A hotel offers a reward program based on the number of nights stayed. The function f(x) represents the number of free nights earned as a function of x, the number of nights stayed. f(x) = Left-bracket StartFraction x Over 10 EndFraction right-bracket Which describes the meaning of f(x)? A customer earns 1 free night per 10 nights stayed. A customer starts with 1 free night and then earns another free night after every 10 nights stayed. A customer earns x – 10 free nights for every 10 nights stayed. A customer earns 10 free nights after x number of nights stayed.

Answer:

C. 6x^2 + 47

Step-by-step explanation:

The value of  f[g(x)]  is 6x² +47, the correct option is C.

A function is a law that derives a relation between two variables.

The function is f(x) = 6x+11

g(x) = x² +6

The operation f(g(x)) = 6 (x² +6) +11

f(g(x)) = 6x² +36 +11

f(g(x)) = 6x² +47

Therefore, the value of  f[g(x)]  is 6x² +47, the correct option is C.

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Answer:

(-x-7)(x+8)

Step-by-step explanation:

-x²-8x-7x-56

-x(x+8)-7(x+8)

(-x-7)(x+8)

Answer:

it is -1(x+8)(x+7)

Answer:

[tex](A)\dfrac{5s^7}{6}\\(B)s^5\\(E)-6rs^5 \\(F)\dfrac{4r}{5^6}[/tex]

Step-by-step explanation:

A polynomial is said to be in standard form when it is written in descending order of the given variable.

From the given polynomial

[tex]+ 8r^2s^4 - 3r^3s^3[/tex]

Therefore, a first term of the polynomial must satisfy the following:

The following satisfies these conditions:

[tex](A)\dfrac{5s^7}{6}\\(B)s^5\\(E)-6rs^5 \\(F)\dfrac{4r}{5^6}[/tex]

Answer:

Show one example of his claim, adding two odd numbers to form an even number

Answer:

C.

Step-by-step explanation:

You cannot prove his conjecture by an example. You must create two generic odd numbers using algebraic expressions. Then you add the two expressions and show that the sum is even.

Answer: C.

Answer:

x = 2

Step-by-step explanation:

I believe the equation you are trying to write is log of 16 with base of 4x-6 is equal to 4, and if that is the case then your answer is 4.

Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well

===================================================

Explanation:

P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55

Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.

The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".

We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.

Answer:

10% of the people at the picnic are neither.

Step-by-step explanation:

To get the answer,

1/2 + 2/5 = 9/10

10/10 - 9/10 = 1/10

1/10 = 10%

Thanks, I hope I got this right!

Answer:

1.08

Step-by-step explanation:

1.01 < x < 1.17

x ≠ 1.20

x ≠ 1.008

x = 1.08

x ≠ 1.18

x ≠ 1.8

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

Option C is the correct answer.

We have,

To determine which number completes the inequality, we need to find the number that is greater than 1.01 but less than both 1.17 and 1.20.

Among the given options, the number that satisfies this condition is 1.08.

Thus,

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

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Answer:

5

Step-by-step explanation:

March,May,June,July,August

Answer:

[tex]Dina= 35[/tex]

Step-by-step explanation:

Given

[tex]Ratio = 4:2:5[/tex]

Peter = 14 more A's than Chris

Required

How many A’s did Dina get?

The order of the ratio is Peter: Chris: Dina

This implies that

[tex]Peter: Chris: Dina = 4:2:5[/tex]

Considering Peter and Chris

[tex]Peter: Chris = 4:2[/tex]

Let the number of Chris' A's be represented by A

This implies that:

Peter's = 14 + A

And as such;

[tex]14 + A : A = 4 : 2[/tex]

Convert ratio to division

[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]

Multiply both sides by A

[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]

[tex]14 + A = \frac{4}{ 2}* A[/tex]

[tex]14 + A = 2* A[/tex]

[tex]14 + A = 2 A[/tex]

Subtract A from both sides

[tex]14 + A-A = 2 A-A[/tex]

[tex]14 = A[/tex]

This means that;

Chris answered 14 while Pete answered 28 (14 + 14)

Considering Chris and Dana

[tex]Chris :Dana = 2:5[/tex]

Replace Chris with 14

[tex]14:Dana = 2:5[/tex]

Convert ratio to division

[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]

Cross Multiplication

[tex]Dina * 2 = 14 * 5[/tex]

Divide both sides by 2

[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]

[tex]Dina= \frac{14 * 5}{2}[/tex]

[tex]Dina= \frac{70}{2}[/tex]

[tex]Dina= 35[/tex]

Hence, Dina had 35 A's

Answer: x = 3

Step-by-step explanation:

-3x+7= -2

     -7    -7

-3x = -9     (divide by -3) ( remember negatives cancel each other out)  

x = 3

Answer:

x=3

Step-by-step explanation:

The first thing that I did to solve this equation was do the opposite of the positive 7 so I subtracted 7 on both sides.

-3x + 7 = -2

      -7  = -7

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

-3x       = -9

Now we have the equation of -3x = -9. From there we will do the reciprocal of -3x so we will divide it on both sides.

