A tour guide organizes vacation packages at a beachside town. There are 7 hotels, 5 cabins, 4 meal plans, 3 escape rooms, and 2 amusement parks. The tour guide chooses either a hotel or a cabin and then selects one of each of the remaining options. FInd the total number of possible vacation packages.

The equations of the lines in the form y=mx+b are-

A line's slope is described like the change in y coordinate to the change in x coordinate. The net y coordinate change is y, whereas the net x coordinate change is x.

Therefore the variation in y coordinate in relation to the variation in x coordinate is written as, dy/dx.

Now, as per the given conditions;

The equation of the line is y = (6 + 4x)²

Simplifying the equation;

y = (6 + 4x)²

  = 36 + 48x + 16x²

y = 16x² + 48x + 36

Now, differentiate the equation to find the tangent slope;

dy/dx = 32x + 48

At the point (6,900),

dy/dx = 32(6) + 48 = 240

Let equation of the tangent at point (a,b) is;

(y - b) = m(x - a)

a = 6, b = 900, m = 240

y - 6 = 240(x - 900)

Write this in y = mx + b form,

y - 6 = 240x - 216000

y = 240x - 215994 (Equation of Tangent line)

The slope of the normal line = -(1/slope of the tangent line) (since they're both perpendicular to each other)

Slope of the normal line = -1/240

The, equation of the normal will become;

y - 6 = (-1/240)(x - 900)

y - 6 = (-x/240) + 3.75

y = (-1/240)x + 9.75

y = - 0.00417x + 9.75 (Equation of Normal line)

Thus, the equation for the normal and tangent has be found.

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The complete question is-

Find the equation of the tangent line and normal line to the curve y = (6 + 4x)² at the point (6,900). Write the equations of the lines in the form y=mx+b. Tangent line: y=

Normal line: y=

Two numbers are drawn without replacement. The only way their product is zero is if one of these numbers is zero. The probability of this happening is

[tex]\dfrac{\dbinom11 \dbinom51}{\dbinom62} = \dfrac{1\cdot5}{15} = \boxed{\dfrac13}[/tex]

In other words,

• there is 1 zero in the list - we draw it with [tex]\binom11 = 1[/tex] way of doing so;

• there are 5 non-zero numbers in the list - we draw 1 of these, with [tex]\binom51 = 5[/tex] ways of doing so;

• there is a total of 6 numbers in the list - we draw 2 of these, with [tex]\binom62 = 15[/tex] ways of doing so.

On the other hand, if the numbers are drawn with replacement and independently of one another, then each number has the same probability of getting drawn each time. There are 6×6 = 36 possible outcomes, each with 1/36 probability of occurring. Their product is zero if at least one of the numbers drawn is zero. The probability of this happening is

[tex]\dbinom21 \dfrac16 \times \dfrac56 + \dbinom22 \left(\dfrac16\right)^2 = \dfrac{11}{36}[/tex]

That is,

• there is 1/6 chance of drawing a zero and 5/6 chance of not drawing a zero. This can selection can happen in [tex]\binom21=2[/tex] ways (zero is drawn first or last);

• there is 1/6 chance of drawing a zero for either selection. This can happen in [tex]\dbinom22=1[/tex] way (zero is drawn both times).

While the probabilities are close, they are not the same! Be careful with which interpretation you choose.

[tex]\dfrac13 = \dfrac{12}{36} > \dfrac{11}{36}[/tex]

Answer:

83/100

Step-by-step explanation:

To turn a decimal into a fraction, place decimal number over its place value.

Place value = 100

Decimal number = 83

Answer:

A triangle can't have two right angles. If a triangle has two right angles, then the sum of its three angles will be more than the two right angles i.e. more than 180∘ which is impossible​.

Answer:

No, it is not possible for a triangle to have two right angles because a triangle's angles add up to 180 degrees, and two right angles add up to 180. A triangle also has three angles, so the third angle cannot be 0 degrees.

The volume of the square frustrum is 1018791.667 cubic feet, the volume of the pyramid is 22019.625 cubic feet and the volume of the Washington Monument is 1040811.292 cubic feet.

