Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?

a. Explain what 120 represents, and how it relates to the cows and chickens.

b. Explain what 48 represents, and how it relates to the cows and chickens.

c. Setup a system, of two equations, to help you solve this riddle.

d. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.​

Answer:

(a-1)^2-9

Step-by-step explanation:

First you divide the coefficient of a by 2, which is 1. Now, do this: [tex](a-1)^2-8[/tex] where the -1 is half the coefficient of a. What this does is get the first two terms: a^2 and 2a, but we have an extra + 1(expanding this out gives [tex]a^2 -2a + 1[/tex]. So we have to subtract 1 to cancel it out. This gives [tex](a-1)^2-9[/tex], because -8-1=9. We can check this by expanding it out, and seeing if it equals our previous equation. Expanding this out gives [tex]a^2-2a+1-9[/tex], which is equal to our originial equation.

1. The average gas price for 2010 is of: $2.22.

2. The linear regression equation is given as follows: y = 0.176x + 0.5.

3. The domain is: [0,∞).

4. The range is: [0.5,∞).

5. Gas is expected to cost $4.55 in 2025.

The linear regression is obtained inserting the points of the table into a linear regression calculator.

The variables of the problem are given as follows:

Hence the points are given as follows:

(0, 0.7), (1,1.04), (2, 1.15), (3, 1.38), (4, 1.86), (5, 1.70), (6, 2.55), (7, 1.29), (8, 2.22), (9, 2.56).

Inserting these points into a calculator, the equation is given as follows:

y = 0.176x + 0.5.

The estimate for 2025 is the numeric value when x = 23, as 2025 is 23 years after 2002, hence:

y = 0.176(23) + 0.5 = $4.55.

The domain and the range are given as follows:

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Answer: Nonlinear.

Step-by-step explanation:

On solving the provided question, significant difference between the four testing conditions is α = 0.10

An alternative hypothesis is one in which the researchers predict a difference (or an effect) between two or more variables, indicating that the observed pattern of the data is not the result of chance.

Null hypothesis:  : μ1 ≥ μ2, There is no significant difference in history test scores between students with different academic major

Alternative Hypothesis: Ha : μ1 < μ2. Exam outcomes in history are substantially more varied among students with different academic specialties.

Determine the significance level. α = 0.10

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The correct statement regarding the scatter plot is given as follows:

The data shows a negative linear association between the number of magazines checked out and the number of books checked out.

The scatter plot, as shown by the image given at the end of the answer, is a series of points of the data-set in the following format:

(Number of books checked out, Number of magazines checked out).

From the graph, the points are given as follows:

(2,4), (3,6), (4,0), (4,2), (5,7), (6,5), (7,2), (9,1).

Inserting these points into a linear regression calculator, the line of best fit is given as follows:

y = -0.36x + 5.18

Which has a negative slope, meaning that it is a negative linear relationship and the first option is correct.

The scatter plot is given by the image shown at the end of the answer.

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The amount of money borrowed by the man from the bank on on 2 May 2000 is  $6346.15.

The formula for calculating simple interest;

SI = P R T/100,

where

In the case of simple interest, the principal is the amount of money that does not change over the course of a year.

Time = 4/12 year

For the given values-

137.50 = P × 6.5 × 4 /1200

P = 137.50 × 1200 / 6.5 × 4

P = $6346.15

Thus, the amount of money borrowed by the man from the bank on on 2 May 2000 is  $6346.15.

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Answer:4

Step-by-step explanation:

distribute 1/2 into x-8 and distribute 2 into 1/8x-1 on other side

1/2x-4+1=1/4x-2

combine like terms

1/4x=1

multiply both sides by 4 to solve x

x=4

By using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

The Pythagorean theorem, also known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

So, draw a figure of the 2 buildings as follows:

(Refer to the  image attached below)

Now, we know that we can get the distance between the rooftops using the Pythagorean theorem.

Pythagorean theorem: c² = a² + b²

Now, insert the values and calculate as follows:

c² = a² + b²

c² = 12² + 16²

c² = 144 + 256

c² = 400

c = √400

c = 20ft

Therefore, by using the Pythagorean theorem, we know that the distance between the rooftops of the two buildings is 20ft.

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The dimensions of the garden would be length = 28 meters and width = 9.5 meters

A database of research funds called Dimensions connects funding to articles, clinical trials, and patents as well as other outcomes. Dimensions is a division of the technology firm Digital Science, which has its global headquarters in London, United Kingdom.

Let the width be = w

Let the length be = L

enclose three side ( 2w+L) = 47 meter

L = 47-2w

Area of field = w*L

Area = w(47 - 2w)

266  = 47w - 2w²

2w² - 47w + 266 = 0

Solving this, we get

w = 14 or w = 9.5

The width should be less than the length so w = 9.5

Length = 47 - 2(9.5)

           = 47 - 19

           = 28 meters.

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Option B. Because when you have quantitative data, but assumptions of normality are not met. This is because, unlike parametric tests, non-parametric tests do not make assumptions about the data's underlying distribution.

Non-parametric tests are often used when dealing with data that is not normally distributed, as they allow for a more accurate analysis of such data. They can also be used when a linearity of the data cannot be assumed and when dealing with ordinal data. Non-parametric tests are more powerful than parametric tests, which makes them a good choice when a more precise analysis is needed.

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Answer:  34.00 and 2.10

Step-by-step explanation:

The polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3 thanks to the factor theorem.

A factor theorem is a tool used in mathematics to thoroughly factor polynomials.

It is a theorem that connects the polynomial's zeros and factors.

The factor theorem states that (x-a) is a factor of f(x) if f(a)=0 and f(x) is a polynomial of degree n 1 and 'a' is any real number.

So, the Factor Theorem states that P(k) must equal zero if (x - k) is a factor of polynomial P(x).

A polynomial function with the zeros 2, 3, and -3 is provided to us. As a result, we can set k = 2, 3, -3.

The Factor Theorem states that P(2), P(3,) and P(-3) must all equal 0.

Tests of each option reveal that only option A is accurate:

f(x) = x³ – 2x² – 3x + 6

Testing each of the three results in:

[tex]\begin{aligned}f(2) & =(2)^3-2(2)^2-3(2)+6 \\& =(8)-(8)-(6)+(6) \\& =0 \stackrel{\checkmark}{=} 0 \\f(\sqrt{3}) & =(\sqrt{3})^3-2(\sqrt{3})^2-3(\sqrt{3})+6 \\& =(3 \sqrt{3})-(6)-(3 \sqrt{3})+6 \\& =0=0 \\f(-\sqrt{3}) & =(-\sqrt{3})^3-2(-\sqrt{3})^2-3(-\sqrt{3})+6 \\& =(-3 \sqrt{3})-(6)+(3 \sqrt{3})+6 \\& =0=0\end{aligned}[/tex]

Therefore, with the help of the factor theorem, polynomial (A) f(x)=x³-2x²-3x+6 has the zeros 2, radical 3, and negative radical 3.

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Complete question:

Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3, and negative radical 3?

a. f(x) = x3 – 2x2 – 3x + 6

b. f(x)= x3 – 2x2 + 3x + 6

c. f(x) = x3 + 2x2 – 3x + 6

d. f(x) = x3 + 2x2 – 3x – 6

The claim to be indicated is that there is enough evidence to reject the null hypothesis and the test statistic would be 21.75

A type of statistical inference called hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution. The parameter or distribution is initially assumed in a preliminary manner. The null hypothesis is also known as H0, because it is the default assumption. Then, the opposite of what the null hypothesis claims is characterized as an alternative hypothesis (designated Ha). Using sample data, the hypothesis-testing technique determines whether or not H0 may be rejected. If H0 is rejected, the statistical inference is that the alternative hypothesis Ha is correct.

How to solve?

If the die is fair, the probability of getting any of the six numbers is equal (1/6).

The test statistic (TS) is given as:

TS=∑(Oi−Ei)2Ei∼χ2n−1

TS=(4−8)^2/8+(13−8)^2/8+…(2−8)^2/8

TS=21.75

In conclusion, the die is unfair.

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Answer:

1/c2

Step-by-step explanation:

Answer: 27.3 %

Step-by-step explanation:

There are 8 blue and 3 red marbles in the bad so total is 11 marbles

We just need to take 3 divided by 11, then timed 100 and will get the percent of 27.27, or I round up to 27.3%

Answer:

x=-12

Step-by-step explanation:

it would be -2=-x-14 then solve as normal algebraic equation

add 14 to each side 12=-x

then divide by -1 on each side so you get x=-12 for the final answer hope this helps

From the given properties of the functions,

Functions given in the picture are 'f', 'g' and 'h'.