-3x/-3 = -9/-3

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

x         =   3

And now we have the answer of x=3.

Answer:

Resistance of 8 feet wire = 0.81 Ω

Step-by-step explanation:

Equation representing the relation between the resistance and length of a cylindrical shaped wire is,

R = ρ.[tex]\frac{l}{A}[/tex]

Here R = Resistance of the cylindrical wire

ρ = Resistivity of the material

l = Length of the wire

A = Cross sectional area of the wire.

If length of the wire = 160 ft

Resistance = 16.2 Ω

By substituting these values in the formula,

16.2 = ρ.[tex]\frac{160}{A}[/tex]

ρ = [tex]\frac{16.2\times A}{160}[/tex]

Similarly, if length of the same wire = 8 ft

From the given formula,

R = ρ.[tex]\frac{8}{A}[/tex]

R = [tex]\frac{16.2\times A}{160}\times \frac{8}{A}[/tex]

  = 0.81 Ω

Therefore, resistance of 8 feet wire will be 0.82 Ω.

Answer:

Independent variable = t

Dependent variable = N

Step-by-step explanation:

Given that the function N(t)=100+15t represents the relation between the number of unread emails, N, and the time, t, measured in days

The independent variable is an input which can be controlled. In the function

N(t)=100+15t

The independent variable is t

While the dependent variable is the output of a function when independent variable has been substituted.

In the function N(t)=100+15t

The number of unread messages depends on the number of time t measured in days as the number of unread messages N is a function of t.

Therefore, the independent variable is N.

Answer: A. 31%

Step-by-step explanation:

First you need to find the area within each circle. This can be found by using the formula: pi * r^2

The area of the circle with radius 8mm is 64 * pi. The area of the circle with radius 14mm is 196 * pi.

196 * pi = 615.75216

64 * pi = 201.06193

Now divide the larger area by the smaller area to get how many times larger the large area is than the small area.

615.75216 / 201.06913 = 3.06239

3.06239 rounds up to 3.1

Now we know the radius of 14mm has an area 3.1 times the area of 8mm. The area of an 8mm radius has 31% of the area of a 14mm radius.

Answer:

0.190

Step-by-step explanation:

I just took the quiz it's 0.190

Probability is the chance of an event to occur from a number of possible outcomes.

The probability of win and away game is 4/21.

It is the chance of an event to occur from a number of possible outcomes.

It is given by:

Probability = Number of required event / Total number of outcomes

We have,

The table with the win and loss record for a local basketball team.

             Home game     Away game

Win            8                       4

Losses       3                       6

The number of games played:

= 8 + 4 + 3 + 6

= 21

The probability of win and away game is:

= 4 / 21

Thus,

The probability of win and away game is 4/21.

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Answer:

72

Step-by-step explanation:

Step 1: Figure out percentages of what he owns

360(0.4) = 144 models he made

360 - 144 = 216 models he bought.=

Step 2: Figure out percentages of what he donated

144(0.25) = 36 models he donated (he made)

216(0.5) = 108 models he donated (he bought)

Step 3: Find the difference

108 - 36 = 72

And we have our answer!

Answer:

​

h(1)=−31

h(n)=h(n−1)+(−7)

​

Step-by-step explanation:

I got it wrong- and then i found the answer :)

The recursive function is h(n) = h(n−1 ) + (−7) where h(1) = −31.

A rule defined such that its definition includes itself.

Example:

F(x) = F(x-1) + c is one such recursive rule.

Given;

h(1) = −31

This means that the function h(n) has the following parameters:

First term = −31

Rate = -7

Hence, the recursive function is h(n) = h(n−1 ) + (−7) where h(1) = −31.

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Answer:

AD || BC

Step-by-step explanation:

Option B : ∠A+∠D = 180°

Given below diagram is of a parallelogram.

A parallelogram is defined as a closed geometric figure that has got 4 straight sides and  opposite sides are parallel to each other.

One of the properties of a parallelogram is that its adjacent angles are supplementary.

Adjacent angles means angles which are either on the just left side or just right side.,

Supplementary angles are those which if added gives 180° as value.

Option A and D are not correct here.

Option C is wrong as adjacent sides of a parallelogram are never parallel.

Taking the angles ∠A and ∠D, we see they're adjacent. And since ABCD is a parallelogram, thus by its property, we've got ∠A+∠D = 180°.

Thus option B: ∠A+∠D = 180° is correct.

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Answer:

Option B

Step-by-step explanation:

I can't do the 'figure question' because it lacks info, but I can answer the point-slope question.

Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' - slope

'(x1, y1)' - point

We are given the slope of 3 and the point (-1, 5).

Replace 'x1', 'y1', and 'm' with the appropriate values.

[tex]y-y_1=m(x-x_1)\rightarrow \boxed{y-5=3(x+1)}[/tex]

Option B should be the correct answer.