The Washington Monument is an obelisc and the volume of the obelisc is the sum of the volumes of the square frustrum and the pyramid, that is:

V = V' + V''                                             (1)

V' = (1 / 3) · (a² + a · b + b²) · h              (2)

V'' = (1 / 3) · b² · h'                                 (3)

Where:

If we know that a = 55 ft, b = 34.5 ft, h = 500 ft and h' = 55.5 ft, then the volume of the Washington monumement is:

V' = (1 / 3) · (55² + 55 · 34.5 + 34.5²) · 500

V' = 1018791.667 ft³

V'' = (1 / 3) · 34.5² · 55.5

V'' = 22019.625 ft³

V = 1040811.292 ft³

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Answer:

144.288

Step-by-step explanation:

yes because I just took the tes

Answer:

y = (-2/3)x + 16/3

Step-by-step explanation:

Any line parallel to y = (-2/3)x has the same slope:  (-2/3).

Then, in this pattern, y = (-2/3)x + c, where c is the y-intercept.

If (4, -8) lives on this new line, then:

-8 = (-2/3)(4) + c, and

-8 = -8/3 + c

This last equation is equivalent to -24/3 + 8/3 + c  => -16/3 = -c.

Therefore the y-intercept is 16/3 = c, and the desired equation is

y = (-2/3)x + 16/3

Answer:

[tex] \large \sf \: 6y - 8[/tex]

Step-by-step explanation:

Let's simplify step-by-step.

8y−2(y+4)

Distribute:

=8y+(−2)(y)+(−2)(4)

=8y+−2y+−8

Combine Like Terms:

=8y+−2y+−8

=(8y+−2y)+(−8)

=6y+−8

=6y−8

Answer:

6y - 8

Step-by-step explanation:

This is a simplifying problem, so we just need to separate and link the like terms.

First we start with the parenthesis by distributing

-2*y + -2*4

-2y - 8

We can the put it back into the equation

8y - 2y + 8

8y and -2y are like terms so we can put them together to get 6y

6y +8

The solution of the graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.

What is Inequality?

To compare two or more mathematical expression in a relation is called an Inequality.

Given that;

The solution sets are;

y < 2x - 8

y > -1/2 x - 3

Now, We draw graph of inequalities.

Then we get,

The graph of the solution set y< 2x - 8 and y > -1/2 x - 3 is shown in image by purple shade.

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Answer:

a = [tex]\frac{d}{M-N^3}[/tex]

Step-by-step explanation:

d = Ma - N³a ← factor out a from each term on the right side

d = a(M - N³) ← isolate a by dividing both sides by M - N³ )

[tex]\frac{d}{M-N^3}[/tex] = a

Answer:

486,732 hope this helps

No the expression x³.x³.x³ is not equivalent to expression x³ˣ³ˣ³.

Given the expression:

x³.x³.x³

here we apply the law of exponent that, when bases are same powers are added.

Two exponential terms with the same base are multiplied, and while the base doesn't change, their powers are added. On the other hand, their powers are removed when two exponential expressions with the same base are split.

therefore, x³.x³.x³ = x ³⁺³⁺³

= x⁹

and in the second expression x³ˣ³ˣ³.

In this expression powers are multiplied.

= x³ˣ³ˣ³.

= x²⁷

therefore both expressions are not equivalent.

Hence the expressions are not equivalent.

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The typical pace of change since the slide's start, -14/3.

Let, the average rate of change is k

(x1,y1) (x2,y2), k= (y2-y1)/(x2-x1)

=10-80/15

=-70/15

k=-14/3

Average = -14/3

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in measurable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The average rate of change is a measure of how quickly on average one quantity changes in relation to another. It provides a general sense of the function's change in value per unit throughout the specified time period. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another. Let's take a closer look at the average rate of change formula.

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Table:

Miles    Hours

  5          4

  40       32

  45       36

The ratio between Miles and Hours is 5:4

In the table, miles = 40 is got by 8 x 5 = 40

So corresponding hours = 8 x 4 = 32

In the table, hours = 36 is got by 9 x 4 = 36

So corresponding miles = 9 x 5 = 45

So the ratios are 5:4 , 40:32, 45:36

Graph can be plotted with number of miles in the x-axis and number of hours in y-axis.

