by-step explanation:

(x + a) is a factor of a function p(x)

that means, that p(x) must have an x-intercept at the point x = -a

This can be written in two different ways,

If (x + a) is a factor of a polynomial function, p(x), then the two statements that are true are:

A factor of a polynomial function is a binomial that, when multiplied by another polynomial, gives the original polynomial function. If (x + a) is a factor of p(x), then p(x) can be written as (x + a)q(x), where q(x) is another polynomial function.

According to the Factor Theorem, if (x + a) is a factor of p(x), then p(a) = 0. This means that the value of the polynomial function at x = a is 0.

Additionally, if p(a) = 0, then there is an z-intercept of the function at (a,0). This is because the z-intercept is the point where the function crosses the z-axis, and this occurs when the value of the function is 0.

Therefore, the two statements that are true are "The value of p(a) must be 0" and "There is an z-intercept of the function at (a,0)".

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Answer:

X=11

Step-by-step explanation:

3x+8x-9=112

11x-9=112

11x=112+9

11x=121

11÷11x=121÷11

X=11

Answer:

where is the image??? u should paste the image tooo.

To prove that there must exist an integer m such that any collection of m integers will either contain a pair whose sum is divisible by 10 or contain a pair whose difference is divisible by 10, we can use the Pigeonhole Principle.

The Pigeonhole Principle states that if we distribute more than n objects into n pigeonholes, then at least one pigeonhole must contain more than one object.

In our case, the objects are the integers, and the pigeonholes are the possible remainders when dividing an integer by 10. Since there are only 10 possible remainders (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9), we can distribute the integers into these 10 pigeonholes based on their remainders when divided by 10.

Now, consider a collection of m integers. We need to show that if m is large enough, there will always be either a pair whose sum is divisible by 10 or a pair whose difference is divisible by 10.

Let's consider the 10 possible remainders when dividing an integer by 10. If any of these remainders have more than one integer assigned to them (pigeonhole contains more than one object), we can easily find a pair that satisfies either condition.

Case 1: Pigeonhole contains more than one integer with a remainder of 0 when divided by 10.

In this case, we have at least two integers x and y such that x ≡ 0 (mod 10) and y ≡ 0 (mod 10). Therefore, their sum x + y is divisible by 10, and we have found a pair whose sum is divisible by 10.

Case 2: Pigeonhole contains more than one integer with a remainder between 1 and 9 (inclusive) when divided by 10.

In this case, we have at least two integers x and y such that x ≡ r (mod 10) and y ≡ r (mod 10), where r is a remainder between 1 and 9. Therefore, their difference x - y is divisible by 10, and we have found a pair whose difference is divisible by 10.

In both cases, we have shown that for any collection of m integers, if m is large enough, there will always be either a pair whose sum is divisible by 10 or a pair whose difference is divisible by 10.

To compute the smallest such integer m, we need to find the smallest value of m for which the Pigeonhole Principle guarantees the existence of the desired pair.

In this case, we have 10 possible pigeonholes (remainders) and the minimum number of integers required to guarantee the existence of a pair is one more than the number of pigeonholes.

Therefore, the smallest integer m is 10 + 1 = 11.

Hence, for any collection of 11 integers, there must exist a pair whose sum is divisible by 10 or a pair whose difference is divisible by 10.

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Answer: Where is the triangle?

Step-by-step explanation: Brainliest pls:)

Answer:

165*6+53+792= 990+845 = 1,835

Step-by-step explanation:

Step-by-step explanation:

Seven more than twice a number is 47. Let's break down this sentence into numbers so you can see what's going on.

"Seven more than twice a number" - This tells you that there is a number, let's call it y, that is 7 more than twice a different number, lets call this x. So in equation form this is y = 7 + 2x. Hmm this seems a little tricky, how do we find the answer? Well if we keep reading, it tells you that the number that is 7 more than twice another number is 47, so we now know that y = 47. So let's redo our equation by substituting y for the number 47:

47 = 7 + 2x

Now we have a workable equation. We need to solve for x. So let's rewrite this equation without changing it, just putting it in different order. Now we have 2x + 7 = 47. So how do we solve for x? First, we subtract 7 from both sides. Remember, when solving for x, anything you do to one side you must do to the other. So now we get this:

2x + 7 = 47 simplifies to 2x = 40

Now if we divide both sides by 2 to get x all by itself, we get x = 20. That is your answer. You can check it by substituting 20 for s in your original equation of 2x + 7 = 47, then you get 2(20) + 7 = 47. It works! Hope this helps!

