HELPPPPPP HELPPPPP PLZZZZZZZZZZZZZZZZ

The largest total area that can be enclosed is 4050 square yards.

Let's the length of the rectangular corral for cattle as x and the length of the rectangular corral for sheep as y.

For the cattle corral:

- Two sides with length x.

- One side with length y.

For the sheep corral:

- Two sides with length y.

- One side with length x.

As, the total fencing required is 270 yards

2x + y + 2y + x = 270

3x + 3y = 270

x + y = 90

Now, area of a rectangle is given by the formula A = length × width.

For the cattle corral = x × y

For the sheep corral= y × x

So, the total area is

= x × y + y × x

= 2xy

From this equation, x + y = 90

x = 90 - y.

Substituting this into the equation for A total:

A total = 2(90 - y)y = 180y - 2y²

To find the maximum area, take the derivative of A_total with respect to y and set it equal to zero.

\(\dfrac{dA_{total}}{dy}\) = 180 - 4y = 0

Solving for y:

180 - 4y = 0

4y = 180

y = 45

Substituting this value of y back into the equation x + y = 90:

x + 45 = 90

x = 45

Therefore, the dimensions that maximize the total area enclosed are x = 45 and y = 45.

So, the maximum area

=2 (45) (45)

= 4050 square yards

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Answer:

12-pack

Step-by-step explanation:

We find the unit cost of each one by dividing its price by the number of juice containers.

4.49/8 = 0.56125

6.59/12 = 0.5491666...

The 12-pack has a lower unit cost, so the 12-pack is a better buy.

Answer:

a=-30

Step-by-step explanation:

Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

\(\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces\)

Answer:

30 squared meters

120/4=30.

Any line that is perpendicular to a given line y = ax + b must have slope -1/a

For the lines -x - 5y = 7 and 5x - y = -9, first, we rewrite them in the slope-intercept form:

y = -x/5 - 7/5

y = 5x + 9

We can check that the slope of the first line is the negative inverse of the slope of the second line. Therefore, the lines are perpendicular.

Answer:

Step-by-step explanation:

water:cleaner = 12:1.5 = 8:1

Answer:

15 cups ??? i dont know tho pay attention in class

Step-by-step explanation:

.....

Answer:

\(g'(y)=3y^2-4y-8\)

Step-by-step explanation:

start by foiling out the given function

\(g(y)=(y-4)(2y+y^2)\\=2y^2+y^3-8y-4y^2\\=y^3-2y^2-8y\)

next, use the power rule to find the derivative

power rule: To use the power rule, multiply the variable's exponent n, by its coefficient a, then subtract 1 from the exponent. If there's no coefficient (the coefficient is 1), then the exponent will become the new coefficient.

\(g'(y)=3y^2-4y-8\)

The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

From the question, we have the following parameters that can be used in our computation:

First = tan(θ)

Second = cos(θ)

The basis trigonometry identity is

sin²(θ) + cos²(θ) = 1

Divide through the equation by cos²(θ)

So, we have

tan²(θ) + 1 = 1/cos²(θ)

Subtract 1 from both sides

tan²(θ) = - 1 + 1/cos²(θ)

Take the square root of both sides

tan(θ) = √[-1 + 1/cos²(θ)]

Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]

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Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To verify if the relation is a function, it must be verified if from each value of x only one arrow departs.

A relation represents a function when each input value is mapped to a single output value.

In mapping notation, with the arrows, it must be verified if there is no input from which more than one arrow departs.

The problem is incomplete, hence the general procedure to verify if the relation is a function was presented.

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The equation y = -8x + 4 represents the given problem.

'The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis.'

According to the given problem,

We know,

Equation of a line can be represented as,

y = mx + c, where, m = slope  

                              c = y-intercept                                            

Slope of the line = -8

Y-intercept of the line = 4

Therefore,

The equation of the line:

⇒ y = -8 + 4

Hence, we can conclude, the equation y = -8x + 4 represents the given line.

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Answer:

Below

Step-by-step explanation:

5 = 1 / (1-r)

1-r = 1/5

r = 4/5

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

From the question, we have the following parameters that can be used in our computation:

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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Answer: y = x/4 -7

Step-by-step explanation: hope this is right i was always good at math

The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.

To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.

The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25

The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;

P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25

Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;

P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)

= 0.25 + 0.25

= 0.5

Therefore, the  probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.

