A suite in a deluxe hotel is rented for 1, 2, or 4 days. The
hotel charges a $100 deposit and $100 per day. Identify the
function that describes this situation and its domain and
range.

In a direct proof, evidence is used to support a claim, On the other hand, a counterexamples is a single example that show the contradictions in a claim.

Evidence means any piece of information that supports the argument being made in a proof which could include mathematical formulas, logic, or theorems that have been previously proven.

Counterexamples are specific examples that disprove a statement made in a proof and are used to show that a proof is not valid and that the argument being made is flawed.

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Step-by-step explanation:

Hi there!

According to the question;

The gradient of line is 1/2 and passes through the point (4,-2).

Since, It has one point and gradient we use one point formula to find the equation of the line.

Note:

One point formula: (y-y1) = m (x-x1)

(4,-2) = (x1,y1)

So, using this formula we get;

(y+2) = 1/2(x-4)

Multiply both sides by 2.

2(y+2) = (1/2)*2(x-4)

2y+4 = x-4

Take 2y+4 in right side

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

Therefore, x-2y-8 = 0 is the required equation.

Hope it helps!

Hi there!

We're given the following information:

With this information, we can go ahead and plug the data into the point slope equation: y - y₁ = m(x - x₁).

Plug in 1/2 for m, and (4,2) for x1 and y1:

\(\sf{y-y_1=m(x-x_1)}\)

\(\sf{y-(-2)=\dfrac{1}{2}(x-4)}\)

\(\sf{y+2=\dfrac{1}{2}(x-4)}\)

\(\sf{y+2=\dfrac{1}{2}x-2}\\\sf{y=\dfrac{1}{2}x-2-2}\\\\\sf{y=\dfrac{1}{2}x-4}\)

Hence, y = 1/2x - 4.

I hope that helps! :)

If f (x) < g(x) for all real 1; The expression that must be true is I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x III. f(x)dx ≤ [8(x)dx is option D. I and II only

I. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f'(c) = (f(b) - f(a)) / (b - a) and g'(c) = (g(b) - g(a)) / (b - a). Since f(x) < g(x) for all x, we have f(b) - f(a) < g(b) - g(a), so f'(c) < g'(c), and thus, f'(x) < g'(x) for all x.

II. f(x) and g(x) have continuous first and second derivatives everywhere, so by the mean value theorem, there exists a point c in the interval (a, b) such that f''(c) = (f'(b) - f'(a)) / (b - a) and g''(c) = (g'(b) - g'(a)) / (b - a). Since f'(x) < g'(x) for all x, we have f'(b) - f'(a) < g'(b) - g'(a), so f''(c) < g''(c), and thus, f''(x) < g''(x) for all x.

III. This statement is not necessarily true. The definite integral of f(x)dx is equal to the area between the curve and the x-axis, and the definite integral of g(x)dx is equal to the area between the curve and the x-axis. The definite integral of a function does not depend on the value of the function at each point, but on the overall shape of the curve, so it is not guaranteed that f(x)dx ≤ g(x)dx just because f(x) < g(x) for all x.

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The complete question goes thus:

Let f and g have continuous first and second derivatives everywhere. If f (x) < g(x) for all real 1; which of the following must be true? I f'(x)sg'(x) for all real x II. f'(x)≤g'(x) for all real x

III. f(x)dx ≤ [8(x)dx

(A) None

(B) I only

(C) III only

(D) I and II only

(E) I, II, and III

Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

Answer:

The two numbers are 182 and 210. I hope this will help you.

Answer:

118 inches

Step-by-step explanati

1 yard is 36 inches, so you just do the math

36+36+36=108+10=118

The minimum average cost per unit is calculated to be 90.1 dollars per unit when 90 units are produced.

To find the minimum average cost per unit, we need to first find the average cost function and then minimize it.

The average cost function is given by AC(x) = C(x)/x.

Substituting C(x) in the above equation, we get:

AC(x) = (810 + 0.1x²)/x

To find the minimum average cost, we need to take the derivative of the average cost function with respect to x, set it equal to zero, and solve for x:

d/dx [AC(x)] = (0.1x² - 810)/x² = 0

0.1x² - 810 = 0

x² = 8100

x = 90

Therefore, producing 90 units will result in a minimum average cost per unit.

To find the minimum average cost per unit, we can substitute x = 90 in the average cost function:

AC(x) = (810 + 0.1x²)/x

AC(90) = (810 + 0.1(90)²)/90

AC(90) = 90.1 dollars per unit (rounded to one decimal place)

Hence, the minimum average cost per unit is 90.1 dollars per unit when 90 units are produced.

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Answer: 12:2, 6:1, 24:4

Step-by-step explanation:

To cover 10000 steps the time taken will be 115 minutes and he will cover at 9:55 AM.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at 8 a.m., Sothy goes for a walk and plans to walk `10000` steps. At 8:23 a.m., his phone tells him that he has taken `2000` steps.

The time will be calculated as,

2000 steps ⇒ 23 minutes

1 Step ⇒ 23 / 2000 minutes

10000 steps ⇒ ( 23 x 10000) / 2000 minutes

10000 steps ⇒ 115 minutes

The time of covering 10000 steps will be at 9:55.

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\(\huge \sf༆ Answer ༄\)

Using section formula ~

\( \sf x = \dfrac{ mx_2 + nx_1}{m + n}\)

\( \sf y = \dfrac{ my_2 + ny_1}{m + n}\)

Midpoint divides a line into ratio of 1 : 1, therefore the values m and n are equal to 1

\( \sf x = \dfrac{ x_2+ x_1}{1 + 1}\)

\( \sf y= \dfrac{ y_2+ y_1}{1 + 1}\)

Next step :

Use the coordinates of given points to find the coordinates of mid point ~

that is ;

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = \dfrac{2 + 3}{2} \)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = \dfrac{2 + 5}{2} \)

Next step :

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:x = 2.5\)

\({ \qquad{ \sf{ \dashrightarrow}}}  \:  \: \sf \:y = 3.5\)

So, the required option is ~

\( \large \sf {(2.5 \: , \: 3.5)}\)

Answer:

11,880.

Step-by-step explanation:

This is given by the number of permutations of 4 from 12

= 12P4

= 12!/(12-4)!

= 12!/8!

=  (12*11*10*9*8*7*6*5*4*4*2*1) / (8*7*6*5*4*4*2*1)

= 12^11*10*9

= 11,880.

Answer:

X = -3.5

Step-by-step explanation:

Answer:

-7/2

Step-by-step explanation:

4x+16=2

  -16      -16

4x= 2-16

4x=-14

/4    /4

x= -7/2

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius is given as,

r = 36 / 2

r = 18 inches

The area of the circle is given as,

A = π x (18)²

A = 3.14 x 324

A = 1,017.36 square inches

The number of square inches of cloth cut from the square will be 1,017.36 square inches. Then the correct option is A.

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The complete question is given below.

A circle is cut from a square piece of cloth, as shown:

A square, one side labeled as 36 inches, has a circle inside it. The circle touches all the sides of the square. The portion of the square outside the circle is shaded.

How many square inches of cloth is cut from the square?

(π = 3.14)

1,017.36 in2

1,489.24 in2

1,182.96 in2

1,276.00 in2

\(f(t)=0.4(1.16)^{t-1}\qquad \begin{cases} x=0.4\\ y=1.16 \end{cases}\implies f(t)=xy^{t-1} \\\\[-0.35em] ~\dotfill\\\\ xy^{t-1}\implies xy^t y^{-1}\implies x\cfrac{y^t}{y}\implies \cfrac{x}{y}y^t\implies \stackrel{\textit{substituting back}}{\cfrac{0.4}{1.16} ~~ (1.16)^t} \\\\\\ \stackrel{\textit{"r" is positive, \Large Growth}}{\cfrac{0.4}{1.16} ~~ (1+0.16)^t \implies f(t)~~ \approx ~~ 0.34 ~~ (1+0.16)^t}\qquad \begin{cases} a\approx 0.34\\\\ r=0.16 \end{cases}\)

Answer:

89, 98

Step-by-step explanation:

When you reverse the digits of the number 89,

the number becomes 98.

98 - 89 = 9

The sum of the digits of the number 89 is

8 + 9 = 17

To find the vertical asymptotes of a rational function, we need to set the denominator equal to zero and solve for x.

To find the vertical asymptotes of a rational function, you need to determine the values of x that make the denominator of the function equal to zero.

