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The total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.

According to the question,

We have the following information:

You built a driveway ½ mile long to your new house. You have an 8-foot-wide road ditch on both sides of the road.

a) Now, the length of the ditch will be equal to the length of the driveway.

Length of ditch = 1/2 mile

b) Measurement of the road ditch in square feet:

Area of rectangle = length*width

Converting length into feet:

1 mile = 5280 feet

1/2 mile= 2640 feet

Area of ditch =(2640)*8

Area of ditch =21,120 square feet

Now, ditch is on both sides:

So, total area of ditch = 2*21,120

Total area of ditch = 42,240 square feet

Hence, the total length of the road ditch is 1/2 mile and the measurement in square feet of the road ditch is 42,240 square feet.

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Answer: 0.051, 0.134, 0.2, 0.46

Step-by-step explanation:

Step-by-step explanation:

[tex] \sf - 18p = p^2+81 [/tex]

Moving all the expression to the Left side of the equation,

[tex] \sf -18p + p^2 - 81 = 0 [/tex]

To find the discriminant of the above equation we can simply use the Quadratic formula.

The discriminant formula of a quadratic equation[tex] \sf ax^2 + bx + c = 0 \: is \: (d = b^2 - 4ac )[/tex]

Where d represents the discriminant

a, b and c are the coefficient of the above equation,

p^2, here coefficient of p² is a = 1

-18p, here coefficient of p is b = -18

81, here the number is constant so coefficient is c = 81.

So simply by substituting the value of a, b and c in the above discriminant formula we get,

[tex] \sf d = b^2 - 4ac [/tex]

[tex] \sf d = (-18)^2 - (4 \times 1 \times 81) [/tex]

[tex] \sf d = 324 - 324[/tex]

[tex] \sf d = 0 [/tex]

Therefore, The discriminant of 18p = p² + 81 is 0.

Answer:

0 (zero)

Step-by-step explanation:

To find the discriminant of the quadratic equation -18p = p² + 81, we first need to rewrite the equation in standard form, which is of the form ax² + bx + c = 0.

[tex]\begin{aligned}-18p&=p^2+81\\p^2+81&=-18p\\p^2+81+18p&=-18p+18p\\p^2 + 18p + 81 &= 0\end{aligned}[/tex]

Compare the coefficients of the rewritten quadratic equation with the standard form:

The discriminant of a quadratic equation in the form ax² + bx + c = 0 is given by the formula:

[tex]\boxed{\textsf{Discriminant} = b^2 - 4ac}[/tex]

Substitute the values of a, b, and c into the formula:

[tex]\begin{aligned}\textsf{Discriminant} &= (18)^2 - 4(1)(81)\\&=324-4(81)\\&=324-324\\&=0\end{aligned}[/tex]

Therefore, the discriminant of the given quadratic equation is zero.

The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.

Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.

Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.

Every function has a domain (input variable) and a range (output variable) or codomain.

Constant donation = $7

Variable donation per mile = $0.25

Function, F(d) = 7 + 0.25m

where d = the total amount donated

m = the total miles the person walks

Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.

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Each set of prices should be matched with the correct percentage of increase or decrease as follows:

Mathematically, percentage increase can be calculated by using this formula:

Percentage increase = [original price - new price]/new price × 100

At original price: $63.00 and new price: $56.07, we have:

Percentage decrease = [63.00 - 56.07]/56.07 × 100

Percentage decrease = 6.93/56.07 × 100

Percentage decrease = 0.124 × 100

Percentage decrease = 12.4%.

At original price: $98.00 and new price: $108.78, we have:

Percentage increase = [108.78 - 98.00]/98.00 × 100

Percentage increase = 10.78/98.00 × 100

Percentage increase = 0.11 × 100

Percentage increase = 11%.

At original price: $37.50 and new price: $34.50, we have:

Percentage decrease = [37.50 - 34.50]/34.50 × 100

Percentage decrease = 3/34.50 × 100

Percentage decrease = 0.087 × 100

Percentage decrease = 8.7%.

At original price: $12.25 and new price: $13.23, we have:

Percentage increase = [13.23 - 12.25]/12.25 × 100

Percentage increase = 0.98/12.25 × 100

Percentage increase = 0.08 × 100

Percentage increase = 8%.

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Answer:

4(13)

Step-by-step explanation:

[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]

Answer:

Below

Step-by-step explanation:

Any of the following  

-9    -8   -7   -6   -5   -4   -3  -2

The change in temperature in United States since last night is -6 degree centigrade.

Given the temperature in United States last night is = -9 degree C

Now the temperature is = -3 degree C

So the change in temperature is given by,

= Final Temperature - Initial Temperature

= -9 - (-3)

= -9 + 3

= -6 degree C

Hence the change in temperature in United States since last night is -6 degree centigrade.

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The true equations are :

2 + 7 = 9

8 × 5 = 4 0

6 ÷ 3 = 2

2 - 1 = 1

We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.

The first true equation is 2 + 7 = 9.