From the graph given for function 'f',

y - intercept = 1

Increasing in the interval → (-∞, -0.8] and (0.6, ∞)

Decreasing in the interval → [-0.8, 0.6]

From the table given for the function 'g',

Decreasing in the interval → [-2, 2]

y-intercept = -1

For function 'h',

h(x) = 4x³ + 3

Table of the input-output values for function will be,

x           h(x)

-2         -29

-1            -1

0            3

1             7

2           35

Therefore, function 'h' will increase in the interval → (-∞, ∞)

y-intercept → y = 3

Therefore, from these properties of the functions we conclude,

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Th number of possible ways for

a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)

b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)

In this question, we have been given that there are four players. the select cards from the standard deck of 52 cards.

We need to find the number of possible ways for given situations.

(a) each player gets exactly 13 cards.

Using combination, we get an expression,

^{52}C_13 * ^{39}C_13 * ^{26}C_13 * ^{13}C_13

= 52! / (13! 13! 13! 13!)

= 53644737765488792839237440000

(b) each player gets seven cards and the rest of the cards remain in the deck

Using combination, we get an expression,

^{52}C_7 * ^{45}C_7 * ^{38}C_7 * ^{31}C_7 * ^{24}C_24

= 52! / (7! 7! 7! 7! 24!)

Therefore, a) each player gets exactly 13 cards = 52! / (13! 13! 13! 13!)

b) each player gets seven cards and the rest of the cards remain in the deck = 52! / (7! 7! 7! 7! 24!)

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This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.

1. When salt is dissolved in water, the chemical bond between the salt atoms is broken by the water molecule.

2. When a teaspoon of salt is added to water, the salt molecules fill any open places in the water. Since water is a fluid with atoms that may move around freely, when salt is dissolved in it, these open spaces are filled, making salt particles invisible.

3. The resulting solution becomes denser. The mass of the solution increases when salt is added to water. As a result, the solution's density rises.

4. This procedure demonstrates that there is room between matter particles. The existence of salt ions is indicated by their accommodation in water.

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For the octagon whose measure of angle is (9w + 8)°, the value of w is 14.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

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Answer:

he octagon whose measure of angle is (9w + 8)°, the value of w is 14.

Step-by-step explanation:

What is angle?

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

Angle of regular octagon = 9w + 8

Since, angle of an octagon is 135°

Equate 9w + 8 to 135,

9w + 8 = 135

9w = 127

w = 14.11

w = 14

The required value of w is 14.

i hope this helps !!!!!

The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

What is the unit price?

The average price of a product is calculated by dividing the total sales revenue by the total units sold. Managers must define "comparable" units when a single product is sold in variants, such as bottle sizes.

To find the unit price of an object, You divide the price by the Object. We need to find how much an object cost per unit.

Let, us consider an Example we have 50lbs of Kulfi (Object) that cost 8.00 dollars(price).

To find the Unit cost, We take the 8.00 and divide it by 50, which results in 0.16 cents per pound. We can check this by multiplying 0.16 by 50=8.00

So, Object= Number of units in cell = C2

Price of Object = B2

Unit Price Formula = D2

Therefore, by considering the above example.,

Object = C2 = 50

Price = B2 = 8.00

D2 Formula= Price of Object/ Number of Units

Therefore, The formula for D2 to be placed in order to find the unit price is D2 = B2/C2.

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Answer: x≥3

Step-by-step explanation:

The correct statement regarding the rate of change of the functions is given as follows:

The amount of wood required has a constant rate of change, but the amount of glass does not.

The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.

For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.

For the glass function, we have that:

Hence the rate of change is not constant, and then the second statement is the correct statement.

The table is given by the image shown at the end of the answer.

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The required regression equation is y = -2.78x + 48.5 for the line of best fit where x represents the month and y represents the time.

The table is given in the question.

As per the given table, the required solution would be as:

Let x represents the month and y represents the time

[tex]\bar{x}[/tex] = (1+2+3+4+5+6)/6 = 21/6 = 3.5

[tex]\bar{y}[/tex] = (47+43+39+36+35+33)/6 = 233/6 = 38.83

Sum of x = 21

Sum of y = 233

Mean x = 3.5

Mean y = 38.8333

Sum of squares (SSX) = 17.5

Sum of products (SP) = -48.5

Regression Equation = y = bx + a

b = SP/SSX = -48.5/17.5 = -2.77143

a = MY - bMX = 38.83 - (-2.77×3.5) = 48.53333

y = -2.78x + 48.5

Thus, the required regression equation is y = -2.78x + 48.5 for the line of best fit.