Answer:

Step-by-step explanation:

Common ratio = 2nd term/1st term = 4/-16 = -1/4

[tex]a_{n}=a_{n-1}*r\\a_{n}=a_{n-1}*\frac{-1}{4}\\\\a_{n}=\frac{-1}{4}a_{n-1}[/tex]

Answer:

Common ratio = 2nd term/1st term = 4/-16 = -1/4

Step-by-step explanation:

Y = 2x + 5

By plugging the slope and coordinates into point slope form, you can get the answer in slope intercept form.

Answer: Y=24000-3000x

9000=24000-3000x

-15000=-3000x

x=5 years

first we need to set the equation

at plug in all the information we have. In our case, we know cars value or y =9000, we need to find what is the x value

2

we need to subtract 24000 on both sides, and then divide by -3000 on both sides, and find out for x in years

Step-by-step explanation:

The model of the car's value, y, in dollars, after x years is:

y = -3000x + 27000

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

Let x represent the number of years and y represent the value in dollars.

Since the new car worth is $27000, hence b = 27000. Also it depreciating in value by $3,000 per year, hence m = -3000. The car value is given by:

y = -3000x + 27000

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Answer:

  5

Step-by-step explanation:

The number of cells in a tile is 4, so the board dimension cannot be odd, but must be a multiple of 2 in order to have the number of cells divisible by 4.

If the tiles are colored in an alternating pattern, tiles must have 3 of one color and 1 of the alternate color. Hence the total number of tiles used to cover a board must be even (so the numbers of each color match). Then the board dimension must be divisible by 4.

In the given range, there are 5 such boards:

  4×4, 8×8, 12×12, 16×16, and 20×20

Answer: The vertex of the function is (-1, -7).

Step-by-step explanation: We are given to find the vertex of the following function.

We know that the vertex of the function is given by (h, k).

So, for the given function f(x), the vertex will be (-1, -7).

The graph of the function f(x) is shown in the attached figure, where the vertex is at the point (-1, -7).

Thus, the vertex of the function is (-1, -7).

The vertex of the function  f(x) = |x + 1| - 7 is (-1,-7)

The function is given as:

f(x) = |x + 1| - 7

The above function is an absolute value function

An absolute value function is represented as:

f(x) = a|x – h| + k

Where, the vertex is (h,k)

So, we have:

(h,k) = (-1,-7)

Hence, the vertex of the function  f(x) = |x + 1| - 7 is (-1,-7)

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Answer:

Proportion of blue marbles in in sample = 9/40

Step-by-step explanation:

Total number of blue marbles in a jar is given by 25%

Lets find the probability of blue marble in the jar of the given sample:

Proportion of blue marbles in in sample = Total number of blue marbles in sample/ Total number of marbles in sample

Where

Total number of blue marbles in sample = 9

Total number of marbles in sample = 9 + 15 + 16

Total number of marbles in sample = 40

SO

Proportion of blue marbles in in sample = 9/40

or

Proportion of blue marbles in in sample = 9/40

Answer:

It'll take approximately 34 years from today.

Step-by-step explanation:

in order to solve this problem we first need to find the rate of change, "k", to do that we will use the given information where the population was 1400 five years ago and its now 1000. Applying this data to the equation gives us:

[tex]A = A_0*e^{k*t}\\1000 = 1400*e^{5*k}\\1400*e^{5*k} = 1000\\e^{5*k} = \frac{1000}{1400}\\ln(e^{5*k}) = ln(\frac{1000}{1400})\\5*k = ln(1000) - ln(1400) \\k = \frac{ln(1000) - ln(1400)}{5} = -0.06729[/tex]

We now know the value for "k", we can estimate how many years it will take for the bird population to dip below 100. We have:

[tex]100 = 1000*e^{-0.06729*t}\\e^{-0.06729*t} = \frac{100}{1000}\\ln(e^{-0.06729*t} = \frac{1}{10}\\-0.06729*t = ln(0.1)\\t = -\frac{ln(0.1)}{0.06729} = 34.22[/tex]

It'll take approximately 34 years from today.

Answer:

O C. y = 3.80.2.01%

Step-by-step explanation:

ur welcome

The exponential regression equation that fits these data is y= 2.26 (3.0[tex]2)^x[/tex].

As, in an exponential function is one in which an independent variable, x, is increased to the power of a constant.

As a result, when plotting these data points, we see that an exponential curve provides the best fit, and the following equation provides the best fit is

y= 2.26 (3.0[tex]2)^x[/tex]

Thus, the requires exponential regression equation is y= 2.26 (3.0[tex]2)^x[/tex].

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Answer: C

Step-by-step explanation:

The slope stays the same but the y-intercept is moved up 7 units.

Answer:

y = -4x - 13

Step-by-step explanation:

Use point - slope form to convert to y = mx + b form

1. Find the slope using y2 - y1 / x2 - x1

    3 + 5 / -4 + 2

    m = -4

2. Plug into point - slope form: y - y1 = m (x - x1)

    y + 5 = -4 (x + 2)

    Distribute

    y + 5 = -4x - 8

    Subtract 5 from both sides

    y = -4x - 13