A rectangular area is to be enclosed and divided into thirds. The family has $920 to spend for the fencing material. The outside fence costs $10 per foot instaled, and the dividers cost $20 per foot installed. Let x represent the lenght (in feet) of a side perpendicular to the dividers, and let y represent the length (in feet) of a side parallel to the dividers.
Write an equation that represent the area of the enclosed rectangle in terms of the variable y.
A(y) = ___
Find A"(y) = ___

The cost of each entity: each pen is $\(1.75\), each folder is $\(2.50\), and each notebook is $\(1.75\).

Let's assign variables to the costs of each supply:

Let the cost of each pen be P dollars.

Let the cost of each folder be F dollars.

Let the cost of each notebook be N dollars.

According to the given information, we can form the following equations:

For Shane:

\(4P + 3F + 2N = 12.25 (Equation \ 1)\)

For Cheryl:

\(4F + 6N = 22 (Equation \ 2)\)

For Isaiah:

\(2P + F + 3N = 10.25 (Equation \ 3)\)

To solve this system of equations, we can use substitution or elimination method.

Using the elimination method, let's multiply Equation 2 by 2 and Equation 3 by 4 to eliminate F:

\(8F + 12N = 44 (Equation \ 4)\\8P + 2F + 12N = 41 (Equation \ 5)\)

Now, subtract Equation 4 from Equation 5 to eliminate F:

\(8P + 2F + 12N - (8F + 12N) = 41 - 44\\8P - 6F = -3\)

Simplifying further, we have:

\(8P - 6F = -3 (Equation \ 6)\)

Now, let's multiply Equation 1 by 4 and Equation 3 by 3 to eliminate N:

\(16P + 12F + 8N = 49 (Equation \ 7)\\6P + 3F + 9N = 30 (Equation \ 8)\)

Now, subtract Equation 8 from Equation 7 to eliminate N:

\(16P + 12F + 8N - (6P + 3F + 9N) = 49 - 30\\10P + 9F - N = 19\)

Simplifying further, we have:

\(10P + 9F - N = 19 (Equation \ 9)\)

Now we have a system of equations consisting of Equation 6, Equation 9, and Equation 2:

\(8P - 6F = -3 (Equation \ 6)\\10P + 9F - N = 19 (Equation \ 9)\\4F + 6N = 22 (Equation \ 2)\)

To find the values of P, F, and N, we can solve this system of equations using any suitable method, such as substitution or elimination.

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Using half-angle formulas When u = 120 degrees, sin(u/2) = √3 / 2, cos(u/2) = 1/2, and tan(u/2) = √3.

To determine the quadrant in which u/2 lies, we need to know the sign of u/2. If u is positive, then u/2 is also positive, and if u is negative, then u/2 is also negative. If u is equal to 0, then u/2 is also equal to 0.

To find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas, we need to know the values of sin(u) and cos(u) as well as the quadrant in which u/2 lies.

The half-angle formulas are as follows:

sin(u/2) = ±√((1 - cos(u)) / 2)

cos(u/2) = ±√((1 + cos(u)) / 2)

tan(u/2) = sin(u/2) / cos(u/2)

The signs of sin(u/2) and cos(u/2) depend on the quadrant in which u/2 lies. If u/2 is in the first or fourth quadrant, then sin(u/2) is positive, and if u/2 is in the second or third quadrant, then sin(u/2) is negative. If u/2 is in the first or second quadrant, then cos(u/2) is positive, and if u/2 is in the third or fourth quadrant, then cos(u/2) is negative.

To determine the values of sin(u/2) and cos(u/2), we first need to find the value of cos(u) using the half-angle formula:

cos(u) = 1 - 2 sin^2(u/2)

Once we have found the value of cos(u), we can use the half-angle formulas to find the values of sin(u/2) and cos(u/2).

For example, if u = 120 degrees, then u/2 = 60 degrees, which is in the first quadrant. We know that cos(u) = -1/2, so we can use the half-angle formulas to find the values of sin(u/2) and cos(u/2):

sin(u/2) = √((1 - cos(u)) / 2) = √((1 + 1/2) / 2) = √(3/4) = √3 / 2

cos(u/2) = √((1 + cos(u)) / 2) = √((1 - 1/2) / 2) = √(1/4) = 1/2

tan(u/2) = sin(u/2) / cos(u/2) = (√3 / 2) / (1/2) = √3

Therefore, when u = 120 degrees, sin(u/2) = √3 / 2, cos(u/2) = 1/2, and tan(u/2) = √3.

