A farmer needs to fence a rectangular piece of land. She wants the length of the field to be 80 feet longer than the width. If she has 1080 feet of fencing material, what should be the length and width of the field?

The minimum of this quadratic function is -55.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function T = n²- 10n - 30, we have:

Axis of symmetry, Xmax = -(-10)/2(1)

Axis of symmetry, Xmax = 10/2 = 5.

For the vertex of T = n²- 10n - 30, we have:

T = n²- 10n - 30

T(5) = 5²- 10(5) - 30

T(5) = -55.

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The volume of the figure is 704 cubic centimeters.The correct option is B. 704 cubic centimeters.

The volume of the figure, need to calculate the volumes of the cube and the right triangular prism separately, and then add them together.

Volume of the cube:

The length of each side of the cube is given as 8 cm. The formula for the volume of a cube is V_cube = [tex]side^3.[/tex] Substituting the given value, we have V_cube = [tex]8^3[/tex] = 512 cubic centimeters.

Volume of the right triangular prism:

The base of the right triangular prism is a right triangle with one side measuring 8 cm and the other side measuring 6 cm. The height of the prism is given as 8 cm.

The formula for the volume of a right triangular prism is V_prism = base area * height. The base area of a right triangle is  [tex](1/2) * base * height[/tex]Substituting the given values, we have V_prism = [tex](1/2) * 8 cm * 6 cm * 8[/tex]cm = 192 cubic centimeters.

Add the volumes of the cube and the right triangular prism:

V_figure = V_cube + V_prism = 512 cubic centimeters + 192 cubic centimeters = 704 cubic centimeters.

The volume of the figure is 704 cubic centimeters.

The correct option is B. 704 cubic centimeters.

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Answer:

FE = 12

DE = 20

Step-by-step explanation:

Part A

We can solve for FE by equating the ratios of the triangles' sides. Remember we can only do this because the triangles are similar, so the scale factor between the side lengths is the same.

[tex]HE : GH = FE : DF[/tex]

↓ plugging in the given values

[tex]9 : 12 = FE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{9}{12} = \dfrac{FE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{FE = 12}[/tex]

Part B

We can solve for DE using the same technique.

[tex]GE : GH = DE : DF[/tex]

↓ plugging in the given values

[tex]15 : 12 = DE : 16[/tex]

↓ representing as fractions

[tex]\dfrac{15}{12}= \dfrac{DE}{16}[/tex]

↓ multiplying both sides by 16

[tex]\boxed{DE = 20}[/tex]

Answer: 6 years

Step-by-step explanation:

75,000*15% = 11,250

11,250*6 = 67,500

75,000-67,500 = 7500

7500 is worth less than 15,000

5 years would have been 18,750; more than 15,000

The probability of getting at one hit is 2/5

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 which is equivalent to 100%

Probability = sample space / total outcome

The sample space of getting at least 1 hit.

is 4.

Total outcome = 10

probability to get at least one hit = 4/10

= 2/5

Therefore the probability of getting atleast one hit is 2/5

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Answer:

1 calculate the Expected values for opening a sample of 100 cards

By using trigonometry, the missing sides are

Example 1: x = 16.7

Example 2: x = 3.2

Example 3: x = 23.5

Example 4: x = 9.3

From the question we are to determine the value of the missing sides in the given triangles

We can determine the value of the missing sides by using SOH CAH TOA

Example 1

Angle = 42°

Opposite side = x

Hypotenuse = 25

Thus,

sin (42°) = x / 25

x = 25 × sin (42°)

x = 16.7

Example 2

Angle = 75°

Opposite side = 12

Adjacent side = x

Thus,

tan (75°) = 12 / x

x = 12 / tan (75°)

x = 3.2

Example 3

Angle = 36°

Hypotenuse side = x

Adjacent side = 19

Thus,

cos (36°) = 19 / x

x = 19 / cos (36°)

x = 23.5

Example 4

Angle = 53°

Opposite side = x

Adjacent side = 7

Thus,

tan (53°) = x / 7

x = 7 × tan (53°)

x = 9.3

Hence,

The missing sides are 16.7, 3.2, 23.5 and 9.3

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The required sample size for a margin of error of less than 0.04 is given as follows:

n = 601.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The margin of error is defined as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

We have no estimate, hence the proportion is used as follows:

[tex]\pi = 0.5[/tex]

For a margin of error of 0.04, the sample size is obtained as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.04}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.04}\right)^2[/tex]

n = 601.