Answer:

6×9-11+28÷4

50

54-11+7

If cholesterol level were changed to being measured in grams instead of milligrams, the correlation between fat content and cholesterol level would not be affected.

This is because correlation is a measure of the strength and direction of the linear relationship between two variables, and converting the units of measurement does not change the underlying relationship between the variables. So, the correlation coefficient of 0.75 would remain the same whether cholesterol level is measured in milligrams or grams.

The correlation between fat content and cholesterol level for the 20 different brands of American cheese slices is 0.75. If you change the measurement of cholesterol level from milligrams to grams (1 gram = 1000 milligrams), it will not affect the correlation. The correlation coefficient will remain 0.75, as it is unit-less and only represents the strength and direction of the relationship between the two variables.

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The number is 5/2 or 2.5

7 is added to six times a number, the result is 22

The number sentence is interpreted this way:

7+6n=22

6n=22–7

6n=15

The goal here is to find out the value of n.

Let’s divide both sides of the equation with 6

6n/6=15/6

n= 5/2 or 2.5

Let’s check by substituting the value of n to the given equation.

Always remember to follow the PEMDAS rule. We will deal with Multiplication and Addition after.

If n=2.5

7+6n=22

7+6(2.5)=22

7+15=22

22=22

Given the result, this means that the value of the number represented by n is 2.5 or 5/2.

Answer:

3x+7=22   <- That's the equation

3x -7=22-7

  3x =15

3/3  =15/3

  x =5

Step-by-step explanation:

Hope this Helps !!!

Answer:

3:25 pm

Step-by-step explanation:

How much time do they need for tours

Empire State Building : 1 hour 10 minutes

Central Park                   2 hour 50 minutes

Times Square                1 hour

                                       -------------------------------

                                      4 hours 60 minutes

but 60 minutes = 1 hour  so subtract 60 minutes and add 1 hour

4 hours 60 minutes

+1        -60

--------------------------------

5 hours

They need 5 hours for the tours

We have to be at dinner at 8:25 so we need to start 5 hours earlier

8:25

- 5

------------------

3:25

We can start no later than 3:25 pm

Answer:

3.25

Step-by-step explanation:

First convert into minutes

1 hour = 60 minutes

Empire state building:

60 + 10 = 70

Central park:

60 + 60 + 50 = 170

Times square:

60

Now add all minutes together.

70 + 170 + 60 = 300 minutes.

Convert into hours:

300 / 60 = 5 hours.

8 - 5 = 3

So, Gabby's family can start their tour at 3:25 at most to get to dinner on time.

Hope this helped.

Answer:

1-50

Step-by-step explanation:

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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After finding the z score, total 49.865% you could expect to score between 60 and 120.

Math exams mean(μ) = 120

Math exams standard deviation(σ) = 20

We have to determine the percent you could expect to score between 60 and 120.

The area total included to the left of any score or value is indicated in the Z-score table (x). The top row and the first column of the Z-table represent the Z-values, while all of the numbers in the middle represent the areas.

P(60 < x < 120) = P((60 - 120)/20 < (x - μ)/σ < (120 - 120)/20)

Simplifying

P(60 < x < 120) = P((-60)/20 < (x - μ)/σ < 0/20)

P(60 < x < 120) = P(-3 < Z < 0)

We can write this as

P(60 < x < 120) = P(Z > -3) - P(Z < 0)

P(60 < x < 120) = 0.99865 - 0.5

P(60 < x < 120) = 0.49865

P(60 < x < 120) = 49.865%

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Answer:

The rate of change is positive 96%

Step-by-step explanation:

.96 = 96%

a. \(r^2 = 0.1024\): Approximately 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

b. \(r^2 = 0.0169\): Only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

c. \(r^2 = 0.1600\): Approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

d. \(r^2 = 0.8649\): About 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

What is variance?

