A garden is in the shape of a square with a perimeter of 36 feet. The garden is surrounded by two
fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from th
first fence on the outside. If the material used to build the two fences is $1.15 per foot, what was the
total cost of the fences?

The distance of P at north of Q is 34.98 km.

The distance of P at east of Q is 19.39 km.

The distance of P at the given directions is calculated by resolving the vector into vertical and horizontal components.

The distance of P at north of Q is calculated as follows;

Py = d sinθ

Py = 40 km x sin (61)

Py = 34.98 km

The distance of P at east of Q is calculated as follows;

Px = d cosθ

Px = 40 km x cos (61)

Px = 19.39 km

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Answer:

Step-by-step explanation:

To calculate the stock price, you can multiply the earnings per share (EPS) by the benchmark PE ratio.

The stock price would be:

$3.64 x 21 = $76.44

So you would pay $76.44 per share for the stock of The Dahlia Flower Company.

Answer:

We can solve this equation by using substitution. We substitute each value of x in the given set and check which one makes the equation true.

Let’s start with A. 8(x - 20) = 304 becomes 8(49 - 20) = 304 which simplifies to 8(29) = 304 which is not true.

Let’s try B. 8(x - 20) = 304 becomes 8(none of these - 20) = 304 which simplifies to 8(-20) = 304 which is not true.

Let’s try C. 8(x - 20) = 304 becomes 8(29 - 20) = 304 which simplifies to 8(9) = 304 which is not true.

Finally, let’s try D. 8(x - 20) = 304 becomes 8(21 - 20) = 304 which simplifies to 8(1) = 304 which is not true.

Therefore, none of these values of x make the equation true

Step-by-step explanation:

Answer: 5.26

Step-by-step explanation:

458,930/87,178 =
5.264 =
5.26

The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Answer: Yes

Step-by-step explanation:

For questions like this, youve been given a value for x, and a value for y.

Plug in and see if it works out!

[tex]3x^2- 6x - 9 = y[/tex]

[tex]3(1)^2- 6(1) - 9 = -12[/tex]      ----- Plugging in for x and y

[tex]3 - 6 - 9 = -12[/tex]

[tex]-12 = -12[/tex]

Since -12 is indeed equal to -12, we conclude the statement is true;

In terms of the graph, this translates to, "Yes, the point (1, -12) is on the graph of [tex]y = 3x^2- 6x - 9[/tex]

So your answer is Yes

The standard form equation of the ellipse as described in the task content is;

It is evident from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the x-axis and b represents the distance from the center to each vertex on the y-axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/2² + y²/5² = 1

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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The length of the hypotenuse is 28.3

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

A right angle triangle is a triangle that has one of it's angles has 90°. And Pythagoras theorem is applied to only right angled triangle.

If a and b are the legs of the triangle and c is the other side(hypotenuse) then,

c² = a²+b²

c² = 19² +21²

c² = 361+441

c² = 802

c = √802

c = 28.3

therefore , if the two legs are 19 and 21, the length of the other side is 28.3

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Its value is always one greater than the sample size.

In statistics, the degree of freedom represents the number of values in the final calculation of a statistic that is open to varying. In other terms, it is the number of distinct data points used to calculate a statistic.

The degree of freedom (df) for a sample data set is equal to the sample size minus one (df = n - 1), where 'n' represents the sample size. This means that the sample size is always one less than the degree of freedom.

The answer choices do not accurately depict the concept of the degree of freedom. The sum of all differences between the data values and the sample mean may not equal zero. The value of the degree of freedom does not always equal the sample size; rather, it is always one less than the sample size. Therefore, the correct statement is always that its value exceeds the sample size by one.

Although part of your question is missing, you might be referring to the full question:
Which of the following is true with regard to the degree of freedom?
The sum of all the differences between the data value and the sample mean can be any number
The sum of all the differences between the data value and the sample mean is always zero
Its value is always one more than the sample size
Its value is the same as the sample size

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Using percentage, the correct answer is "The value of P is $3,500 and it corresponds to 70% of her salary".

The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. In ratio form, it is expressed as 30:100, and in fraction form, as 30/100. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100".

First, we need to calculate L.

1/3 or 33.33% of L spend on gift.

2/5 or 40% of L spent on savings.

This would leave her with $200 for miscellaneous expenses:

= 100% - (33.33% + 40%)

= 100% - 73.33%

= 26.67%

So, 26.67% = $200 for miscellaneous expenses

Rule of three, to calculate L.

26.67% is $200.

100% will be:

= (100 X 200) ÷ 26.67

= 20000 ÷ 26.67

= $750

L= $750

Now we going to calculate K.

"K is twice the amount of L".

K = L X 2

K = 750 X 2

K= $1,500

Finally, we going to calculate P.

P = J - K

J = $5,000

K = $1,500

P =$5,000 - $1500

= $3,500

Rule of three

5000 is 100%

3500 will be:

= 3500 x 100 ÷ 5000

= 350000 ÷ 5000

P = 70%

The value of P is $3,500 and it corresponds to 70% of her salary.