The second true equation is 8 × 5 = 4 0.

The third true equation is 6 ÷ 3 = 2.

The fourth true equation is 2 - 1 = 1.

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Answer:

t - 10 = 61

Step-by-step explanation:

We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61

so t = 71.

The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

In the question ,

it is given that ,

the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,

In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .

In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .

that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

let us find the roots of the function ,

f(x) [tex]=[/tex] 0

x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0

taking x³ common ,

x³(x² - 8x [tex]+[/tex] 16) = 0

x³(x² - 4x - 4x + 16) = 0    .... by using splitting the middle term method

x³(x(x - 4) - 4(x - 4)) = 0

x³(x - 4)(x - 4) = 0

which means x³ [tex]=[/tex] 0   and x-4 = 0  

that is x=0    and x = 4 .

So , the roots of the function f(x) are x=0 and x=4 .

This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.

Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³  is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .

The given question is incomplete , the complete question is

What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?

(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞

(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞

(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞

(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞

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Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.

When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.

Hope this helps.

Step-by-step explanation:

After finding the rate of change, this table representing a linear function can be completed as follows:

x                         y

1                        0

2                       10

5                       40

10                      90

Mathematically, the rate of change can be calculated by using this formula;

Rate of change, k = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, k = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x as follows:

Rate of change, k = (40 - 0)/(5 - 1)

Rate of change, k = 40/4

Rate of change, k = 10.

For the first blank, we have:

10 = (40 - y)/(5 - 2)

10 = (40 - y)/3

30 = 40 - y

y = 40 - 30

y = 10.

For the second blank, we have:

10 = (90 - 40)/(x - 5)

10 = (50)/(x - 5)

10x - 50 = 50

10x = 50 + 50

10x = 100

x = 10.

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Answer:

3/2 month

Step-by-step explanation:

Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?

When x = months:

Sandy: 10x + 60

Randy: 20x + 45

You are looking for x when:

Sandy = Randy

10x + 60 = 20x + 45

subtract 45 from both sides:

10x + 60 - 45 = 20x + 45 - 45

10x + 15 = 20x

subtract 10x from both sides:

10x + 15 - 10x = 20x - 10x

15 = 10x

divide both sides by 10:

15/10 = 10x/10

x = 15/10

reduce:

x = 3/2

It will take 3/2 months of Sandy and Randy to have the same amount of money.

[3/2 month also equals 1.5 months, depending on the format of the answer you need]

The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario

Let the number of hours be given as h.

Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:

c = 3 + (5 × h)

c = 3 + 5h

where c = total cost

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Answer: put it in a caculator

Step-by-step explanation:

Combine 18x^3 and 5x^3.

Combine x^2 and 6x^2.

Combine 9x and −14x.

Add −3 and 11.

The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.

It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:

= 16 + 15 + 16 + 8 + 17

= 72 feet

The area will be:

= Area of triangle + Area of rectangle

= (1/2 × base × height) + (length × width)

= (1/2 × 8 × 17) + (15 × 16)

= 68 + 240

= 308ft²

Therefore, the correct option is B.

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The probability that the sum of the two die rolls is 9 is 4 / 11.

Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that the sum of the two die roll is 9 = number of sides that roll a sum of 9 / total number of sides that at least one of them is a 5

number of sides that roll a sum of 9 =(4,5) (6 , 3), (3 , 6), ( ,4) = 4

total number of sides that at least one of them is a 5 = (1, 5), (2, 5), (3, 5), (4, 5) , (5, 5), (6, 5), (5, 1), (5, 2) , (5, 3), (5, 4), (5, 6) = 11

Probability that the sum of the two die roll is 9 = 4/11

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The office manager will either put up a clearer calculation and model the equation to ascertain money remaining at each quaintly bought or a graph to present his calculations

A graph is a representation of data, it helps to analyze data clearly with lesser time

The calculation the office manager will do is to multiply the number of lamps with the unit price then subtract from the amount set aside to spend on new equipment

The calculation

let the money left be z

10000 = 300 * 72 + z

10000 = 21600 + z

subtraction

z = 10 000 - 21600

z = - 16000

The calculation shows that the money will not be enough

The equation is modeled as

y = 10000 - 300x

where x is the number of bulbs

y is amount left

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In hypothesis testing, the assumption for the Ztest for a mean when the σ is known then n > 30. Hence the answer is : None of the above

Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis. Given the data, the test provides evidence for the hypothesis's plausibility.

Statistical analysts put a hypothesis to the test by measuring and examining a random sample of the population under consideration. Because the distributions of small samples are not normal, a t-test is required. If the sample size is large (n> 30), statistical theory predicts that the sample mean is normally distributed and that a z test for a single mean can be used.

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Answer:  

48

Step-by-step explanation:

The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d)  .

In the question ,

four set of sides is given ,

we need to find the set of side that forms a right triangle ,

we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .

Option(a)

the sides are 4 , 8 , 11.

