A kayak rental company charges $25.00 to rent a kayak and $3.50 for each half hour it is used. Which linear function best represents the total cost of renting a kayak for 4 hours?

Answer:

89.44

Step-by-step explanation:

using the Pythagorean Theorem: \(a^{2} +b^{2}=c^{2}\)

\(80^{2} +b^{2} =120^{2} \\6400+b^{2} =14400\\b^{2} = 8000\\b = 40\sqrt{5}\)

120 is the hypotenuse so it would be c in the equation.

To solve, I simplified and isolated the variable. I got the square root of 8000 simplified (but idk how to write that out lol)

This answer is closest to 89.44

*Hope this helped! Have a great day/ night wherever you are! : )*

Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

Learn more about median of numbers in https://brainly.com/question/26177250

#SPJ11

Answer:false

Step-by-step explanation:

K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

To know more about triangle click-

brainly.com/question/17335144

#SPJ1

Answer:

1185

Step-by-step explanation:

A Parallel Line means the slope must be the same as the Given Line. A Perpendicular Line means the slope must be the negative reciprocal of the Given Line.

For Row A: Parallel is 12, Perpendicular is 6

For Row B: Parallel is 2, Perpendicular is 11

For Row C: Parallel is 9, Perpendicular is 16

For Row D: Parallel is 4, Perpendicular is 13

In Row E's case, 0 doesn't have a negative reciprocal, so you go with the equation that has a straight line down but no Y-Intercept.

For Row E: Parallel is 15, Perpendicular is 7

Row A = 72

Row B = 22

Row C = 144

Row D = 52

Row E = 105

Sum = 395

Code = 395 × 3 = 1185

Answer:

11.18

Step-by-step explanation:

Pythagorean Theorem:

a² + b² = c²

The hypotenuse is c.

10² + b² = 15²

Square 10 = 100

Square 15 = 225

100 + b² = 225

225 - 100 = 125

Find the Square Root of 125.

11.18033989 or 11.18

The grounded ends of the guy wires are 15 meters apart.

Using the Pythagorean theorem, we can calculate the length of the base (distance between the grounded ends of the guy wires).

Let's denote the length of the base as 'x.'

According to the problem, the height of the tower is 20 meters, and the length of each guy wire is 25 meters. Thus, we have a right triangle where the vertical leg is 20 meters and the hypotenuse is 25 meters.

Applying the Pythagorean theorem:

x² + 20² = 25²

x² + 400 = 625

x² = 225

x = √225

x = 15

Therefore, the grounded ends of the guy wires are 15 meters apart.

Learn more about Pythagorean theorem on

https://brainly.com/question/343682

#SPJ1

Answer:

21 yards

Step-by-step explanation:

4*21/4

84/4

21

Answer:

21yards multiplication

Step-by-step explanation:

Given parameters:

Number of curtains  = 4

Amount of fabric needed = \(5\frac{1}{4}\)yards

Unknown:

How much of fabric is needed  = ?

Solution:

   A curtain requires \(5\frac{1}{4}\)yards  = \(\frac{21}{4}\)yards

  Now to make 4 curtains, we would need  \(\frac{21}{4}\) x 4 = 21yards.

The perimeter of the card is 32 centimeters. Perimeter of a square is given by 4x, where x is the length of each side of the square.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

In this case, x=4.

Therefore, the perimeter of the card is 4x = 4(4) = 32.

The perimeter of a square is determined by multiplying the length of each side by 4. In this case, the length of each side of the square tank you card is x=4. Therefore, the perimeter of the card can be calculated by multiplying 4 with 4 which is equal to 32 centimeters. This means that the perimeter of the tank you card when x=4 is 32 centimeters.

Perimeter of a square is given by 4x, where x is the length of each side of the square.

Learn more about square here

https://brainly.com/question/29192128

#SPJ4

Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

\(H_0: p \leq 0.5\)

\(H_1: p > 0.5\)

The test statistic is given by:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

For this problem, the parameters are:

\(n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5\)

The value of the test statistic is:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.7708 - 0.5}{\sqrt{\frac{0.5(0.5)}{48}}}\)

\(z = 3.75\)

Considering a right-tailed test, as we are testing if the proportion is greater than a value, with a significance level of 0.05, the critical value for the z-distribution is \(z^{\ast} = 1.645\).

Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

To learn more about the z-distribution, you can take a look at https://brainly.com/question/16313918

Answer: 10

Step-by-step explanation: there are 8 sides and if u were to divide by 80 by 8, u would get 10

hope this helps! :)

Answer:

what are the choices

Step-by-step explanation:

Answer: is there suppose to be a pic?