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Answer:

Answer is B. 3x^2 +2x - 2.5

Step-by-step explanation:

Just factor out and simplify.

[tex]\frac{0.25x^2*(3x^2+2x-2.5)}{0.25x^2}[/tex]

x cannot be 0 or else the denominator is 0 making the function undefined.

Answer:

it is B

Step-by-step explanation:

The six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

To find 6 rational numbers between 3 and 4, we can start by finding the difference between 4 and 3, which is 1.

We can then divide this difference by any number and add it to 3

So that the number will be less than 4 but greater than 3

Now, we can add this gap size successively to 3, starting with the first rational number after 3, to find the six rational numbers between 3 and 4:

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

So, the six rational numbers between 3 and 4 are: 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

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3√4x/5

the / slash before the 5 is over so you put the 3√4x at the top of the fraction and the 5 at the bottom, so it would be 3√4x divide 5

Answer:

a. The linear model that represents the height of the plant after d days can be expressed as:

h(d) = 1.5d + 5

where h(d) is the height of the plant in centimeters after d days, and 1.5d represents the growth rate of 1.5 cm per day multiplied by the number of days (d). The constant term 5 represents the initial height of the plant, which is 5 cm.

b. To find the height of the plant after 20 days, we can substitute d = 20 into the linear model:

h(20) = 1.5(20) + 5

= 30 + 5

= 35

So, the height of the plant after 20 days will be 35 cm.

The answer to each statement are:

a. ST is tangent to circle R at point T - True

b. m<RST ≅ m<SRT - False

c. m<STR ≅ m<QPR - True

A tangent is a straight line drawn in such a way that it intersects externally a point on the circumference of a circle. Thus it touches a circle externally at a point on its boundary.

Considering the diagram and information given in the question, given a circle with center R and tangents PQ, ST. It can be deduce that the statements that are true or false are:

i. ST is tangent to circle R at point T - True

ii. m<RST ≅ m<SRT - False

ii. m<STR ≅ m<QPR - True

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Answer:

16

Step-by-step explanation:

starting from month 2, how many more months will A be as tall as B?

A grows at 1.75 in per month

B grows at 1.5in per month

so 7.5+1.75x = 11+1.5x

solve for x

x=14

so from month 2, need to go for another 14 mos.

so at month 16, they'll be same height

Answer: you pay 18$

Step-by-step explanation:96 ounce×1pound/16ounce×3$/1pound=18$

The amount the cashier charged is incorrect. Based on the given information, the amount of fruit purchased is 96 ounces, which is equivalent to 6 pounds. Therefore, the total cost of the fruit should be 6 pounds x $3 per pound = $18.

The error the cashier made was converting ounces to pounds incorrectly. 96 ounces is equivalent to 6 pounds, not 1,536 pounds. The cashier multiplied 96 by 16 (the number of ounces in a pound) instead of dividing by 16 to get the number of pounds.

14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

What is the Central Limit Theorem (CLT)?

According to the CLT, the distribution of sample means from a population with mean μ and standard deviation σ, will be approximately normal with mean μ and standard deviation σ/√n, where n is the sample size.

In this case, the population mean is 589 grams and the population standard deviation is 16 grams. We are picking a sample of 23 fruits at random, so the standard deviation of the sample means will be:

σ/√n = 16/√23 ≈ 3.33

To find the value of x such that 14% of the time the sample mean will be greater than x, we need to find the z-score that corresponds to the 86th percentile of the standard normal distribution. We can use a table or a calculator to find that z-score:

z = invNorm(0.86) ≈ 1.08

The sample mean is normally distributed with a mean of 589 grams and a standard deviation of 3.33 grams. Using the formula for z-score:

z = (x - μ) / (σ / √n)

We can solve for x:

x = z × (σ / √n) + μ

x = 1.08 × (16 / √23) + 589

x ≈ 594.33 grams

Therefore, 14% of the time the mean weight of 23 fruits will be greater than approximately 594.33 grams.

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The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.

Here we have

The inequality |2x + 2| > 6

To graph the solution to the inequality |2x + 2| > 6,

we can start by rewriting the inequality as two separate inequalities without the absolute value:

2x + 2 > 6 or 2x + 2 < -6

Simplifying these inequalities, we get:

2x > 4 or 2x < -8

x > 2 or x < -4

Therefore,

The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.

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Answer:

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] - [tex]\frac{1}{3}[/tex]

[tex]\frac{9}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{5}{12}[/tex]

Helping in the name of Jesus.

Answer: x=22

Step-by-step explanation:

see image for explanation

The leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I is 10

If a third-degree function has zeros 14, I, and -I, it can be factored as: f(x) = a(x - 14)(x - I)(x + I)

'a' denotes the leading coefficient.

We may use the knowledge that the function's output is -110 when x = 3 to calculate the value of 'a'.

Substituting x = 3 into the function's factored form yields:

f(3) = a(3 - 14)(3 - I)(3 + I) = -110

When we simplify this equation, we get:

a(-11)(3 - I)(3 + I) = -110

a(-11)(9 - I^2) = -110

a(-11)(9 + 1) = -110 (since I2 = -1)

a(-11)(10) = -110

-110a = -1100

a = 10

Hence , the third-degree function's leading coefficient is 10.