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The Solution using two methods are 323, .291, the correct option is B`.

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.

Given;

Frank is a champion fish charmer who can charm fish with .62 probability of success

He attempts to charm 100 fish, what's the probability he'll charm

between 60 and 80 inclusive

Now, probability out of 100

=62

This is between 60 and 80

So, 323

Therefore, the probability will be 323 and .291

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The scientific notation of the product of the given numbers is \(5.291 \times 10^{12}\).

Given, \((4.81 \times 10^{16} ) (1.1 \times 10^{-4} )\).

We need to write the scientific notation of the product.

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

Now, \((4.81 \times 10^{16} ) (1.1 \times 10^{-4} )=4.81 \times 1.1 \times 10^{16} \times10^{-4}\)

\(=5.291 \times 10^{16-4} =5.291 \times 10^{12}\)

Hence, the scientific notation of the product of the given numbers is \(5.291 \times 10^{12}\).

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Answer:C

Step-by-step explanation:

5.291 times 10 Superscript 12

Answer:

Step-by-step explanation:

To find a function's inverse, you first switch the x and y coordinates, and then solve for the new y. The same goes for finding an inverse's function. We have:

\(y=\frac{x+4}{11}\) We will switch the x and y variables and then solve for the new y:

\(x=\frac{y+4}{11}\) and

11x = y + 4 so

11x - 4 = y and

11x - 4 = f(x) which is choice C.

Step-by-step explanation:

Hey there!!!

Simply use distance formula to find the distance between two points.

The given points are; A (5,8) and B (-2,3).

Using distance formula.

\(d= \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \)

Put all values.

\(d = \sqrt{ {( - 2 - 5)}^{2} + {(3 - 8)}^{2} } \)

Simplify them.

\(d = \sqrt{ {( - 7)}^{2} + ( { - 5)}^{2} } \)

\(d = \sqrt{49 + 25} \)

\(d = \sqrt{74} \)

Therefore the distance between two points is 8.602units Or 9 units.

Hope it helps....

The distance between the two coordinate points is √74

Distance is the length between two coordinates in an x-y plane.

To calculate the distance between the two points, we use the formula below.

Formula:

From the question,

Given:

Substitute these values into equation 1

Hence, the distance between the two co-ordinate points is √74.

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If the 11th graders prefer hotdogs at a rate of 70%, the bar for 11th graders would show 70% percentage.

A segmented bar chart is a graphical representation of data that is divided into different segments. It is typically used to compare different categories of data. In this case, the bar chart is used to compare the lunch preference of different grades. The bar for 11th graders would show the percentage of 11th graders who prefer hotdogs. If 70% percentage of 11th graders prefer hotdogs, then the bar for 11th graders would show 70%. The bar chart can also show the percentage of 11th graders who prefer other lunch options, such as sandwiches, salads, etc. This information can help school administrators to better understand the lunch preferences of their students and make informed decisions about what types of food to serve for school lunch.

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Answer:

im 1000000000900

Step-by-step explanation:

Answer:

T (2, -9)

Step-by-step explanation:

The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

Proportional

Step-by-step explanation:

Proportional, because the graph goes through (0, 0).  If the line crossed the y-axis elsewhere, the function would NOT be proportional.

Answer:

Step-by-step explanation:

Angle BAC = Angle ACD = 50 degrees, because they are alternate angles.

Angle ACB = 180 - (50 + 80) = 50 degrees, because angles in a triangle sum up to 180 degrees.

Since Angle BAC = Angle BCA, triangle ABC is isosceles.

Answer:

The triangle is an isosceles triangle because 2 of the sides have the same measure and 1 of the sides does not.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The foci are horizontally aligned.

horizontal ellipse:

(x-h)²/a² + (y-k)²/b² = 1

center (h,k)

vertices (h±a,k)

length of minor axis = 2b

foci (h±c,k), c² = a²-b²

Apply your data and solve for h, k, a, and b.

foci (±3√19, 6)

h = 0

k = 6

Length of minor axis = 2b = 10

b = 5

foci (h±3√19, 6)

c = 3√19

c³ = a² - b²

171 = a² - 25

a²  = 196

x²/196 + (y-6)²/25 = 1

The values of a, b, and c for the given characteristic equation A³ + aA² + bA + c = 0 are a = -9, b = 31, and c = -34 for the matrix A = \(\begin{bmatrix}4 & 0 & 0 \\5 & 3 & 2 \\-2 & 0 & 2 \\\end{bmatrix}\).

To find the values of a, b, and c for the characteristic equation A³ + aA² + bA + c = 0, we need to calculate the characteristic polynomial of matrix A and equate it to zero.

Given matrix A:

A = \(\begin{bmatrix}4 & 0 & 0 \\5 & 3 & 2 \\-2 & 0 & 2 \\\end{bmatrix}\)

To calculate the characteristic polynomial, we need to find the determinant of the matrix (A - λI), where λ is an eigenvalue and I is the identity matrix.

Let's subtract λ from the diagonal elements of A:

A - λI = \($\begin{bmatrix}4-\lambda & 0 & 0 \\5 & 3-\lambda & 2 \\-2 & 0 & 2-\lambda \\\end{bmatrix}$\)

Now, calculate the determinant of (A - λI):

det(A - λI) = (4-λ)((3-λ)(2-λ) - 0) - 0 - (5(2-λ) - (-2)(3-λ)0)

= (4-λ)(6-5λ+λ²) - (10-5λ)

= (4-λ)(λ² - 5λ + 6) - (10-5λ)

= λ³ - 5λ² + 6λ - 4λ² + 20λ - 24 - 10 + 5λ

= λ³ - 9λ² + 31λ - 34

Now, comparing the characteristic polynomial with the equation A³ + aA² + bA + c = 0, we can identify the coefficients:

a = -9

b = 31

c = -34

Therefore, the values of a, b, and c for the given characteristic equation A³ + aA² + bA + c = 0 are a = -9, b = 31, and c = -34.

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Answer:

74 inches

Step-by-step explanation:

If his cousin is 40 inches tall, and Zach is 6 inches less than twice his height, solve for 40*2-6, which is 74.

Answer:

True

Step-by-step explanation:

the decimal does not continue further making it a terminating decimal

Answer: True

Step-by-step explanation: If I'm wrong I'm very sorry.

Answer:

Thus, 37/50 is the equivalent fraction to 74/100.

Therefore, 37/50 of the animals in the shelter are dogs.

Step-by-step explanation:

Given

Given that 74% of the animals at an animal shelter are dogs.

To determine:

About what fraction of the animals at the shelter are dogs?  

Using the equation to find a fraction equivalent to 74%

 \(\:74\%=\:\frac{74}{100}\)

Divide numerator and denominator by 2

         \(=\frac{\frac{74}{2}}{\frac{100}{2}}\:\:\)

Cancel the common factor 2.

        \(=\frac{37}{50}\)

Thus, 37/50 is the equivalent fraction to 74/100.

Therefore, 37/50 of the animals in the shelter are dogs.

There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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Answer:

Approx 3 hours.

Step-by-step explanation:

750 + 255c = 1605

255 c = 855

c = approximately 3 hours.

Answer:

The crew worked 6 hours.

Step-by-step explanation:

$255 x 6 = $1530

Add the "Per Day Fee" of $75

$1530 + $75 = $1605 Dollars

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}+1=0\)

\(\\ \rm\Rrightarrow \sqrt{3tan(2x-10)}=-1\)

\(\\ \rm\Rrightarrow 3tan(2x+10)=1\)

\(\\ \rm\Rrightarrow tan(2x+10)=1/3\)

\(\\ \rm\Rrightarrow 2x+10=18\)

\(\\ \rm\Rrightarrow 2x=8\)

\(\\ \rm\Rrightarrow x=4\)

Answer:

3 1/6

Step-by-step explanation:

5 1/2 =  5 3/6

         -

2 1/3 =  2 2/6

            _____

              3 1/6

Given:-

To find:-

Answer:-

Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;

\(\implies V = \pi r^2 h \\\)

where ,

Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;

\(\implies V \propto h \\\)

So , we can write;

\(\implies \dfrac{V_s}{V_l}=\dfrac{h_s}{h_l}\\\)

\(\implies \dfrac{V_s}{18\ oz}=\dfrac{6\ in.}{8 \ in.}\\\)

\(\implies V_s = \dfrac{6(18)}{8} \\\)

\(\implies \underline{\underline{ V_s =13.5 \ oz}} \\\)

Hence the volume of the smaller cup is 13.5 oz .

and we are done!