This are functions that increases geometrically. The value of x for the expression is true is 1

This are functions that increases geometrically. Given the expression below:

\(625=5^{6-2x}\)

Write both sides to the base of 5

\(5^4 = 5^{6-2x}\)

Cancel the base to have:

4 = 6 - 2x

-2x = -2
x = 1

Hence the value of x for the expression is true is 1

Learn more on indices here:  https://brainly.com/question/10339517

#SPJ4

Answer:

a) 1

Step-by-step explanation:

edg 2022

Answer:

164.85 m

Step-by-step explanation:

You have a right triangle with 60 as the side opposite the 20° angle and you are looking for the adjacent side to that angle.

The trig function to use is the tangent of an angle = opp/adj

Let x = distance from you to the base of plateau

So,  tan 20 = 60/x

x tan 20 = 60

x = 60/tan 20

x = 164.85 m

You must memorize the definitions all of the trig functions so you can do a problem like this one. OK?

The distance covered by the rover is the perimeter of the trapezoid, and it is 40 meters.

See attachment for the path followed by the rover.

From the attached graph, we have the following lengths

\(AD = 9m\)

\(AB = 2m\)

\(DC = 14m\)

Next, we calculate the distance BC using the following Pythagoras theorem

\(BC^2 = AD^2 + x^2\)

Where:

\(x = 12\)

So, we have:

\(BC^2 = 9^2 + 12^2\)

\(BC^2 = 225\)

Take positive square root of both sides

\(BC = 15\)

The distance covered is the sum of the side lengths of the trapezoid.

So, we have:

\(Distance =AD + AB +DC + BC\)

This gives

\(Distance =9m+ 2m +14m + 15m\)

Add the lengths

\(Distance =40m\)

Hence, the distance covered by the rover is 40 meters

Read more about distance at:

https://brainly.com/question/13136492

Answer:

8cm³

Step-by-step explanation:

This is a problem finding volume through water displacement.

When you drop an object in water, its volume is the change in the height of the water.

In picture two the height of the water is at 25, and in picture one the height is at 17.

25-17=8

Step-by-step explanation:

pure acid is a 100% acid solution.

x = ml of 100% solution

1×x + 0.3×400 = 0.75×(400 + x)

x + 120 = 300 + 0.75x

0.25x = 180

x = 720 ml

we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).

When multiplying two powers, if their bases are the same, then you simply add the exponents:

   \(\frac{8^5*8^3*8^2}{8^8} =\frac{8^{5+3+2}}{8^8} =\frac{8^{10}}{8^8}\)

When dividing two powers, if their bases are the same, you simply minus the exponents.

  \(\frac{8^{10}}{8^8}=8^{10-8}=8^2\)

Thus when the expression is simplified, the answer as a power is \(8^2\)

Answer: 8^2

Hope that helps!

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

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

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

To learn more about annual interest rate click here: brainly.com/question/20631001

#SPJ11

The interval around the mean that contains 99.7% of the commute times is approximately 16.5 to 36.9 minutes.

In statistics, the normal probability distribution, also known as the bell curve, is commonly used to model random variables such as commute times. It is characterized by its mean (average) and standard deviation. In this case, John's commute time follows a normal distribution with a mean of 26.7 minutes and a standard deviation of 5.1 minutes.

To determine the interval that contains 99.7% of the commute times, we can use the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% falls within two standard deviations.

- Approximately 99.7% falls within three standard deviations.

Since we know that John's commute time is normally distributed with a mean of 26.7 minutes and a standard deviation of 5.1 minutes, we can calculate the interval as follows:

Lower bound: Mean - (\(3 * standard deviation\)) = 2\(6.7 - (3 * 5.1) = 26.7 - 15.3 = 11.4 minutes\)

Upper bound: Mean + (\(3 * standard deviation\)) = 2\(6.7 + (3 * 5.1) = 26.7 + 15.3 = 42 minutes\)

Therefore, the interval around the mean that contains 99.7% of John's commute times is approximately 11.4 to 42 minutes.

Learn more about probability distribution

brainly.com/question/29062095

#SPJ11

The idealized regression line is y = β₀ + β₁x + ε, and the least-squares regression line is Y = b₀ + b₁x. Four assumptions for regression inference are linearity, independence, homoscedasticity, and normality. The standard error of the regression slope is affected by the spread, sample size, and relationship strength. The formula for the standard error of the slope is SEb₁ = √[ Σ(\(y_i - Y_i\))² / (n-2) ] / √[ Σ(\(x_i\) - X)² ]. If there is no association between two variables, the slope of the regression line should be zero.

There are two equations commonly used in regression analysis: the idealized regression line and the least-squares regression line.

The equation for the idealized regression line is

y = β₀ + β₁x + ε

where

y is the dependent variable

x is the independent variable

β₀ is the intercept

β₁ is the slope

ε is the error term

The equation for the least-squares regression line is

Y = b₀ + b₁x

where

Y is the predicted value of y

x is the independent variable

b₀ is the intercept

b₁ is the slope

There are four assumptions and conditions that must be met in order to perform inference for regression

The relationship between the independent variable and dependent variables is called Linearity . To check linearity, plot the dependent variable against the independent variable and look for a straight-line pattern.