In statistics, variance is a measure of the spread or dispersion of a set of data points around the mean. It quantifies the average squared deviation of each data point from the mean.

The coefficient of determination, denoted as \(r^2\), represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges between 0 and 1, where 0 indicates no linear relationship, and 1 indicates a perfect linear relationship.

To determine the coefficient of determination, we square the linear correlation coefficient (r) to find \(r^2\).

Let's calculate the coefficient of determination for each given linear correlation coefficient:

\(a. r = -0.32\\\\r^2 = (-0.32)^2 = 0.1024\)

The coefficient of determination, \(r^2\), is approximately 0.1024. This means that about 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

\(b. r = 0.13\\\\r^2 = (0.13)^2 = 0.0169\)

The coefficient of determination, \(r^2\), is approximately 0.0169. This means that only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

\(c. r = 0.40\\\\r^2 = (0.40)^2 = 0.1600\)

The coefficient of determination, \(r^2\), is 0.1600. This means that approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

\(d. r = 0.93\\\\r^2 = (0.93)^2 = 0.8649\)

The coefficient of determination, \(r^2\), is approximately 0.8649. This indicates that about 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

In summary:

a. \(r^2 = 0.1024\): Approximately 10.24% of the variance in the dependent variable can be explained by the independent variable(s).

b. \(r^2 = 0.0169\): Only about 1.69% of the variance in the dependent variable can be explained by the independent variable(s).

c. \(r^2 = 0.1600\): Approximately 16% of the variance in the dependent variable can be explained by the independent variable(s).

d. \(r^2 = 0.8649\): About 86.49% of the variance in the dependent variable can be explained by the independent variable(s).

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Kayla would have approximately $554.93 in the account after 12 years, rounded to the nearest dollar.

Learn more about To calculate the amount Kayla would have in the account after 12 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

In this case, Kayla deposits $380 every quarter, so the principal amount (P) is $380. The annual interest rate (r) is 3.3% or 0.033 as a decimal. The interest is compounded quarterly, so n = 4. The number of years (t) is 12.

Plugging these values into the formula:

A = $380 * (1 + 0.033/4)^(4*12)

Calculating the exponent:

A = $380 * (1 + 0.00825)^(48)

A = $380 * (1.00825)^(48)

Using a calculator, we can calculate the value of (1.00825)^(48) ≈ 1.464096

A = $380 * 1.464096

A ≈ $554.93

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Hi Student!

Usually the first step that I take for any problem would be to gather any important information that would be needed in the problem.  However, for this problem, it is pretty straight forward because we just need to solve for the unknown which is x.

Add 3 to both sides

Divide 8 from both sides

For the first equation, we were able to solve for x and get that the solution for the unknown is 1.25

Subtract 5 from both sides

Divide both sides by 7

For the second equation, we are able to solve for x and get that the solution for the unknown is 19/7

Subtract 6 from both sides

Divide both sides by 4

For the final equation, we are able to solve for x and get that the solution for the unknown is -0.25

Answer:

1) \(x=\frac{5}{4}=1\frac{1}{4}\)

2) \(x=\frac{19}{7}=2\frac{5}{7}\)

3) \(x=-\frac{1}{4}\)

Step-by-step explanation:

1) 8x - 3 = 7

1. Group all constants on the right side of the equation

\(8x-3=7\)

Add 3 to both sides:

\(8x-3+3=7+3\)

Simplify the arithmetic:

\(8x=7+3\)

Simplify the arithmetic:

\(8x=10\)

2. Isolate the x

\(8x=10\)

Divide both sides by 8:

\(\frac{8x}{8}=\frac{10}{8}\)

Simplify the fraction:

\(x=\frac{10}{8}\)

Find the greatest common factor of the numerator and denominator:

\(x=\frac{5\cdot 2}{4\cdot 2}\)