Let's check the limit of our example function as x approaches each of the vertical asymptotes:

As x approaches 1 from the left side: f(x) approaches negative infinity

As x approaches 1 from the right side: f(x) approaches positive infinity

Therefore, x = 1 is a valid vertical asymptote.

As x approaches 3 from the left side: f(x) approaches positive infinity

As x approaches 3 from the right side: f(x) approaches negative infinity

Therefore, x = 3 is also a valid vertical asymptote.

The values of x that make the denominator zero are the vertical asymptotes of the function.

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Answer:

All are acute

Step-by-step explanation:

Acute angles are any angles that are less than 90°.

Right angles are angles that measure 90°.

Obtuse angles are angles that are more than 90°.

As we can see, 24, 29, and 32 are all less than 90°, making them all acute.

Best of Luck!

Answer:

Angles A and C are alternate exterior angles.

Answer:

Step-by-step explanation:

Let the volume of 25% ethanol be x, then volume of 85% ethanol will be (20 - x)

The ethanol content is:

11.67 gallons of 25% ethanol and

20 - 11.67 = 8.33 gallons of 85% ethanol

Answers:

1.) 1 and 1/2

2.) 1/2

Answer:

1.A=bh/2

2A=bh

2A/b=h

  answer                   check

2.f(x)=21-6x               f(5)=21-6(5)            

 g(x)=2x/5-11            f(5)=21-30

21-6x=2x/5-11            f(5)=-9

21=32x/5-11              g(5)=2(5)/5-11

(5)32=32x/5(5)         g(5)= 10/5-11

160=32x                    g(5)=2-11

5=x                             g(5)=-9

3. f(7)=3(7)-7

   f(7)= 21-7

   f(7)= 14

Step-by-step explanation:

Answer:

x ≤ -15

x ≥ -8

Step-by-step explanation:

filled line is either ≤ or ≥

≤ - line to the left

≥ - line to the right

The rate at which the swimming pool fill, in gallons per minute is 9 gallons per minute which is the D option.

It is given in the question that it takes 14 minutes to fill the swimming pool with 126 gallons of water.

We have to find the rate at which the swimming pool fill, in gallons per minute.

We know that,

Rate at which the swimming pool fill = Total gallons of water/ Time taken to fill

Hence, we can write,

Rate at which the swimming pool fill =  126 gallons/14 minutes = 9 gallons/minute which is the D option.

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With a speed of 6.67 ft/sec is the length of her shadow moving when she is 25 ft from the base of the pole.

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

15 dx/dt = 6(4+dx/dt)

15 dx/dt = 24 +6 dx/dt

15 dx/dt -6 dx/dt = 24

9 dx/dt = 24

dx/dt = 24/9 = 2.67 ft/sec for how fast her shadow was lengthening.

The speed of the length of her shadow would be this speed added to her traveling speed: 2.67 + 4 = 6.67 ft/sec.

Therefore, 6.67 ft/sec is the required answer.

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Step-by-step explanation:

For this given problem we have the following statements and reasons:

1) SD is vertical to HT,

Reason: Given

2) SDH and SDT are right angles

Reason: Right angle congruence theorem

3) SH=≈ST

Reason: Given

4) BD=≈BD

Reason: Reflexive property

5) SHD=≈STD

Reason: SAS

This is not a probability model because at least one probability is less than 0

From the question, we have the following parameters that can be used in our computation:

Color      Probability

Red          0.3

Green      -0.2

Blue         0.2

Brown      0.4

Yellow      0.2

Orange     0.1

The general rule is that

The smallest value of a probability is 0, and the maximum is 1

In the above, we have

P(Green) = -0.2

Hence, it is not a probability model

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Question

Color      Probability

Red          0.3

Green      -0.2

Blue         0.2

Brown      0.4

Yellow      0.2

Orange     0.1

determine why it is not a probability model. choose the correct answer below.

a. this is not a probability model because the sum of the probabilities is not 1.

b. this is not a probability model because at least one probability is greater than 0.

c. this is not a probability model because at least one probability is less than 0.

d. this is not a probability model because at least one probability is greater than 1.

The rule is to take your x, y, coordinate and take the opposite of each sign in order to rotate 180 degrees. Hence, if C is at 36, C's image point will be at -3, - 6. In quadrant 3, right here, the picture point will be.

Therefore, the correct option is a) (-3, -6)

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