The points to be plotted are (5, 4), (40,32) and (45, 36). Joint these points to get a straight line on the graph.

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Answer:

  11)  KI = 28

  12) PR = 22

Step-by-step explanation:

You want the base segment lengths KI and PR, given relations between those segments and the corresponding midsegment of the triangle.

A midsegment is a line segment that joins midpoints of other line segments, usually the midpoints of triangle sides or opposite sides of a quadrilateral. In the case of a triangle, the midsegment is parallel to the third side, and half its length. This relation is used to solve these problems.

  KI = 2·AB

  (x +37) = 2(x +23) . . . . substitute given expressions

  x +37 = 2x +46 . . . . . . eliminate parentheses

  37 = x +46 . . . . . . . . . . subtract x

  28 = x +37 . . . . . . . . . . subtract 9

The length of KI is 28 units.

  PR = 2·HG

  (x +30) = 2(19 +x) . . . . substitute given expressions

  x +30 = 38 +2x . . . . . eliminate parentheses

  22 = x +30 . . . . . . . . subtract (x+8)

The length of PR is 22 units.

__

Additional comment

As you can see here, there is no real reason to find the value of x, then substitute it back into the expression for the segment of interest. We can, and did, solve directly for the value of that expression.

As with any algebraic manipulation, any operation performed on one side of the equal sign must also be performed on the other side of the equal sign. When we say "subtract ()", we mean "subtract () from both sides of the equation."

In problem 11, x=-9. In problem 12, x=-8. Negative values of x work just fine, as long as the resulting segment lengths are positive.

Answer:

[tex]r \times \cos( 0) = - 6 \\ r = - \frac{6}{ \cos(0) } \\ r = - 6 \sec(0) \\ \\ r \times \cos(0) = 10 \\ r = \frac{10}{ \cos(0) } \\ r = 10 \sec(0) [/tex]

If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.

According to the statement

We have to find that the value of the width.

So, For this purpose, we all know that the

A rectangle may be a form of quadrilateral, whose opposite sides are equal and parallel.

From the given information:

the length of a rectangle is fourfold its width. if the perimeter is at the most 106 centimeters

Then

L = 4w --------The length of a rectangle is fourfold its width.

2w + 2L ≤ 106 ------- the perimeter is at the most 130 centimeters.

Now, if substitute the primary equation into the second inequality you may get

2w + 2 • (4w) ≤ 106.

Therefore, the inequality model becomes 2w + 2 • (4w) ≤ 106.

So, If you solve the inequality you will have a final answer w ≤ 10. The greatest value being 10.

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Answer:

0.5L

Step-by-step explanation:

240ml = 1 cup

120ml = 1/2 cup

80ml = 1/3 cup

60ml = 1/4 cup

^ add together and get 500ml, change unit to liters and your set will hold 0.5l

The roots of the quadratic equation represented by the graph are;  x = -2.5 and x = 2.5.

The solutions to the equation 2x² + x = 11 will be given by the points at which the graph intercepts the x-axis.

By looking at the graph, we can clearly see that the graph intercepts the x-axis at x = -2.5 and x = 2.5.

The roots are located between -3 and 3.

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Answer:

***4.4+ 1.5 * 2 / 0.5*** = 10.4

***3-2.5/3+1 1/3*** = 3.5

Step-by-step explanation:

Yes, the pole will fit in the box when kept diagonally.

In order to fit the pole in rectangular prism or cuboid, it has to be kept diagonally. Now, we need to calculate the length of body diagonal of cuboid. The length of body diagonal of cuboid should be greater than pole to fit it.

The length of body diagonal of cuboid can be calculated by the formula -

Diagonal = √(l² + b² + h²)

Keep the values in formula to find the diagonal of rectangular prism

Diagonal = √(10² + 9² + 8²)

Taking square of the three numbers to find the diagonal of rectangular prism

Diagonal = √100 + 81 + 64

Taking sum of numbers present on Right Hand Side of the equation

Diagonal = √245

Taking square root of the number

Diagonal = 15.65 feet

Hence, as the diagonal of rectangular prism is greater than shower curtain pole, it will definitely fit.