The coordinate of the vertex B after the transformation of the given trapezoid is (-2, 2).

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

As per the given graph, the coordinate of vertex B is (-5, 4).

After the translation (x, y) → (x + 3, y - 2), the new coordinate can be obtained as,

(-5, 4) → (-5 + 3, 4 - 2)

⇒ (-2, 2)

Hence, the coordinate of B after the transformation is (-2, 2).

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Answer:

"2-3 inches of snow":)

Step-by-step explanation:

The Qualitative information is "2–3 inches of snow".

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques.

Here, given that,

A local meteorologist reports the day's weather. "Currently sunny outside, 34°F. Skies will become overcast later this afternoon, as temperatures drop to 25°F, with windy conditions out of the north at 10–15 miles per hour. Radar indicates 2–3 inches of snow expected to fall later tonight."

Now , we know that the qualitative information is "2–3 inches of snow".

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if the vertex is at the origin, and the focus point horizontally to the right-side 1/8 units away from the vertex, well, that means is a horizontal parabola with a "p" value of +1/8, so

\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=0\\ k=0\\ p=\frac{1}{8} \end{cases}\implies 4(\frac{1}{8})(~~x-0~~) = (~~y-0~~)^2\implies \cfrac{1}{2}x=y^2\implies \boxed{x=2y^2}\)

The defendant was charged with aggravated assault. During the trial, the victim testified that the defendant beat her savagely.

In this case, aggravated assault refers to a more severe form of assault that involves the intentional causing of serious bodily harm to another person. The victim's testimony plays a crucial role in providing evidence and establishing the defendant's guilt. The prosecution will likely present other evidence, such as medical reports or eyewitness testimonies, to support the victim's claim.

It's important to note that the final verdict will depend on the judge or jury's assessment of the evidence presented during the trial. The defense will have an opportunity to cross-examine the victim and present their own evidence or witnesses to challenge the victim's testimony. The defendant's attorney may also argue for a lesser charge or attempt to establish that the defendant acted in self-defense. Ultimately, the court will weigh all the evidence and decide whether the defendant is guilty of aggravated assault based on the standard of proof beyond a reasonable doubt.

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Answer:

Henry needs 15 pints of paint altogether

Step-by-step explanation:

If Henry uses 2 pints of red paint and 3 pints of yellow paint to get a specific color, and he now uses a total of 9 pints of yellow, then

3 x 3 = 9 (yellow)

We know that what you do on one side, you do on the other.

2 x 3 = 6 (red)

You add

9 + 6 = 15. (Red and yellow paint)

Which will lead you to the conclusion of 15 pints.

Answer:

Henry will need 15 pints altogether.

Step-by-step explanation:

Add: 6 + 9 = 15 pints

The estimate for the sum of the numbers is 230, and the actual sum of the numbers is 209.

To estimate the sum of the numbers, we can round each number to the nearest ten and then add them together. When rounding off to the nearest tens, we look at the number at the tenth position. If it is five and above, we round it off to the next nearest tens number and if it is below five, we round it off to the previous nearest tens number.

76 rounds to 80   since 6 is above 5
6 rounds to 10 since 6 is above 5
25 rounds to 30 since 5 is located at 5 and above interval
5 rounds to 10 since 5 is located at 5 and above interval
10 rounds to 10 since 0 is below 5
87 rounds to 90 since 7 is above 5

So, the estimate for the sum of the numbers is: 80 + 10 + 30 + 10 + 10 + 90 = 230

To find the actual sum of the numbers, we simply add them together without rounding:

76 + 6 + 25 + 5 + 10 + 87 = 209

The complete question is: 76. 6 25. 5 10. 87 =

What was Sela's estimate and what is the actual sum of the number?

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