calculate r-squared,--the coefficient of determination--given that the linear correlation coefficient, r, is 0.817. what does this tell you about the explained variation and the unexplained variation of the data about the regression line?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Mathematically, it can be expressed as c² = a² + b² where c is the length of the hypotenuse and a and b are the lengths of the other two sides. The theorem can be proven using Euclidean geometry.

In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In short it is written as: a² + b² = c²

For example, if the sides are 6cm and 8cm, the hypothenuse will be:

c² = 6² + 8²

c² = 100

c = ✓100

c = 10cm

Learn more about Pythagoras on:

https://brainly.com/question/343682

#SPJ1

Answer:

f(5)=21

Step-by-step explanation:

f(1) =5

f(2) =9

f(3)= 13

f(4)=17

there for f(5) =21 all added by four more

The probability of getting at least one question wrong on a 6 question multiple-choice test is 0.9874

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(get one question right) = 1/2

P (get all questions right) = (1/2)^6

P(get one question wrong) = 1 - P (get all questions right)

P(get one question wrong) = 1 - (1/2)^6

P(get one question wrong) = 0.9874

Learn more about probability at: brainly.com/question/251701

#SPJ4

Answer:

w = 19

Step-by-step explanation:

w = 4 + 3p

w = 4 + (3 x 5) since p = 5

w = 4 + (15)

w = 19

Answer:

w = 19

If the equation is w = 4 + 3p, we can substitute the 'p' for five.

To solve for w, we need to first solve 3 times 5.

Now, just solve.

Therefore if p = 5, w = 19.

The instantaneous voltage across the capacitor is 4/53 * (-cos (106 t - 25)) (volts).

The instantaneous voltage across a capacitor is given by v(t) = 1/C * integral(i(t)dt) where C is the capacitance of the capacitor.

For the current i(t) = 4 sin (106 t - 25), the voltage across the capacitor can be found using the following definite integral:

v(t) = 1/C * integral(4 sin (106 t - 25)dt) from 0 to t

v(t) = 4/106C * (-cos (106 t - 25)) from 0 to t

So, the instantaneous voltage across a 2-F capacitor for this current will be:

v(t) = 4/53 * (-cos (106 t - 25)) (volts)

To learn more about voltage here:

https://brainly.com/question/20815020

#SPJ4

Answer: D

Step-by-step explanation: y (Waffle cones) = 13 (Waffle cones sold during first hour) + x (Waffle cones sold during remaining hours.)

Zegen saves $1000 every month for their new house.

By definition, saving is income minus spending. Investment refers to physical investment, not financial investment. That saving equals investment follows from the national income equals national product identity.

Given here: Zegen's income is $6000 and the fixed expenses are $3000 with flexible expenses $2000

Thus we savings = Income-expenditure

Savings = 6000-5000

            =1000

Again it is given that the savings are put aside for the downpayment of a house

Hence, Zegen saves $1000 every month for their new house.

Learn more about incomes and savings here:

https://brainly.com/question/15709251

#SPJ1

Answer:

c = 3n + 5

Step-by-step explanation:

The equation c = 3n + 5 fits the data in the table. When n = -7, c = -7 * 3 + 5 = -16. When n = -6, c = -6 * 3 + 5 = -13. When n = 3, c = 3 * 3 + 5 = 14. When n = 5, c = 5 * 3 + 5 = 20. And when n = 9, c = 9 * 3 + 5 = 32. All the values of c in the table match the values predicted by the equation c = 3n + 5. Therefore, c = 3n + 5 is the correct equation for the data.

Answer:

-25

Step-by-step explanation:

= (20-25)(16+4)/-8+(3×4)

= (-5×20)/(-8+12)

= -100/4

= -25

Answer:

768

Step-by-step explanation:

2 gallons is 32 cups. Times 32 by the servings which is 24. 32 times 24 equals 768

Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

Mathematical operations including addition, subtraction, multiplication, and division are required. They result in the following when combined: An equation, some information, and an arithmetic operator Values, parameters, and operations like adds, omissions, multiplications, and divisions make up a statement of fact. Different phrases and words can be contrasted and compared.

Here,

Given :

=> 2x² / x² -1

=> 2x² / x² -1  *  x² -1 /x² -1

=> 2x²(x²-1) / (x² -1)²

=> 2x⁴ - 2x² / (x⁴ + 1 - 2x²)

=>  2x² (2x² - 1 ) / (x⁴ + 1 - 2x²)

Therefore , the solution of the given problem of expression comes out to be 2x² (2x² - 1 ) / (x⁴ + 1 - 2x²) .

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The expression that irrational are:

B. 2–√. 3–√

C. 27−−√. 3–√

D. 57–√2−57–√

The square root of a non-perfect square is an irrational number, meaning that it cannot be expressed as a finite decimal or as a fraction of two integers.

In options B and C, the square root of 3 and the square root of 27 respectively are both irrational because 3 and 27 are not perfect squares.

In option D, both 57-√2 and 57-√ are irrational numbers because 57 is not a perfect square and the square roots of 2 and 3 are irrational.

Option A and E can be simplified to finite decimal or fraction, therefore they are rational numbers.

A fraction is not always expressed as a decimal. A fraction is a way of representing a number as a ratio of two integers, for example, 1/2 or 3/4. While a decimal is a way of expressing a number as a sum of powers of 10, for example, 0.5 or 0.75. A fraction can be converted to a decimal and vice versa, but they are not the same thing.

Learn more about Rational Vs Irrational Expressions here:

https://brainly.com/question/15837135

#SPJ4

The correct answer of this expression is (b) g>-6.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

a formula expression with the first part signifying a mathematical item and the second part signifying a statement about mathematical objects

given that;

-3 (g + 5) > 3

divide both side by -3, we get

⇒ g + 5 > 3/-3

⇒ g + 5 > -1

subtract both side by 5

⇒ g > -1 -5

⇒ g > -6

so the correct answer is g > -6

To learn more about expression visit:

brainly.com/question/30350742

#SPJ1

Answer: The actual selling price should be around $3472 and 22 cents.

Answer:

Step-by-step explanation:

elish as you know me lacey i will be glad to help you the correct awnser is 3472 dollars and 22 cents

Answer:

3 hours

Step-by-step explanation:

Given,
Distance = 180 miles
Speed = 60 miles per hour
Distance/Speed = Time
Thus, Time taken is 180/60
Which is 3 hours

The Walmart is 2.8 miles away from her home. The result is obtained by using the speed formula in constant motion.

Speed is the change in position per unit of time. It can be expressed as

v = d/t

Where

A student walked to Walmart, bought a bike, and rode it home.

Determine the distance between the Walmart and her home!

Let's say

The distance traveled when student walked and the riding a bike is the same. It is the distance between the Walmart and her home.

d₁ = d₂ = d

So, we get t.

d₁ = d₂

v₁t₁ = v₂t₂

3.5t = 14(1 - t)

3.5t = 14 - 14t

3.4t + 14t = 14

17.5t = 14

t = 17.5/14

t = 0.8 hour

Substitute t in the walking speed formula!

d₁ = v₁t₁

d₁ = 3.5(0.8)

d₁ = 2.8 miles

d = d₁ = 2.8 miles

Hence, the distance between the Walmart and her home is 2.8 miles.

Learn more about speed here:

brainly.com/question/30432499

#SPJ4

The area of rhombus KLMN is 287.3 in²

A rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

Given that, a rhombus KLMN with diagonals KM and NL,

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O, so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Therefore, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

= 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

Learn more about rhombus, click;

https://brainly.com/question/27870968

#SPJ1

As per the standard deviation the proportion of observations is in the interval between each pair of values is 190 and 310

The term in math known as standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the mean of a population is 250 and its standard deviation is 20.

Then the proportion of observations is in the interval between each pair of values is calculated as,

We have interval (190,310) and we can express this interval as:

=> (190,310) = (250−3⋅20, 250+3⋅20)

According to this interval , we have that k=3.

Based on the value of the constant the required percent of observations in interval(190,310) is at least 88.9%

To know more about standard deviation here.

https://brainly.com/question/16555520

#SPJ4

Using distributive property, each expressions are write in an appropriate form. The expression are shown below.

This characteristic states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend separately by the number and then combining the results collectively.

According to the property, the outcomes are the same whether the numbers in parenthesis are added before or after multiplication. In situations when the polynomial cannot be combined together before being multiplied, the distributive property is very helpful. Using this property the following expression are solved.

4(6 + 7) = 4.6 + 4.7

14.1 - (14 - 9) = 14 (1 - 9)

5 (z - 10) = 5.z - 5.10

8.6 + 8.2 = 8 (6 + 2)

To know more about distributive property refer to:

https://brainly.com/question/2807928

#SPJ1

If in the survey of a survey of a community, 55%. The percentage of the people who don't like to listen to the radio as well as watch the television​ is 15%.

The number of people who like to listen to the radio as well as watch the television = 35%.

So,

The number of people who like to listen to the radio but don't like to watch the television

=  55% - 35%

= 20%

The number of people who like to watch television but don't like to listen to the radio =  65% - 35% = 30%.

The percentage of people who don't like to listen to the radio as well as watch the television

= 100% - (35% + 20% + 30%)

= 100% - 85%

= 15%

Therefore  15% of the people in the community don't like to listen to the radio or watch the television.

Learn more about percentage here:https://brainly.com/question/24877689

#SPJ1

Answer:

see below

Step-by-step explanation:

road 1 100km/h x hrs

road 2 80km/hr y hrs

total 6hours

total 530 km

100x+80y=530

x+y=6

x=6-y

100(6-y) + 80y =530

600-100y+80y =530

20y=70

y=3.5

x =6-3.5 =2.5

Answer: x =2.5 y= 3.5

Step-by-step explanation:

Answer:

Depreciation is the decrease in value of an asset over time. We know that the value of the equipment depreciates at a rate of 20% per year, and after 5 years the equipment is worth $98,304. We can use this information to set up an equation to find the original value of the equipment.

Let X be the original value of the equipment.

We know that:

X * (1 - 0.20)^5 = 98304

Where (1 - 0.20) is the depreciation rate, and the exponent 5 is the number of years.

We can solve for X by using the following steps:

X * (1 - 0.20)^5 = 98304

X * (0.8)^5 = 98304

X = 98304 / (0.8)^5

X = $143,680

So, the original value of the equipment was $143,680.

Step-by-step explanation:

Answer:

There are 31 quarters.  

There are 47 dimes.  

Step-by-step explanation:

let q = number of quarters

let d = number of dimes

d = 16 + q      

.10d + .25q = 12.45  Multiply through by 100

10d + 25q = 1245       Substitute 16 + q for d

10(16 + q) + 25q = 1245    Distribute the 10

160 + 10q + 25q = 1245  Combine like terms

160 + 35q = 1245  Subtract 160 from both sides

160 - 160 + 35q = 1245 - 160

35q = 1085  Divide both sides by 35

q = 31

There are 31 quarters.    

Substitute 31 for q

d = 16 + 31

d = 47

There are 47 dimes.

Check:

d = 16 + q

47 = 16 + 31

47 = 47  Checks

.10d + .25q = 12.45

.10(47) + .25(31) = 12.45

4.70 + 7.75 = 12.45

12.45 = 12.45  Checks.

Answer:

There are 31 quarters and 47 dimes.

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Values of the coins:

Given a coin bank contains $12.45 in quarters and dimes:

Given there are 16 more dimes than quarters:

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases} 0.25q + 0.10d = 12.45\\d = q + 16\end{aligned}[/tex]

Substitute the second equation into the first equation to eliminate d:

[tex]0.25q+0.10(q+16)=12.45[/tex]

Solve the equation for q to find the number of quarters:

[tex]\begin{aligned}0.25q+0.10(q+16)&=12.45\\0.25q+0.10q+1.6&=12.45\\0.35q+1.6&=12.45\\0.35q&=10.85\\q&=31\end{aligned}[/tex]

Therefore, there are 31 quarters.

Substitute the found value of q into the second equation and solve for d:

[tex]\begin{aligned}d &= q + 16\\&= 31 + 16\\&= 47\end{aligned}[/tex]

Therefore, there are 47 dimes.

The combined perimeter and area of all three rectangular corrals can be represented algebraically as follows:

Total perimeter = 3 * (12x - 4) = 36x - 12

Total area = 3 * (5x^2 - 2x) = 15x^2 - 6x

Let x be the width of each rectangular corral.

L = 5x - 2

          P = 2(L + x)

             = 2(5x - 2 + x)

             = 2(6x - 2)

             = 12x - 4

         A = L * x

             = (5x - 2) * x

             = 5x^2 - 2x

So, the total perimeter and area of the three corrals can be represented algebraically as a function of x, the width of each corral.

Complete Question:

"A rancher has three rectangular corrals. They have the same dimensions. The length is five times the width minus two. How can the combined perimeter and area be represented algebraically? Let x be the variable."

To know more about perimeter and area, click on the link below:

brainly.com/question/11957651

#SPJ4

The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

To know more on pints quarts conversion

https://brainly.com/question/17732315

#SPJ4

Logistic regression is a statistical method used for modeling the relationship between a dependent variable and one or more independent variables. Unlike multiple regression, which is used for continuous outcome variables, logistic regression is used for categorical outcome variables, such as yes/no or pass/fail. The key differences between logistic regression and multiple regression are as follows:

a) Logistic regression does not have "b" weights - Logistic regression models the relationship between the independent variables and the dependent variable by using the logit transformation. The logit transformation maps the continuous range of values of the dependent variable to a binary range of values, allowing the estimation of the probability of a specific event. Unlike multiple regression, which uses beta (b) coefficients to quantify the strength and direction of the relationship between the independent variables and the dependent variable, logistic regression models the relationship through the use of odds ratios.

b) Logistic regression is not immune to sources of bias - Like any statistical method, logistic regression is susceptible to sources of bias, such as omitted variable bias and measurement error. It is important to be aware of these potential sources of bias and to address them through appropriate data cleaning and variable selection procedures.

c) Logistic regression predicts a categorical outcome variable - As mentioned, logistic regression is specifically designed for categorical outcome variables, such as yes/no or pass/fail. The model predicts the probability of the dependent variable taking a specific value and uses a threshold value to convert the predicted probabilities into binary outcomes.

d) Logistic regression does not log-transform the predictor variables - Unlike some statistical methods, such as log-linear regression, logistic regression does not log-transform the predictor variables. This is because the logit transformation is already applied to the dependent variable in order to model its relationship with the independent variables.

In conclusion, logistic regression is a powerful tool for modeling the relationship between a dependent categorical variable and one or more independent variables. It is important to understand its key differences from multiple regression and to be aware of potential sources of bias in order to use this method effectively.

Here you can learn more about Logistic regression

https://brainly.com/question/27785169#

#SPJ11

The percentage decrease is 19.4%

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

(Original Cost - New Cost) / Original Cost x 100 equals the percentage decrease.

In this case, the original cost is $36 and the new cost is $29, so we plug these values into the formula:

Percentage decrease = ($36 - $29) / $36 x 100 = $7 / $36 x 100 = 0.1944 x 100 = 19.44%

We can round the answer to the nearest tenth of a percent:

19.44% rounded to the nearest tenth is 19.4%

So the percentage decrease is 19.4%

Learn more about percentage

brainly.com/question/24877689

#SPJ1

The kinetic energy of the object is 4 * π^2 * m * r^2 * n^2, which is option D.

The kinetic energy of an object with mass m and velocity v can be calculated as 1/2 * m * v^2.

In this case, the velocity of the object can be calculated as the circumference of the circle (2 * π * r) multiplied by the number of revolutions per second (n), so v = 2 * π * r * n.

Substituting this expression for v into the equation for kinetic energy, we get:

1/2 * m * (2 * π * r * n)^2 = 1/2 * m * (4 * π^2 * r^2 * n^2) = 4 * π^2 * m * r^2 * n^2.

To learn more about kinetic energy, visit:

https://brainly.com/question/26472013#

#SPJ11

The tire will need to rotate 38.2 times to travel the whole length of the street.

We will first compute the tire's circumference in order to determine how many times it will need to revolve while traveling the distance of the roadway.

The formula for determining a circle's circumference may be used to get the tire's circumference because it is circular.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 3.5ft and π = 3.14

∴ C = 3.14 × 3.5

C = 10.99ft

Therefore, the circumference of the tire is 10.99ft

The tire will need to turn 38.2 times to travel the whole length of the street. We will now divide the street's length by the tire's circumference to determine how many times it tire will need to turn to go its whole length.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 420 ft ÷ 10.99 ft

Number of times the tire will have to turn = 38.2165 times

Number of times the tire will have to turn ≅ 38.2 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 38.2 times

To know more about Circumference visit:

https://brainly.com/question/28757341

#SPJ1