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Answer:

y = -2.78x + 48.5

Step-by-step explanation:

I just took the test like 2 seconds ago...

(i) The percentage of dogs of this breed that weigh less than 53 pounds P(X<53) = 50.0%

(ii) The percentage of dogs of this breed that weigh less than 46 pounds P(X<46) = 15.2%

(iii) The percentage of dogs of this breed that weigh more than 46 pounds P(X>46) = 84.8%

What is Standard Deviation?

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values of the set tend to be near to the mean (also known as the expected value), whereas a high standard deviation shows that the values are spread out over a larger range.

Solution:

Mean weight (μ) = 53 pounds

Standard deviation (σ) = 6.2 pounds

The z-score for any given weight, 'X', is given by the following expression;

z = (X - μ)/σ

(i) P(X<53)

Since 53 pounds is exactly the mean weight, 50% of the dogs weight more than 53 pounds while 50% weight less than 53 pounds.

P(X<53) = 50.0%

(ii) P(X<46)

z = (46-53)/6.2

z = -1.12

this is equivalent to 15.2 percentile

P(X<46) = 15.2%

(iii) P(X>46)

P(X>46) = 100% - P(X<46) = 100% - 15.2%

P(X>46) = 84.8%

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The 90% confidence interval for the population mean estimate is  (1362.9167,1637.0833).

Given that,

n=36 residents

Standard deviation = 500 dollars

Mean u = 1500 dollars

X = 1500 dollars

(1-α)% = 90%

(1-α)= 0.9

α = 0.10

α/2 = 0.05

Z α/2 = Z 0.05

Z α/2 = 1.645

90%-confidence interval for the population mean estimate is

=X ± Z α/2 (σ/√n)

= 1500 ± (1.645)(500/√36)

=(1362.9167,1637.0833)

Therefore, the 90%-confidence interval for the population mean estimate is  (1362.9167,1637.0833).

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Answer:

48 movies

Step-by-step explanation:

8/16=1/2

24/48=1/2

The derivative dy/dt when the x coordinate's rate of change 18 feet is 13.5 feet.

Given,

The radius of the circular track in which the jogger runs = 70 feet

The coordinates of the jogger = (42, 56)

The rate of change in x coordinate = 18 feet/sec

Let (x,y) be the coordinates

We have to find dy/dt;

Then we know x,y satisfies the equation of the circle as

x² + y² = 70²

Let us differentiate this implicit function with respect to t

2x dx/dt + 2y dy/dt = 0

At this point, dx/dt 18 and x = 42. y = 56

Substitute to have

2 × 42 × 18 + 2 × 56 dy/dt = 0

1512 + 112 dy/dt = 0

dy/dt = 1512/112

dy/dt = 13.5 feet

Therefore,

The derivative dy/dt here is 13.5 feet

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The diameter of the circle is 30 feet.

What is diameter?

The center of the circle is the midpoint of a line segment that connects two points on the circle's perimeter, and this line segment is indicated by the diameter of a circle.

The diameter of a circle is precisely equal to twice the radius' length.

Let us suppose the diameter of a circle is D then, the area is computed according to the formula

[tex]A = \frac{\pi D^2}{4}[/tex]

where

A is the area and D is the diameter.

Plug A = 225 pi in the above equation,

[tex]225 \pi =\frac{\pi D^2}{4} \\225 = \frac{D^2}{4} \\D^2 = 900\\D = 30[/tex]

Hence, the diameter of the circle is 30 feet.

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The additive inverse of (-4x - 8)  is  4x+8.

What is Additive Inverse?

Additive inverse refers to any number that when added to the original number gives the result as zero. For instance, the additive inverse of 8 is -8 as 8 + (-8) = 0. It is possible to get the additive inverse of negative numbers too. For example, the additive inverse of -10 will be 10 as -10 + 10 = 0.

The additive inverse of any given number can be found by changing the sign of it. The additive inverse of a positive number will be a negative, whereas the additive inverse of a negative number will be positive. However, there will be no change in the numerical value except the sign. For example, the additive inverse of 8 is -8, whereas the additive inverse of -6 is 6.

The addition of a number and its additive inverse is equal to the additive identity.

we know that (-4x - 8)  +  (4x+8) = 0 .

Hence, The additive inverse of (-4x - 8)  is  4x+8.

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