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Answer: 329/100

Step-by-step explanation:

3 29/100 is the answer

To find the slope, we must know the equation

 --> \(slope = \frac{y2-y1}{x2-x1}\\\)

Now using the information given, (-2,1) and (2,6), let's plug that into the equation

--> \(slope = \frac{6-1}{2--2} = \frac{5}{4}\)

In this case, the slope is 5/4

Hope that helped!

Answer:

\(\rn\hookrightarrow 5/4\)

Step-by-step explanation:

\(Solution,\\\\Let,\\(x_1,y_1)=(-2,1)\\\\(x_2,y_2)=(2,6)\\\\Now,\\\\\rn\hookrightarrow Slope=\frac{y_2-y_1}{x_2-x_1}\\\\\rn\hookrightarrow Slope=\frac{6-1}{2-(-2)} \\\\\rn\hookrightarrow Slope=\frac{5}{4}\)

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Solving a system of equations we will see that the values are:

x = 115

y = -38.25

We know that the sum of two adjacent angles is always 180°, then we can write two linaer equations:

8y + 4x + 26 = 180

4y - 12 + 3x = 180

We can simplify that to get the system of equations:

4x + 8y = 154

3x + 4y = 192

To solve this, we can take the difference between twice the second equation and once the first equation to get:

2*(3x + 4y) - (4x + 8y) = 2*192 - 154

6x + 8y - 4x - 8y = 230

2x = 230

x = 230/2

x = 115

Then the value of y is:

3*115 + 4*y = 192

4y = 192 - 3*115

y = (192 - 3*115)/4

y = -38.25

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Using the normal distribution and the central limit theorem, it is found that:

a) The 95% confidence interval for the population mean resistance, in ohms, is (0.57, 0.67).

b) 0.2358 = 23.58% probability that an average of 52 resistances is 0.62 ohms or higher.

Normal Probability Distribution

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

Question a:

We have that:

The confidence interval is:

\(\overline{x} \pm M\)

The margin of error is:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which:

The first step is finding the critical value, which is z with a p-value of \(\frac{1 + \alpha}{2}\), in which \(\alpha\) is the confidence level.

In this problem, \(\alpha = 0.95\), thus, z with a p-value of \(\frac{1 + 0.95}{2} = 0.975\), which means that it is z = 1.96.

Then:

\(M = 1.96\frac{0.2}{\sqrt{52}} = 0.05\)

\(\overline{x} - M = 0.62 - 0.05 = 0.57\)

\(\overline{x} + M = 0.62 + 0.05 = 0.67\)

The 95% confidence interval for the population mean resistance, in ohms, is (0.57, 0.67).

Item b:

\(s = \frac{0.2}{\sqrt{52}}\).

The probability is 1 subtracted by the p-value of Z when X = 0.62, thus:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.62 - 0.6}{\frac{0.2}{\sqrt{52}}}\)

\(Z = 0.72\)

\(Z = 0.72\) has a p-value of 0.7642.

1 - 0.7642 = 0.2358.

0.2358 = 23.58% probability that an average of 52 resistances is 0.62 ohms or higher.

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Answer:

A

Step-by-step explanation:

A= 125

Step-by-step explanation:

in a triangle all angles add up to 180

Do 180-55= 125

hope this helps :)

Answer:

what's the question though ?

The equation that models the relationship between the number of guests, x, and the total charge, y is A. y = 450 + 125x. The base charge for a single guest is $450, and for each additional guest, the charge increases by $125. So, we add 125 times the number of additional guests to the base charge of $450.

As a result, the new rectangle's dimensions are 8 inches long and 10 inches wide.

A rectangle's perimeter (P) is the sum of the lengths of its four sides. A rectangle possesses two equal lengths as well as two equal widths since its opposite sides are equal.

Given data:

Perimeter of the rectangle = 2(length + width)

Put the values:

26 = 2(8 + x)

26 = 16 + 2x

26 - 16 = 2x

10 = 2x

x = 10/2

x = 5 inches

For the New rectangle:

Length = 8 inches (same)

Twice of wide = 2*(5 inches) = 10 inches

As a result, the new rectangle's dimensions are 8 inches long and 10 inches wide.

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Complete question:

Timur cuts out a rectangle that has a perimeter 26 inches and a length of 8 inches. He cuts out another rectangle that is the same length and twice as wide. Find the new dimensions.