The sum of two numbers is 15. Using x to represent the smaller of the two numbers, translate "the sum of twice the smaller number and two more than the larger num ber" into a variable expression. Then simplify.

it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\) Thus, option C is correct.

The correct function that models this scenario is:

\(C(x) = 3.75x if x < 6\)

\(C(x) = 3.25x + 5 if x > = 6\)

This is because for rentals less than 6 hours, the cost is simply $3.75 per hour, so the function is  \(C(x) = 3.75x\)  . For rentals of 6 hours or more, there is a discounted hourly rate of $\(3.25\) per hour, but there is also a $5 processing fee, so the function is \(C(x) = 3.25x + 5\)  .

Option (a) is incorrect because it does not include the $5 processing fee for rentals of 6 hours or more.

Option (b) is incorrect because it has the wrong conditions for the hourly rate discounts. It specifies that the discount starts at x = 6, but the correct condition is \(x > = 6.\)

Option (c) is correct, as it has the correct conditions and the correct formula for calculating the cost.

Option (d) is incorrect because it has the wrong condition for the hourly rate discounts (x < 5 instead of x < 6), and it does not include the $5 processing fee for rentals of 6 hours or more.

Therefore, it has the correct conditions and the correct formula for calculating the cost. \(C(x) = 3.25x + 5 if x > = 6\)

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The acceptable and realistic ways to to change the confidence interval to contain zero are;

Reasons:

The confidence interval is given by the following formula;

\(CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}\)

When the mean, \(\overline x\), is positive and large, both values, \(\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}\), and \(\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}\), will be positive.

Therefore, Martha has to either intervene to reduce the mean also known as x-bar

Increasing the confidence level will increase the allowable error such that \(\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}\), and the interval will contain zero

Therefore;

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Answer:

7x2−4x/5

Step-by-step explanation:

7x2−4x over 5

To create a spider plot showing the effect on profit of varying the availability of resources, follow these steps:

1. Start by setting up your base-case values for each resource. This will be the starting point for your spider plot.

2. Next, create a series of data points for each resource by varying its availability between 90% and 110% of the base-case value in 2% increments. For example, if the base-case value for a resource is 100, you would create data points at 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, and 110.

3. Plot these data points on a spider plot, with the base-case value at the center and the varying values radiating outwards. Each resource should have its own line or "spider leg" on the plot.

4. Finally, add labels and a legend to your spider plot to make it easy to understand which resource is represented by each line and what the varying values mean.

By following these steps, you can create a spider plot that clearly shows the effect on profit of varying the availability of resources.

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Answer:

Step-by-step explanation:

question

Answer:

the tank at the pet store

Step-by-step explanation:

5x4x2 = 40

35<40

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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The values of {m} that is greater than 4.6 represent the solution of the given inequality.

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

The given inequality is -

5m - 7 > 16

Adding 7 on both sides, we get -

5m - 7 + 7 > 16 + 7

5m > 23

m > 23/5

m > 4.6

Therefore, the values of {m} that is greater than 4.6 represent the solution of the given inequality.

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Answer:

The valid point is (5/2, 5)

Step-by-step explanation:

In order to check which ones are valid we will apply all of them to the expression.

(5,15):

\(\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}5 - \frac{1}{5}15 \geq 0\\\\-1 \geq 0\)

False.

(1/2, 5):

\(\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{1}{2} - \frac{1}{5}5 \geq 0\\\\-\frac{4}{5} \geq 0\)

False.

(5/2, 5):

\(\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}\frac{5}{2} - \frac{1}{5}5 \geq 0\\\\0 \geq 0\)

True.

(2,5):

\(\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}2 - \frac{1}{5}5 \geq 0\\\\-\frac{1}{5} \geq 0\)

False

(-1,0):

\(\frac{2}{5}x - \frac{1}{5}y \geq 0\\\\\frac{2}{5}(-1) - \frac{1}{5}0 \geq 0\\\\-\frac{2}{5} \geq 0\)

False.

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer: 12* 0 *(0 + 3) or 12*-3 *(-3+3)

Probably not formatted correctly

the area of the rectangle will be 1.5w².

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Area of rectangle is A = a*b

The given length of the rectangle is w

The width will be 1.5w

So the rectangle of the white figure is Area = w*1.5w = 1.5 w²

hence the area of the rectangle will be 1.5w².

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Answer:

f(x) = x⁴-11x³+37x²-29x-78

Step-by-step explanation:

The zeros -1 and 6 are real zeros, so we'll use them directly.

The zero 3-2i is complex, and ALL complex zeros come in pairs. So we use the complex conjugate of 3-2i for the other zero: 3+2i.