Independence, The observations are independent of each other. To check independence, ensure that there is no relationship between the residuals (the difference between the observed value and the predicted value) and any other variables.

The constant variance of errors across independent variable of all level is called homoscedasticity. To check homoscedasticity, plot the residuals against the predicted values and look for a consistent spread of points around zero.

Normality, The errors are normally distributed. To check normality, plot a histogram of the residuals and look for a roughly bell-shaped distribution.

The formula for the standard error for the slope is

SEb₁ = √[ Σ(\(y_i\)- \(Y_i\))² / (n-2) ] / √[ Σ(\(x_i\) - X)² ]

where

\(y_i\), observed value of variable which is dependent for the ith observation

\(Y_i\) is the predicted value of the dependent variable for the ith observation

\(x_i\), the observed value of variable which is independent for the ith observation

X is the mean of the independent variable

n is the sample size

The formula for the sampling distribution for regression slopes is

b₁ ~ N(β₁, σ² / Σ(\(x_i\) - X)²)

where

b₁, least-squares regression line's slope

β₁ is the true population slope

σ² is the variance of the errors

If there is no association between two variables, the slope of the regression line should be zero. it depicts that the variable which is independent has no effect on the variable which is dependent.

To know more about regression line:

https://brainly.com/question/7656407

#SPJ4

Answer:

5/6

Step-by-step explanation:

2 1/3=2 2/6

1 1/2= 1 3/6

2 2/6- 1 3/6=5/6

Answer:

The answer is -19/6

Step-by-step explanation:

Hope that helps!

The expression (68 = 7v) . v can be simplified as follows:

(68 = 7v) . v = 68v = 7v^2

The expression ‖v‖= 2 represents the magnitude or length of vector v, which is equal to 2. Similarly, ‖u‖= 7 represents the magnitude or length of vector u, which is equal to 7. Given that u . v = 3, we need to simplify the expression (68 = 7v) . v.

To simplify the expression (68 = 7v) . v, we use the distributive property of dot product. According to the properties of the dot product, we can distribute the scalar value (68 = 7v) to both components of vector v.

Multiplying the scalar value 68 with vector v gives us 68v. Furthermore, since v . v represents the dot product of vector v with itself, it can be written as v^2.

Therefore, the simplified expression is 68v = 7v^2, which represents the result of distributing the scalar value and simplifying the dot product expression.

To learn more about expression refer here:

https://brainly.com/question/28170201#

#SPJ11

Answer:

a) The Margin of Error = 0.26

b) The 99% Confidence Interval = ( 2.84, 3.36)

Step-by-step explanation:

a) Margin of Error

The formula for Margin of Error =

z × Standard deviation/√n

From the above question

The z score for 99% confidence interval = 2.576

Standard deviation = 0.72

n = Random number of samples = 50

Margin of Error =

2.576 × 0.72/√50

= 1.85472 /√(50)

= 0.2622970178

Approximately to 2 decimal places = 0.26

b) 99% Confidence Interval

= Mean ± Margin of Error

Mean = 3.1mm

Confidence Interval = 3.1 ± 0.26

3.1 ± 0.26

= 2.84

3.1 + 0.26

= 3.36

The 99% Confidence Interval = ( 2.84, 3.36)

Answer: B

Step-by-step explanation:

y= x/5 + 3 if that helps

To find the margin of error we have to use the formula,

Margin of error =  Z * ơ / √n ,

Where

z = critical factor

ơ = population standard deviation

n = sample size

Now we have to find confidence interval

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-ME

Where margin of error ME = zr/√n

Given that;

Mean = ц

Standard deviation r = 25

Number of samples n = 41

Confidence interval = 95%

z(at 95% confidence) = 1.96

Xbar = 60.............(1)

Xbar + E = 66.........(2)

from equating both the equations we get

E= 6

and for finding the value of margin of error we know that its the half of the E

Margin of error = E/2

=6/2

=3

Therefore , the Margin of error is 3

To know more about the margin of error

https://brainly.com/question/16835723

#SPJ4

The equation that relates x and y is xy = 12. The solution has been obtained by using proportions.

What is proportion?

Two numbers are compared. It is known as a proportion in mathematics. The law of proportion states that if two sets of given numbers rise or decrease in the same ratio, they are considered to be directly proportionate to one another. Else, they are inversely proportion.

We are given that y varies inversely as x.

This implies that

⇒y ∝ 1/x

⇒xy = k

We are given when x = 5, y is 2.4. So, we get

⇒5 * 2.4 = k

⇒k = 12

Thus, we get xy = 12.

Hence, the equation that relates x and y is xy = 12.

Learn more about proportion from the given link

https://brainly.com/question/870035

#SPJ1

Your answer is the center image.

hope this helps.