Factor out and cancel the greatest common factor:

\(x=\frac{5}{4}\)

2) 5 + 7x = 24

1. Group all constants on the right side of the equation.

\(5+7x=24\)

Subtract 5 from both sides:

\(5+7x-5=24-5\)

Group like terms:

\(7x+5-5=24-5\)

Simplify the arithmetic:

\(7x=24-5\)

Simplify the arithmetic:

\(7x=19\)

2. Isolate the x

\(7x=19\)

Divide both sides by 7:

\(\frac{7x}{7}=\frac{19}{7}\)

Simplify the fraction:

\(x=\frac{19}{7}\)

3)  5 = 6 + 4x

1. Swap sides

\(5=6+4x\)

Swap sides:

\(6+4x=5\)

2. Group all constants on the right side of the equation

\(6+4x=5\)

Subtract 6 from both sides:

\(6+4x-6=5-6\)

Group like terms:

\(4x+6-6=5-6\)

Simplify the arithmetic:

\(4x=5-6\)

Simplify the arithmetic:

\(4x=-1\)

3. Isolate the x

\(4x=-1\)

Divide both sides by 4:

\(\frac{4x}{4}=\frac{-1}{4}\)

Simplify the fraction:

\(x=\frac{-1}{4}\)

----------------------

Why learn this:

Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?

Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.

---------------------

Terms and topics

The most common use of linear equations is to solve problems involving an unknown variable, generally (but not always) x, and a known constant.

Solving linear equations requires isolating the unknown variable on one side of the equation and simplifying the remainder. Anything done to one side of the equation must also be done to the other when simplifying.

An equation of:

\(ax+b=0\)

A typical linear equation with one unknown is in which a and b are constants and x is the unknown variable. In this case, we would isolate x by removing b from both sides of the equation before solving for it. We'd then multiply both sides of the equation by a, yielding the following result:

\(x = -\frac{b}{a}\)

-------------------

Learn More About Linear Equations With One Unknown

The circumference of the Ferris wheel is equal to the distance it travels in one complete rotation. In this case, the Ferris wheel rotates three times, so the distance it travels is three times the circumference of the wheel.

We can set up an equation to solve for the diameter of the wheel using the given information.Circumference of the Ferris wheel = distance it travels in one complete rotation = 235.5 ft / 3 = 78.5 ftCircumference of the Ferris wheel = πd, where d is the diameter of the Ferris wheel.78.5 = πdDivide both sides by π to solve for d.d = 78.5 / π ≈ 25.01 ftTherefore, the diameter of the Ferris wheel is approximately 25.01 feet.Explanation:To find the diameter of the Ferris wheel, we need to start by using the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.

Since we know that the Ferris wheel travels 235.5 feet in three rotations, we can find the distance it travels in one complete rotation by dividing this distance by three. This gives us a distance of 78.5 feet per rotation .Next, we can set up an equation using the formula for the circumference of a circle:78.5 = πd Divide both sides by π to isolate d:d = 78.5 / πWe can use a calculator to find an approximate value for this expression :d ≈ 25.01Therefore, the diameter of the Ferris wheel is approximately 25.01 feet.

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Answer:

\(d =7\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point (3, 0)

Point (3, -7)

Step 2: Find distance d

Answer:

11250 cm^3

Step-by-step explanation:

45cm × 25cm × 10cm =11250cm

Answer:

(-2/5, 11/5)

Step-by-step explanation:

We can use the formula for finding a point that divides a line segment into a given ratio. Let P be the point on the line segment QR that partitions it in the ratio 2:3. Then we have:

P = ( (3x2 + 2x1)/(3+2), (3y2 + 2y1)/(3+2) )

where (x1, y1) = (-8, -8) is the coordinates of Q and (x2, y2) = (2, 7) is the coordinates of R.

Substituting the values, we get:

P = ( (32 + 2(-8))/(3+2), (37 + 2(-8))/(3+2) )

P = ( (-2/5), (11/5) )

Therefore, the coordinates of the point P on the directed line segment QR that partitions it in the ratio 2:3 are (-2/5, 11/5).

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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