Now, set up your factors. There are four zeros, so four factors:

(x- -1)(x-6)(x-(3-2i))(x-(3+2i)) = (x+1)(x-6)(x- 3-2i)(x- 3+2i)

Next, the instructions say "with real coefficients" so we must multiply everything out and combine like terms. I recommend starting with the two real factors: (x+1)(x-6) = x²-5x-6.

then multiply the two complex factors:

    (x- 3-2i)(x- 3+2i) = x²-3x+2ix-3x+9-6i-2ix+6i-4i² [remember that i²=-1!!]

                              = x²-6x+13

and finally multiply the two trinomials that you get; you'll have 9 terms to combine.

Answer:

14.6

Step-by-step explanation:

using the trigonometry ratio

cosine

cos35= 12/BC

BC= 12/cos35

BC = 14.64

Answer:

\(A = 2\)

\(B = -1\)

\(C = -9\)

Step-by-step explanation:

Given

\(2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C\)

Required

Find A, B and C

Rearrange the expression

\(2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C\)

\(2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C\)

To do this, we simply compare the expressions on both sides of the equation.

So, we have:

\(Ax\² = 2x\²\) --- (1)

\(8Ax + Bx = 15x\) --- (2)

\(16A + 4B + C = 19\) --- (3)

Divide both sides by x² in (1)

\(Ax\² = 2x\²\)

\(A = 2\)

Divide both sides by x in (2)

\(8Ax + Bx = 15x\)

\(8A + B = 15\)

Substitute 2 for A.

\(8*2 + B = 15\)

\(16+ B = 15\)

Make B the subject

\(B = 15 - 16\)

\(B = -1\)

Substitute 2 for A and -1 for B in (3)

\(16A + 4B + C = 19\)

\(16*2 + 4*-1 + C = 19\)

\(32 - 4 + C = 19\)

\(28 + C = 19\)

Make C the subject

\(C = 19 - 28\)

\(C = -9\)

Answer:

it D

Step-by-step explanation:

I just used elimination like a small brain

like so

when a = 1, b = 0, c = 3, d = -3

x^3 + 8x – 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D

Answer:

See Below

Step-by-step explanation:

The boundary line follows the graph of y = 2x - 4 because it represents the line of maximum or minimum values the graph could take. y = 2x - 4 has a y-intercept of -4 because it is in slope-intercept form. It also has a slope of 2, so to find another point on the line, you can go up two and right one. Also, this inequality has a solid line because it is "less than or equal to" and a solid line represents the values that equal.

Answer:

  x = 2

  m = 15/4

  a = 5/4

Step-by-step explanation:

When the "base" lines are parallel, all of the triangles are similar. That means corresponding segments are proportional, including corresponding parts of segments.

We see that x corresponds to a partial segment marked 3. That same top-bottom correspondence has another pair of segments marked 2 and 3. That means x=2.

  x/3 = 2/3   ⇒   x = 2

__

The segments marked 'm' and 'a' are "whole side" segments, so we need to put those in proportions with corresponding whole sides. If we use the bottom side, we find ...

  a/3 = 5/(3+6+3) = 5/12   ⇒   a = 5/4 = 1 1/4 . . . . . multiply by 3

and

  m/(6+3) = 5/12   ⇒   m = 15/4 = 3 3/4 . . . . . multiply by 9

__

  x = 2

  m = 15/4

  a = 5/4

Answer:

3, 2√2, √7

Step-by-step explanation:

compute the square roots of the next three prime numbers:

√7

√11

√13

Therefore, the next three terms of the sequence are:

{1, √2, √3, 2, √5, √7, √11, √13}

chatgpt

chat

Answer:

Area of Shaded Area = 18.3

Step-by-step explanation:

P.S - The exact question is -

Given - In the following diagram, a quarter circle has been constructed using an isosceles right triangle whose legs measure 8 inches.

To find - Which of the following represents the area of the shaded region, rounded to the nearest tenth of a square inch?

Proof -

We know that,

Area of a quarter circle = \(\frac{1}{4} \pi r^{2}\)

Also,

We know that ,

Area of isosceles Triangle = \(\frac{1}{2}*Base*Height\)

Now,

Given that,

Radius of quarter circle = 8 inches

Base of Isosceles Triangle = 8 inches

Height of Isosceles Triangle = 8 inches

∴ we get

Area of a quarter circle = \(\frac{1}{4} \pi (8)^{2}\) = 16\(\pi\)

Area of isosceles Triangle = \(\frac{1}{2}*8*8\) = 32

Now,

Area of Shaded area = Area of a quarter circle - Area of isosceles Triangle

                                 = 16\(\pi\) - 32

                                 = 50.265 - 32

                                 = 18.265 ≈ 18.3

⇒Area of Shaded Area = 18.3

Answer:

$312

Step-by-step explanation:

10% of $600 is $60

So $60*4=$240

$600-$240=$360

1%=$6

So $6*8=$48

$360-$48=$312

The domain of the expression is \((-\infty, \infty)\) because the expression is a polynomial.

This is the same as the set of all real numbers.

Answer:

The desired dot product is -1

Step-by-step explanation:

To find the dot product of the given vectors, multiply the magnitudes of the 'i' and 'j' terms together, separately, and then add the results:

dot product of u and v = (-4)(2) + (7)(1) = -8 + 7 = -1

The desired dot product is -1

Answer:

The volume of a rectangular prism is the product of the length, width, and height. In this case, the length is 38 inches, the width is 26 inches, and the height is 20 inches. So the volume is:

38 inches * 26 inches * 20 inches = 19,760 cubic inches

Therefore, the maximum amount of food that the container can hold is 19,760 cubic inches of food.

Step-by-step explanation:

The maximum amount of dog food the storage container can hold is 19,760 cubic inches of food. Hence, option (c) is the correct option.

To solve the question :

In order to find the maximum amount of dog food the storage container can hold, it is required to calculate the volume of the rectangular prism i.e.,

V = l × w × h

Given dimensions of the storage box,

The length (l) = 38 inches

The width (w) = 26 inches, and

The height (h) = 20 inches.

Hence, the volume :

V = 38 × 26 × 20

V = 19,760 cubic inches of food

The maximum amount of dog food the storage container can hold is 19,760 cubic inches.

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Answer:

True

Step-by-step explanation:

The statement given above in the question is correct. It is mentioned that men are free to create a list of women's according to their preferences. There will be order sequence of women and men places them in queue of their preference. The men proposes the women with highest ranking in the list then it is possible that all men gets their preferred choice.

Answer:

1 out of 6

Step-by-step explanation:

Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.

Answer:

11,100

Step-by-step explanation:

1% of 30,000 is 300 so if we times 300 by 37 we get 11,100

there is 11,100 sheep in 37%.

hope this helps :)

Answer:

C) 0.36

Step-by-step explanation:

4÷11= 0.36363636363636

so it's 0.36 with a line over it indicating a repeating decimal

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

13. The difference of two matrices is the term-by-term difference. For example, the bottom right term is the difference of the bottom right terms ...

  (-6) -(5) = -11

__

14. The scalar multiple of a matrix is the scalar multiplied by each term of the matrix. For example, the upper right term is ...

  3(1) = 3

__

15. The matrix product is the dot product of the rows of the left matrix with the columns of the right matrix. For example, the product term in row two, column one is the dot product of row 2 of C and column 1 of B:

  [9, -2, 4]·[-2, -7, 10] = 9(-2) +(-2)(-7) +4(10) = -18 +14 +40 = 36

_____

It is convenient to let an appropriate tool help with this. Many graphing calculators and spreadsheets are able to do these functions easily.

Answer:

  a) increasing (0, ∞); decreasing (-∞, 0)

  b) min: (0, 0); max: DNE

  c) inflection points: (-√6/3, 1/4), (√6/3, 1/4);

      up: (-√6/3, √6/3); down: (-∞, -√6/3) ∪ (√6/3, ∞)

Step-by-step explanation:

The intervals of increase or decrease can be found from the sign of the slope, that is, the sign of the first derivative. That derivative is ...

  f'(x) = ((x^2 +2)(2x) -x^2)(2x)/(x^2 +2)^2

  f'(x) = 4x/(x^2 +2)^2

(a) f'(x) is positive for x > 0, hence ...

  the function is increasing on (0, ∞)

  the function is decreasing on (-∞, 0)

__

(b) f'(x) is zero for x=0, a local minimum. f(0) = 0.

  minimum: (0, 0)

  maximum: DNE

__

(c) The second derivative is ...

  f''(x) = ((x^2+2)^2·4 -(4x)(2)(x^2 +2)(2x))/(x^2 +2)^4

  = (8 -12x^2)/(x^2 +2)^3

Inflection points are where the second derivative is zero, or ...

  8 -12x^2 = 0

  x^2 = 2/3

  x = ±√(2/3) = ±(√6)/3

The values of f(x) there are x^2/(x^2 +2) = (2/3)/(2/3 +2) = (2/8) = 1/4

The points of inflection are (x, y) = (-√6/3, 1/4), (√6/3, 1/4).

The function is concave up between these inflection points

  f(x) is concave up on the interval (-√6/3, √6/3)

  f(x) is concave down on (-∞, -√6/3) ∪ (√6/3, ∞)

Answer:

if you are trying to find x:

c) 1/12=x     d)1/30=x

Step-by-step explanation:

2/3x=8

2=24x

1/12=x

3/5x-10=8

3/5x=18

3=90x

1/30=x