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hello

the answer to the question is:

y = a tan(bx – c) + d

a = 1, b = 1, c = π/2

the midline is y = d, so y = 0 and there's no vertical shift

the vertical stretch is 1, so label the y-axis so the inflection point of the curve is 1 above the midline, 1, and the other inflection point is 1 below the midline, −1

the period is:

T = π/b ----> T = π

the phase shift is:

PS = c/b ----> PS = π/2

and also, there's no amplitude for tangent and cotangent, there is only the vertical stretch that takes the place of an amplitude

Tamika Clark's total travel expense this month is $362.90.

Given that the supervisor for the county is Tamika Clark.

Every month, she makes the trip to the three schools in her district.

Her travel costs for this month include 246 miles at a cost of $0.55 per mile, $180.70 for meals, and $46.10 for other expenses.

We must determine the whole cost of her.

To calculate Tamika Clark's total travel expenses this month, we need to add up her expenses for miles traveled, meals, and miscellaneous items.

Miles traveled:

246 miles x $0.55 per mile = $135.30

Meals: $180.70

Miscellaneous: $46.90

Total travel expenses:

$135.30 (miles traveled) + $180.70 (meals) + $46.90 (miscellaneous) = $362.90

Therefore, Tamika Clark's total travel expense this month is $362.90.

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The variables in this problem are classified as follows:

In the context of this problem, the number of siblings is the only discrete variable, as is the only variable that cannot assume decimal values.

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Answer:

9 + x ≥ -23

Step-by-step explanation:

'At least' here means the lowest possibility of the sum 9 + x can equal -23, which means 9 + x can also be greater than -23. So the sum is either equal to -23 or greater than -23.

The correct options are 1) B, 2) A and 3) D.

1) The table shows the work hour and earned money of Logan we need to build an equation to relate both the variables,

So, let the earned money be y and the hour worked be h,

So,

He worked 45 hours to earn $495,

So, in one hours he earned = $495/45 = $11

Therefore, the equation that relate both the variables is,

y = 11h

2) To represent the amount Mr. Kelly pays per month; we can divide the total rent paid for the year by the number of months.

So, if his yearly rent is $12564, so per month he must be paying =

12564 / 12 = $1047

Therefore, the equation that represents the amount Mr. Kelly pays per month is: 1047m = c

3) The relation given shows the quantity of apples bought to its corresponding cost,

So, considering the point (4, 10) by which the graph passes,

So, this mean that, 4 pounds of apple cost $10,

So, 1 pound = 10/4 = $2.5

Hence the cost per pound is $2.5.

Hence the answers are 1) B, 2) A and 3) D.

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Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

[tex]A = P \times e^{rt}[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

[tex]A = P \times (1 + r)^t[/tex]

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

[tex]3P = P \times e^{rt}[/tex]

Dividing both sides by P, we get:

[tex]3 = e^{rt}[/tex]

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

[tex]A = P \times (1 + r)^t[/tex]

[tex]A = $8,000 \times (1 + 0.0275)^{22.313}[/tex]

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

New Jersey has the greatest population density in 2013

Since we know that,

Population density  is defined as the number of people per square at any given point in time.

Total people / total area = population density

In emerging countries, population density is higher than in developed countries.

Now for the state :  Connecticut

Population = 3596080

Area = 4842

Therefore,

Density = 3596080/4842

             = 742.68

Now for the state :  Massachusetts

Population = 6692824

Area = 7800

Therefore,

Density = 6692824/7800

             = 858.05

Now for the state :  New Jersey

Population = 8899339

Area = 7354

Therefore,

Density = 8899339/7354

             = 1210.13

Now for the state :  New Jersey

Population = 1051511

Area = 1034

Therefore,

Density = 8899339/7354

             = 1016.93

Hence population Density of  New Jersey is greatest.

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Answer:

3.6

Step-by-step explanation:

Sine rule:   a/SIN A  =  b/SIN B  =   c/SIN C.

right-angled triangle, so angle N = 90°.

x/sin 32  = 6.8/sin 90

x = (6.8 X sin 32) / sin 90

= 3.6

The rate of change of y with respect to x for the given linear relationship is 10.

To determine the rate of change of y with respect to x, we can calculate the slope of the linear relationship between x and y using the formula:

slope = (change in y) / (change in x)

Given the values in the table:

x: -8.5, -6.5, -2.5, -1

y: -92, -72, -32, -17

We can calculate the change in y and change in x between any two points.

For example, between the first two points (-8.5, -92) and (-6.5, -72), the change in y is:

change in y = -72 - (-92) = -72 + 92 = 20

And the change in x is

change in x = -6.5 - (-8.5) = -6.5 + 8.5 = 2

Using the formula for slope:

slope = (change in y) / (change in x) = 20 / 2 = 10.

Therefore, the rate of change of y with respect to x is 10.

This means that for every unit increase in x, y increases by 10 units.

We can perform the same calculations for the other points in the table and observe that the rate of change of y with respect to x remains constant at 10.

Hence, the rate of change of y with respect to x for the given linear relationship is 10.

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Answer:

The graph of g is a reflection over the y-axis.  Let's call the points of a regular function before the reflection is done (x, y).  When a function is reflected over the y-axis, you get the opposite y values as (x, -y).  So with a point like (-2, -3), a reflection over the y-axis would give us (-2, 3), where x stays the same but y becomes the opposite.

The true statement is that the box-plot indicates that:

To determine the validity of this statement, we compare the minimum weekly salary of men (represented by the lower end of the box-plot whisker) to the median of women's earnings (represented by the line inside the box).

If the median of women's earnings is less than the minimum salary of men, then more than 50% of women earn less than the minimum weekly salary of men.

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Answer:

subsidiaries hi sus

Step-by-step explanation:

scientific 2 is the answer

b) The inverse function of ƒ(x) is given by: ƒ⁻¹(x) = (1 - x) / x

c) The domain of ƒ⁻¹(x) is all real numbers except for 1.

d) The solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

(a) To show that f(x) = 1 / (x + 1), we need to simplify the expression f(x) and demonstrate that it is equivalent to 1 / (x + 1):

f(x) = [2(x - 1) / (x² - 2x - 3)] - (1 / (x - 3))

f(x) = [2(x - 1) / (x - 3)(x + 1)] - (1 / (x - 3))

f(x) = [2(x - 1) - (x + 1)] / (x - 3)(x + 1)

f(x) = [2x - 2 - x - 1] / (x - 3)(x + 1)

f(x) = (x - 3) / (x - 3)(x + 1)

f(x) = 1 / (x + 1)

Therefore, we have shown that f(x) = 1 / (x + 1).

(b) To find the inverse function of ƒ(x), we interchange the roles of x and y and solve for y:

x = 1 / (y + 1)

xy + x = 1

xy = 1 - x

y = (1 - x) / x

Therefore, the inverse function of ƒ(x) is given by:

ƒ⁻¹(x) = (1 - x) / x

(c) The domain of ƒ⁻¹(x) can be determined by looking at the domain of the original function f(x), which is x > 3.

For ƒ(x), the range is all real numbers except for 1 (since f(x) = 1 / (x + 1)).

Therefore, the domain of ƒ⁻¹(x) is all real numbers except for 1.

(d) Given g(x) = 2x² - 3, we are asked to solve (ƒ o g)(x) = 1/8.

(ƒ o g)(x) means we need to substitute g(x) into ƒ(x):

ƒ(g(x)) = 1 / (g(x) + 1)

Substituting g(x) = 2x² - 3:

ƒ(2x² - 3) = 1 / (2x² - 3 + 1)

ƒ(2x² - 3) = 1 / (2x² - 2)

1 / (2x² - 2) = 1 / 8

8 = 2x² - 2

2x² = 10

x² = 5

x = ±√5

Therefore, the solutions for (ƒ o g)(x) = 1/8 are x = √5 and x = -√5.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 5.6\%\to \frac{5.6}{100}\dotfill &0.056\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 500[1+(0.056)(3)] \implies A=500(1.168)\implies A = 584[/tex]

Answer:

Answer:

I = $ 84.00

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5.6%/100 = 0.056 per year,

then, solving our equation

I = 500 × 0.056 × 3 = 84

I = $ 84.00

The simple interest accumulated

on a principal of $ 500.00

at a rate of 5.6% per year

for 3 years is $ 84.00.

Step-by-step explanation:

Note that the   curvature of the curve defined by the function y = 3x² - 2x +4   at point x = 2 is approximately 0.0002.

To find the curvature   of the curve defined by the function, we need to first find the second derivative of the function.

y = 3x² - 2x + 4

Taking the first derivative of y with respect to x

y' = 6x - 2

Taking the second derivative of y with respect to x:

y'' = 6

So the second derivative of y is a constant 6.