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Answer:

155000 milliliters of water

Step-by-step explanation:

We Know

The platoon drank 155 liters of water.

How many milliliters did the platoon drink?

1 liter = 1000 milliliters

155 liters = 155 x 1000 = 155000 milliliters of water

So, the platoon drank 155000 milliliters of water.

The platoon drank 155,000 milliliters of water.

1 liter = 1000 milliliters

Therefore, 155 liters = 155,000 milliliters

So, the platoon drank 155,000 milliliters of water.

Answer: ∠HDG

Step-by-step explanation:

Starting Angle: ∠HDE

Possible Supplement: ∠HDG

The polynomial function of lowest degree with rational coefficients P(x) = x⁴ + 20x² - 125

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

To find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. √5,5i​.

Since √5 and 5i​ are zeros, then their conjugates -√5, and -5i​ are also zeros.

So,

So, the factors of the polynomial are

So, multiplying the factors together, we get the polynomial.

So, P(x) = (x  - √5)(x - 5i)(x + √5)(x + 5i)

= (x  - √5)(x  + √5)(x - 5i)(x + 5i)

= [x² - (√5)²][x² - (5i)²]

= [x² - 5][x² - (5²i²)]

= [x² - 5][x² - 25(-1))]

= [x² - 5][x² + 25]

Expanding the brackets, we have

= [x² - 5][x² + 25]

= [x² × x² + 25x² - 5x² + 25 × (-5)]

= x⁴ + 20x² - 125

So, P(x) = x⁴ + 20x² - 125

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Option B is correct because the tangent of angle a is greater than 1 when a is between 0 and pi/4. Option G is correct because the tangent of angle a is also greater than 1 when a is between 3pi/4 and pi.

When tan(a) > 1, this means that the tangent of angle a is greater than the length of the adjacent side divided by the length of the opposite side in a right triangle. Since the adjacent and opposite sides of a unit circle have a length of 1, this means that the opposite side of angle a is less than 1.

To determine where angle a could be on the unit circle, we need to find the angles whose tangent is greater than 1. Since tangent is positive in the first and third quadrants, the angles we need to consider are in the first and third quadrants.

In the first quadrant, the angle whose tangent is 1 is pi/4, and the tangent increases as the angle increases. Therefore, angle a could be between 0 and pi/4 (option B).

In the third quadrant, the angle whose tangent is 1 is 5pi/4, and the tangent decreases as the angle increases. Therefore, angle a could also be between 3pi/4 and pi (option G).

Therefore, options B and G are correct, and angles a could be located in the regions described by these options on the unit circle.

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The approximate solution(s) to the given functions are x= -4/3, 3/2.

The given functions are f(x)=6x² and g(x)=x+12.

Set the functions equal to each other, then solve for the variable.

f(x)=g(x)

6x² = x+12

6x²-x-12=0

By splitting middle term we get

6x²-9x+8x-12=0

3x(2x-3)+4(2x-3)=0

(2x-3)(3x+4)=0

2x-3=0 and 3x+4=0

x= -4/3, 3/2

Therefore, the approximate solution(s) to the given functions are x= -4/3, 3/2.

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this is the total cost for the round trip, the answer is (C) 583.20.

what is round trip ?

A round trip refers to a journey from a starting point to a destination and then back to the starting point. In other words, it involves traveling to a place and then returning to the original location.

In the given question,

To calculate the cost of gasoline for the round trip, we need to first find the total amount of gasoline they will use. We can calculate this by dividing the distance of the trip by the RV's average gas mileage:

Total gasoline used = distance ÷ gas mileage

Total gasoline used = 1,701 miles ÷ 10.5 miles per gallon

Total gasoline used = 162 gallons (rounded to the nearest whole number)

Now, we can find the total cost of gasoline by multiplying the total amount of gasoline used by the average cost of a gallon of gasoline:

Total cost of gasoline = total gasoline used × cost per gallon

Total cost of gasoline = 162 gallons × 3.60 per gallon

Total cost of gasoline = 583.20

Since this is the total cost for the round trip, the answer is (C) 583.20.

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Answer:

[tex]\sf{x = 2}[/tex]

Step-by-step explanation:

Question type: solving equations with variables on both sides.

[tex]\textsf{This is a question with variables on both sides, to solve this we need to get the variable x }[/tex]

[tex]\textsf{alone. (getting the x on one side)}[/tex]

--------------------------------------------------------------

[tex]\sf{-2x~+~4~=~2x~-~4[/tex]

Subtract 4 from both sides.

[tex]\sf{-2x~=~2x~-8[/tex]

Subtract 2x from both sides.

[tex]\sf{-4x~=~-8}[/tex]

Divide both sides by -4.

[tex]\bf{x~=~2[/tex]

Therefore, x would be 2.

[tex]-jurii[/tex]

Answer:

x=2

Step-by-step explanation:

We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.

We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.

We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.

We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.