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Answer:

x=5

Step-by-step explanation:

step 1 : exapnding 2(x+4) will give you 2x +8 , the student made an error in expanding

so it should then be 2x+8 = 6x-12

and then if you move the letters to one side and the numbers to the other you will get :

-4x = -20

x=5

hope this works :)

x=5

Step-by-step explanation:

the student added a minus in 2x and 8 when it's suppose to be an addition that is the error

2(x+4)=6(x-2)

2x+8=6x-12

2x-6x=-8-12

-4x=-20

x= -20/-4= 5

x=5

Answer:

455 is the answer of your question

Based on the rowing speed of the team when rowing with the current and when rowing against, the team rowing speed when there is no current is 14 km/h.

Assuming that x is the rowing rate and y is the rate of the current, the equations needed will be:

2 (x + y) = 40

2 (x  - y) = 16

We can add the x-values of the equation to find the value of x which will be the rowing speed without current:

2x + 2x = 40 + 16

4x = 56

x = 56 / 4

x = 14 km /h

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Greetings from Brasil...

Using set theory to solve this question

Let

D = Dogs Set

C = Cats Set

R = Classroom Set

n(D ∪ C) = n(D) + n(C) - n(D ∩ C)

n(D ∪ C) = 14 + 11 - 3

n(D ∪ C) = 22

Then,

Total = n(D ∪ C) + 24

Total = 22 + 24

The total cost is T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/).

Given:

T(x)={a if x≤2, b if x > 2}

let us take

a= 90x, 0≤x≤2

and, b = 180 + 50x  for x>2

Hence. the total cost be T(x)={ 90x if 0≤x≤2, 180+50x if x > 2}

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The approximate length of string lights the staff needs to decorate the ceiling is 40.25

The complete question is added as an attachment

From the attached figure, we have the following coordinates

A = (5, 16)

B = (17, 10)

C = (14, 4)

D = (2, 10)

Calculate the lengths AB and BC using the following distance formula

d = √[(x2 - x1)^2 + (y2 - y1)^2]

This gives

AB = √[(5- 17)^2 + (16- 10)^2] = 13.4

BC = √[(14- 17)^2 + (4- 10)^2] = 6.7

The approximate length of string lights the staff needs to decorate the ceiling is then calculated as

P = 2 * (AB + BC)

This gives

P = 2 * (13.4 + 6.7)

Evaluate

P = 40.2

Hence, the approximate length of string lights the staff needs to decorate the ceiling is 40.25

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Answer: 40.25

Step-by-step explanation:

Here is a simple example of set-builder notation set builder notation it says " the set of all x's, such that X is greater than 0".

The mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

The critical factor for a 90% confidence interval for the true mean repair cost for stereos is given by;

Critical factor = (x-μ)/(s/√n)

where, x = sample mean repair cost

s =  standard deviation of a sample

n = sample of stereos

μ  = critical value

We have been given that a researcher records the repair cost for 13 randomly selected stereos. a sample mean of $⁢85.52 and a standard deviation of $10.81 are subsequently computed.

Since we don't know the population standard deviation, we used t statistics to create the 90% confidence interval in this case.

So, the 90% confidence interval for the true mean repair cost, μ is ;

⇒ P(-2.015 < t₅ < 2.015) = 0.90  

{As the critical value of t at 5 degrees of  freedom are -2.015 & 2.015 with P = 5%}

⇒ P(-2.015 < (x-μ)/(s/√n) < 2.015) = 0.90

⇒ P(-2.015×(s/√n) < (x-μ) < 2.015×(s/√n)) = 0.90

⇒ P(x - 2.015×(s/√n) < μ < x + 2.015×(s/√n)) = 0.90

90% confidence interval for

⇒ μ = (x - 2.015×(s/√n) , x + 2.015×(s/√n))

Here, x = $85.52, s  = $10.81, and n = 13

⇒ μ = (85.52 - 2.015×(10.81/√13) , 85.52 + 2.015×(10.81/√13))

⇒ μ = (79.47, 91.56)

Hence, the mean repair cost for the stereos is (79.47, 91.56) with a 90% confidence interval.

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Answer:

y = m(x) + t

Step-by-step explanation:

Pretty sure this is the right answer...

Hope this helps! :D