To find the curvature of the curve at point x = 2, we need to evaluate the following formula:

k = |y''| / [1 + (y')²][tex]^{(3/2)}[/tex]

Substituting x = 2 and y'' = 6, we get:

k = |6| / [1 + (6x2 - 2)²][tex]^{(3/2)}[/tex]

= 6 / [1 + (22)²][tex]^{(3/2)}[/tex]

= 6 / [1 + 484][tex]^{(3/2)}[/tex]

= 6 / 485[tex]^{(3/2)}[/tex]

k ≈ 0.0002

Hence,  the curvature of the curve defined by the function y = 3x² - 2x + 4 at point x = 2 is approximately 0.0002.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Find the curvature of the curve defined by the function

y=3x^2 -2x + 4

at point x =2

Answer:

d

Step-by-step explanation:

To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:

Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5

Next year's estimated budget is £6,032 per quarter.

To calculate the percentage difference, we can use the following formula:

Percentage difference = (new value - old value) / old value x 100%

Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%

Therefore, the answer is (d) 3.9%.

The number of ways of selecting a committee of 4 women and 3 men from  8 women and 5 men is 700 ways

First, we shall obtain the number of ways to choosing a committee of 4 women from 8 women. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(8, 4) = 8! / [4!(8 - 4)!]

C(8, 4) = 70 ways

Next, we shall obtain the number of ways to choosing a committee of 3 men from 5 men. This is given below:

C(n, r) = n! / [r!(n - r)!]

C(5, 3) = 5! / [3!(5 - 3)!]

C(5, 3) = 10 ways

Finally, we shall determine the Total ways of selecting the committee. Details below:

Total ways of selecting = [C(8, 4)] × C(5, 3)]

Total ways of selecting = 70 × 10

Total ways of selecting = 700 ways

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Answer:

.343656

Step-by-step explanation:

e-5x+1=2

Subtract the 1 to the other side.

e-5x=1

Subtract e to the other side (e is approximately 2.718)

-5x=-1.718

Divide by -5.

x=.343656

.1.1(2-√√-225) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

To solve this problem, we first need to simplify the expression inside the parentheses. The square root of a negative number is an imaginary number, so we can write the expression as follows:

2.1.1(2-√-225) = 2.1.1(2-√(-1)(225))

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We can then simplify the expression as follows:

2.1.1(2-√(-1)(225)) = 2.1.1(2-i*15) = 2.1.1(2-15) = 2.1.1(-13) = -27.31

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The second problem is a bit more complicated. We need to use the fact that the square root of a negative number is an imaginary number. We can write the expression as follows:

3+√-18 = 3+√(-1)(18)

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We can then simplify the expression as follows:

3+√(-1)(18) = 3+i*3 = 3+3i

The ratio that represents Stefan's share is given as follows:

5/14.

Roman is the person that will get more money.

The shares are obtained applying the proportions in the context of the problem.

Stefan and Roman share some money in the ratio 5:9, hence the denominator of the fraction is given as follows:

5 + 9 = 14.

Then the shares are given as follows:

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The measure of side TR is given as follows:

TR = 6.7.

Similar triangles are triangles that share these two features listed as follows:

As the triangles in this problem are similar, the proportional relationship for the side lengths is given as follows:

TR/35 = 5/26.

Hence the length of side TR is given as follows:

TR = 35 x 5/26

TR = 6.7.

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There were 172 children and 165 adults admitted to the amusement park.

Given that the admission fee for children is $1.50, so the total amount collected from children is 1.5c.

Similarly, the admission fee for adults is $4, so the total amount collected from adults is 4a.

We are also given that the total number of people admitted to the park is 337, so we can write the following equation based on the number of people:

c + a = 337

The total admission fees collected is $918.

1.5c + 4a = 918

Now we have a system of two equations.

From the first equation, we can express 'c' in terms of 'a':

c = 337 - a

Substituting this value of 'c' into the second equation:

1.5(337 - a) + 4a = 918

505.5 - 1.5a + 4a = 918

2.5a = 918 - 505.5

2.5a = 412.5

a = 412.5 / 2.5

a = 165

Substituting the value of 'a' back into the first equation:

c + 165 = 337

c = 337 - 165

c = 172

Therefore, there were 172 children and 165 adults admitted to the amusement park.

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