4 + 8 = 11

16 + 64 = 121

80 = 121

we know that 80 121 ,

So , the sides do not form a right triangle

Option(b)

the sides are 6 , 8 , 13

6 + 8 = 13

36 + 64 = 169

100  169

we know that 100 169 ,

So , the sides do not form a right triangle .

Option(c)

the sides are √3, √5 , 8

√3 + √5 = 8

3 + 5 = 64

8 = 64

we know that 8  64 ,

So , the sides do not form a right triangle .

Option(d)

the sides are √3, √13 , 4

√3 + √13 = 4

3 + 13 = 16

16 = 16

Yes , the sides form a right triangle .

Therefore , The sides {√3 , √13 , 4} forms a right triangle  .

The given question is incomplete , the complete question is

Determine which set of side measurements could be used to form a right triangle ?

(a) 4, 8, 11

(b) 6, 8, 13

(c)√3, √5,8

(d)√3, √13, 4

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By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).

A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

In order to plot the system of equations on a graph, we would simplify the second equation as follows:

4u = 2v - 12

Dividing both sides of the equation by 4, we have the following:

4u/4 = 2v/4 - 12/4

u = v/2 - 3

Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.

By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).

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Answer:

b)  f(x) = -16x² + 8x + 30

Step-by-step explanation:

When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.

The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.

Therefore,  f(x) = -16x² + 8x + 30  could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.

If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).

if  price on the tag was $28, but Benjamin paid $15.40 before tax then the percent of discount is 45%.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Benjamin went shopping for a new phone because of a sale. The price on the tag was $28, but Benjamin paid $15.40 before tax

We need to find the percent discount that Benjamin received

Compare the difference between the original price and the discounted price to the original price, and then express that difference as a percentage of the original price.

We can use the following formula:

Percent Discount = (Original Price - Discounted Price) / Original Price × 100%

=28-15.4/28 × 100

=0.45×100

=45%

Hence, Benjamin received a discount of 45%

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The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr

Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray

The equation below relates the radiation intensity and distance:

I₁/I₂ = D₂²/D₁²

where:  I₁ = intensity  at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source

Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot

Using the formula:

100/I₂ = 1²/9²

100/I₂ = 1/81

I₂ = 100 × 81

I₂ = 8100 mR/hr

I₂ = 8100×10⁻³ R/hr                (1 mR/hr = 1×10⁻³ R/hr)

I₂ = 8.1 R/hr

Therefore, the radiation intensity in Roentgens is 8.1 R/hr

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The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively

We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:

sin = opposite/hypotenuse

cos = adjacent/hypotenuse

tan = opposite/adjacent or tan = sin/cos

The opposite is the side the angle of consideration is facing

The hypotenuse is the side the right angle  is facing

The adjacent is the side left after determining the opposite and hypotenuse

1st triangle

tan 25° = b/8   (tan = opp/adj)

b = 8 tan 25° = 3.73m

2nd triangle

sin 21° = x/22    (sin = opp/hyp)

x = 22 sin 21° = 7.88 units

3rd triangle

cos 47° = 28/x    (cos = adj/hyp)

x =  28/cos 47° = 41.06 units

4th triangle

Use Pythagoras' theorem:

12² = 8² + y²

y² = 12² - 8²

y² = 144 - 64

y² = 80

y = √80 = 8.94 units

Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units

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The measurement of angles ∠1 is 126° and ∠2 is 154°.

According to the question,

We have the following information:

We have a figure of two triangles and some of the measurements of the angles are given.

We know that the sum of three angles of a triangle is 180°.

So, for the larger triangle, we have the following expression:

96+30+third angle = 180

Third angle = 180-126

Third angle = 54°

We know that sum of angles on a straight line is 180°.

So, we have:

∠1+54 = 180

∠1 = 180-54

∠1 = 126°

Now, finding the sum of angles in smaller triangle:

126+28+third angle = 180

Third angle = 180-154

Third angle = 26°

Now, angle 2 and this angle will make a straight line.

∠2+26 = 180

∠2 = 180-26

∠2 = 154°

Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.

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The average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.

According to the question,

We have the following information:

A local video store has seen good linear growth in rentals since 2005. In 2009, the store had 23,500 rentals. In 2015, the store had 28,540 rentals.

a) Average rate of change of store's rentals =(Rentals in 2015-rentals in 2009)/Number of years

Now, the number of years passed between 2009 and 2015 is 6 years.

So, we have:

Average rate of change = (28540-23500)/6

Average rate of change = 5040/6

Average rate of change = 840 rentals per year

b) Now, the number of rentals in 2005:

(Number of rentals in 2009-number of rentals in 2005)/4 = 840

Let's take the number of rentals in 2005 to be x.

(23500-x)/4 = 840

23500-x = 3360

-x = 3360-23500

-x = -20140

x = 20,140

Hence, the average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.

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Answer:

Exact Form: 16/3

Decimal Form: 5.3

Mixed Number Form: 5 1/3

Step-by-step explanation:

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .