A square barn measures 42 feet on each side. A goat is tethered outside by a rope that is attached to one corner of the barn, as shown in the bird's eye sketch.

a. suppose the length of the rope is 28 feet. How many square feet of land is the goat able to gaze

b. suppose the length of the rope is made twice as long as in part a. How many square feet of land is the goat now able go gaze

(answer both questions, not just one )
Here's an image that would help

Answer:

Step-by-step explanation:

from cosines theorem:

t² = 11² + 14² - 2•11•14•cos87°

t² = 121 + 196 + 308•0.05236

t² = 333.12688

t = √333.12688

t = 18.2517... ≈ 18.3

It is not a right triangle.

What is the right triangle?

A right triangle is one in which one of the inner angles is 90°. The hypotenuse is the longest side of the right triangle and also the side opposite the right angle, whereas the height and base are the two arms of the right angle.

Here, we have

Given: a triangle has sides with lengths of 35 centimeters, 78 centimeters, and 82 cm.

We have to find is it a right triangle.

To find the right triangle we apply Pythagoras' theorem and we get

82² = 35² + 78²

6724 = 1225 + 6084

6724 ≠ 7309

Their sides are not equal so it is not a right angle triangle.

Hence, it is not a right triangle.

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Answer:

The answer is

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1)\)

where

m is the slope

( x1 , y1) is the point

From the question the point is ( 5 , - 2) and slope is - 2/5

The equation of the line is

\(y + 2 = - \frac{2}{5} (x - 5) \\ y + 2 = - \frac{2}{5} x + 2 \\ y = - \frac{2}{5} x + 2 - 2\)

We have the final answer as

\(y = - \frac{2}{5} x \\ \)

Hope this helps you

Answer:

The answer is C

Step-by-step explanation:

Since the line above the letters is an arrow that means the two points have to create a line like that. Therefore, the answer is DB.

Answer:

DB

Step-by-step explanation:

Why others rejected?

E C

E B is rejected as points are not on one line

Answer:

-200

Step-by-step explanation:

if youre doing normal addition youd get 200 + 200 giving you 400 so -200 + -200 = 400

Answer: C.) mAngleGLI = 2mAngleGLH

Step-by-step explanation:

Hope it helps!!!

For ray LH as the bisector of angle GLI, we can determine that the relation ∠GLI = 2∠GLH holds

An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and scalene.

∠GLI is bisected by LH, hence:

∠GLH = ∠HLI (definition of bisection)

∠GLI = ∠GLH + ∠HLI (angle addition)

∠GLI = 2∠GLH

The information that can be used to determine this is ∠GLI = 2∠GLH

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To obtain the general solution of the given differential equation, we can solve it using the method of integrating factors.

y = (72e^(x²/2) + C) / (x² * e^(x²/2))

The given differential equation is:

x²y + xy - y = 72x³

We can rearrange the equation to the standard linear form:

x²y + xy - y - 72x³ = 0

Now, let's determine the integrating factor, denoted by μ(x):

μ(x) = e^(∫P(x)dx)

= e^(∫x dx)

= e^(x²/2)

Multiplying the entire equation by μ(x):

e^(x²/2) * (x²y + xy - y - 72x³) = 0

Simplifying the equation:

x²y * e^(x²/2) + xy * e^(x²/2) - y * e^(x²/2) - 72x³ * e^(x²/2) = 0

Now, we can rewrite the left-hand side as a derivative using the product rule:

(d/dx)(x²y * e^(x²/2)) - 72x³ * e^(x²/2) = 0

Integrating both sides with respect to x:

∫(d/dx)(x²y * e^(x²/2)) dx - ∫72x³ * e^(x²/2) dx = C

Using the fundamental theorem of calculus, the first term simplifies to:

x²y * e^(x²/2) = ∫72x³ * e^(x²/2) dx + C

Integrating the second term on the right-hand side:

x²y * e^(x²/2) = 72∫x³ * e^(x²/2) dx + C

Now, we can solve the integral on the right-hand side by substituting u = x²/2:

x²y * e^(x²/2) = 72∫e^u du + C

Integrating e^u with respect to u:

x²y * e^(x²/2) = 72e^u + C

Substituting back u = x²/2:

x²y * e^(x²/2) = 72e^(x²/2) + C

Finally, solving for y:

y = (72e^(x²/2) + C) / (x² * e^(x²/2))

To determine the particular solution that satisfies the initial conditions

y(1) = 1 and y'(1) = 1, we substitute these values into the general solution and solve for C.

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If the intended margin of error equals 4 less than with a 0.95 probability, the sample size is 126.

The \(\alpha\) level is calculated by subtracting 1 from the confidence interval and dividing by 2.

\(\alpha\) = (1 - 0.95) ÷ 2

\(\alpha\) = 0.025

Find z inside the Z-table because it has a p-value of 1 - \(\alpha\).

So, z = 1.96 with a p-value = 1 - 0.025 = 0.975.

Now, consider that margin of error M.

M = z × (σ ÷ √n)

The standard deviation is determined as the square root of variance.

σ = √522 = 22.84

With a 0.95 probability, the sample size that requires to be accepted if the expected margin of error is 4 or less is,

The sample size of at least n, in which n is encountered when M = 4. So,

M = z × (σ ÷ √n)

4 = 1.96 × (22.84 ÷ √n)

4√n = 1.96 × 22.84

√n = (1.96 × 22.84) ÷ 4

√n = 11.1916

n = (11.1916)²

n = 125.25 ≈ 126

A sample size of at minimum 126 people is required.

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The Price of the guitar is $ 1418.03

In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to calculate a percentage of a number, multiply it by 100 after dividing it by its whole.

To find the percentage multiply the ratio of the actual value by the total value with 100.          

Here given

Gerardo works in a music store and earns a 6.1% commission on each sale.

Gerardo sells a guitar and earns $86.50  

Here we need to find the Price of the guitar

Since we don't know the price of the guitar

Let's assume that the Price of the guitar is $ x

From the given data,

The commission earned on the guitar = 6.1% of x

=> \(\frac{6.1}{100} \times x\)  

=>  0.061x

Given that

The amount earned by Gerardo on guitar = $86.50  

=> 0.061x = $86.50  

=> x = (86.50)/0.061

=> x = 1418.03

Therefore,

The Price of the guitar is $ 1418.03

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Answer:

1418.03

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

While researchers may have found a strong positive linear relationship between ice cream sales and the crime rate in many cities, it does not necessarily mean that one directly causes the other.

There could be other underlying factors or variables at play that are influencing both ice cream sales and the crime rate. For example, both variables might be influenced by external factors such as weather conditions, population density, or economic factors.

Additionally, it's possible that the observed relationship is coincidental or driven by statistical outliers. Without further evidence and a comprehensive analysis, it is not appropriate to conclude a direct causal relationship between ice cream sales and the crime rate based solely on a positive correlation.

To establish a causal relationship, further research would be needed to identify the specific mechanisms or factors that link ice cream sales to the crime rate in order to determine if there is a direct cause-and-effect relationship between the two variables.

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many cities, researchers have found a strong positive linear relationship between ice cream sales and the crime rate. Explain.

Answer:

x=8/3

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Answer: x = 8/3

Step-by-step explanation:

In respοnse tο the questiοn, we may say that  In 100 years, there will be functiοn arοund 125 grammes left.

Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is a cοnnectiοn between inputs and οutputs where each input results in a single, distinct οutcοme. Each functiοn has a dοmain, cοdοmain, οr scοpe assigned tο it. Functiοns are usually denοted by the letter f. (x). An x is entered. On functiοns, οne-tο-οne capabilities, sο multiple capabilities, in capabilities, and οn functiοns are the fοur main categοries οf accessible functiοns.

Setting t = 0 in the prοvided functiοn will reveal the sample's οriginal quantity:

A(0) = 647

\((1/2)^{(0/30)}\) = 647

As a result, there are 647 grammes οf starting material in the sample.

In οrder tο calculate the amοunt left after 100 years, we must enter t = 100 intο the supplied functiοn:

\(A(100) = 647(1/2)^{(100/30) }= 647(1/2)^{(10/3)}\) ≈ 125.24

Thus, there will be arοund 125 grammes left after 100 years (rοunded tο the nearest gram).

There are 647 grammes οf starting material in the sample.

In 100 years, there will be arοund 125 grammes left.

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The initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.

what is functiοn?

Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput.

The given exponential function is:

A(t) = 647(1/2)^(t/30)

where t is the time in years.

To find the initial amount of the sample, we need to evaluate A(0):

A(0) = 647(1/2)^(0/30) = 647(1) = 647

Therefore, the initial amount of the sample is 647 grams.

To find the amount remaining after 100 years, we need to evaluate A(100):

A(100) = 647(1/2)^(100/30) ≈ 69.35

Rounding this to the nearest gram gives the amount remaining after 100 years as 69 grams.

Therefore, the initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.

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Answer:

44%

0.44 is 44% of 1.

The associative property looks like a + (b + c) = (a + b) + c.

According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.

The associative property is applicable in addition as well as in multiplication.

According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:

(a + b) + c = a + (b + c)

According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:

(a × b) × c = a × (b × c)

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We can write the parametric equations in vector form: (r(t)) = (-t, 1 - t, t), where r(t) represents the position vector of a point on the line at parameter t.

To find the parametric equations for the line of intersection between the planes x + y + z = 1 and x + z = 0, we can solve the system of equations formed by these two planes.

First, let's solve the second equation, x + z = 0, for x in terms of z:

x = -z

Now substitute this expression for x in the first equation:

-x + y + z = 1

-(-z) + y + z = 1

z + y = 1

We have two equations:

x = -z

z + y = 1

To obtain the parametric equations, we can introduce a parameter t and express x, y, and z in terms of t:

x(t) = -t

y(t) = 1 - t

z(t) = t

Therefore, the parametric equations for the line of intersection of the given planes are:

x(t) = -t

y(t) = 1 - t

z(t) = t

Alternatively, we can write the parametric equations in vector form:

(r(t)) = (-t, 1 - t, t), where r(t) represents the position vector of a point on the line at parameter t.

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The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Answer:

4/41

Step-by-step explanation:

The rank of a matrix is equal to the number of non-zero rows in its row echelon form. The value of x for which the given matrix is singular is `19 ± 2√190`.

Given matrix is, A =  [-x  9;  -7  x - 38]

We have to find the value of x for which the given matrix is singular. A matrix is singular if its determinant is zero. Therefore, the determinant of the given matrix must be zero for it to be singular. \(|A| = (-x * (x-38)) - (9 * (-7))|A|\)

\(= -x² + 38x + 63\).

Now, the determinant of the matrix A must be zero as it is a singular matrix. |A| = -x² + 38x + 63

= 0

=> x² - 38x - 63

= 0On solving the quadratic equation, we get; \(x = \frac{38 \pm \sqrt{(-38)^2 - 4(1)(-63)}}{2(1)}\)\(x = 19 \pm 2\sqrt{190}\).

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Answer:

(14, 23)

area = 400 square units

Step-by-step explanation:

Part (a)

To find the point where two equations meet (the point of intersection), equal the equations to each other, then solve for x.  Substitute the found value of x into one of the equations (it doesn't matter which) and then solve for y.  (x, y) is the point of intersection.

Equation 1:  y = 2x - 5

Equation 2:  y = 23

Equate the equations:

            y = y

⇒ 2x - 5 = 23

⇒       2x = 23 + 5

⇒       2x = 28

⇒          x = 28 ÷ 2

⇒          x = 14

Usually we'd substitute the found value of x into one of the equations and solve for y, however, as one of the equations is literally the y value, we don't need to do that.

So y = 23

Therefore, the point of intersection is (14, 23)

Part (b)

The vertices of the triangle will be the points where each pair of lines meet each other.  We have already determined that one pair of lines meets at point (14, 23).

y = 2x - 5 is a diagonal line, y = 23 is a horizontal line, and x = -6 is a vertical line.

So x = -6 and y = 23 meet at (-6, 23)

Now we just need to determine where y = 2x - 5  and  x = -6 meet.

Simply substitute x = -6 into y = 2x - 5:

⇒ y = 2(-6) - 5

⇒ y = -17

Therefore, the point of intersection is (-6, -17)

So we have three points of intersection which are the three vertices of the triangle:

(14, 23)  (-6, 23) (-6, -17)

As y = 23 is a horizontal line and x = -6 is a vertical line, their point of intersection (-6, 23) is a right angle.

Therefore the can determine that the height of the triangle is the difference between the y-coordinates of (-6, 23) and (-6, -17).

Similarly, the base (width) of the triangle is the difference between the x-coordinates of (-6, 23) and (14, 23).

Therefore, the height = 23 - -17 = 23 + 17 = 40

Therefore, the base = 14 - -6 = 14 + 6 = 20

Area of a triangle = 1/2 x base x height = 1/2 x 20 x 40 = 400 square units

see attached diagram

The correct answer is c. frequency polygon.

A chart that contains a continuous line representing the frequencies of scores within a class interval is known as a frequency polygon. Frequency polygons are graphical representations of frequency distributions, which show the number of observations or data points falling within each interval or class.

A histogram, option a, is a graphical representation of data where the data is divided into intervals and displayed as bars. It does not include a continuous line.

Option b, standard deviation, is a measure of the dispersion or spread of a dataset, and it is not directly related to the representation of frequencies.

Option d, frequency distribution, refers to a tabular representation of data that shows the number of observations or data points falling within each interval or class, but it does not include a continuous line plot.

In summary, a frequency polygon is the chart that contains a continuous line representing the frequencies of scores within a class interval.

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The probability that both Event A (the first die is 4 or less) and Event B (the second die is even) will occur is 1/3.

To find the probability that both Event A and Event B will occur, we need to calculate the individual probabilities of each event and then multiply them together.

Event A: The first die is 4 or less.

There are 6 possible outcomes for the first die (numbers 1 to 6), and out of those, 4 outcomes (numbers 1, 2, 3, and 4) satisfy the condition. Therefore, the probability of Event A is 4/6, which simplifies to 2/3.

Event B: The second die is even.

For a fair six-sided die, there are 3 even numbers (2, 4, and 6) out of a total of 6 possible outcomes. Therefore, the probability of Event B is 3/6, which simplifies to 1/2.

To find the probability that both events will occur, we multiply the probabilities of Event A and Event B:

Probability of both events occurring = Probability of Event A * Probability of Event B

P = (2/3) * (1/2)

P = 2/6

P = 1/3

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Answer:

by my best guess, x = -5 (negative five)

Step-by-step explanation:

Answers:

===========================================

Explanation:

You could graph these by hand by determining a bunch of points to plot, but that method is a bit tedious and error prone. I recommend using technology. I used GeoGebra which is a graphing program to get the job done. See the attached image below.

Answer:

3 adults and 4 kids

Step-by-step explanation:

I just went through process of elimination of different possibilities like 2 adults and 5 kids, etc.

Then when I got the right answer all I did was multiply.

adults.) 12 x 3 = $36

kids.) 9 x 4 = $36

Then add both amounts.

$36 + $36 = $72

Answer:

3 adult tickets and 4 kid tickets

Step-by-step explanation:

So, with an equation like this, if you know how many of one of the types of tickets a person bought, then we can make an equation and find out how many of the other kind they bought.

But, since we don't know how many of either type of ticket was purchased, we can basically guess different combinations of the amount of each of the tickets.

We know there are 7 total tickets purchased, with a total price of $72. We also know the price of both adult tickets ($12) and student tickets ($9).

So, with that information, we can make an equation where a represents the number of adult tickets and k represents the total amount of kid tickets.

12a + 9k = 72

Now, let's guess combinations of amounts of each kind of ticket.

let's try 4 adult tickets and 3 kid tickets.

12(4) + 9(3) = 75

Well, 75 is close to 72, so let's try a similar combination.

Let's do the opposite this time. 3 adult tickets and 4 kid tickets.

12(3) + 9(4) = 72

Well, there we go. Just try and make some educated guesses.

Answer:

b

Step-by-step explanation:

B , becausse when percipitation occurs you sweat which is how your body releases heat and cools you down.

When we exercise and the body needs to release heat and cool itself, it engages in the process of b. Perspiration

Perspiration:

When we are exercising therefore and we begin to sweat, this just means that the body is quite hot and needs to cool itself down.

In conclusion, the body uses perspiration to cool itself.

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The proof that shows that ΔPQR ~ ΔTSR  by the AA similarity theorem is shown below.

According to the AA similarity theorem, two triangles that have two pairs of corresponding congruent angles are said to be similar to each other.

Using this theorem, we can prove that triangles PQR and TSR are similar as shown in the proof below.

Statement                              Reason                                      

1. QR | PT                               1. Given

2. <QPR = <STR                    2. Given

3. <QRP and <SRT are right 3. Definition of perpendicular

angles

4. <QRP ≅ <SRT                     4. All right angles are ≅

5. ΔPQR ~ ΔTSR                     5. AA similarity theorem

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Answer:

45.6

Step-by-step explanation:

24% out of 190 = 45.6