Write an equation that has a variable on both sides and x = -11
as a solution.

We know that the sum of all the interior angles of the polygon with sides n is (n - 2)*180.

It is given in the question that,

Sum of all the interior angles of the polygon is 800.

Hence, according to the data given in the question, we can write,

(n - 2)*180 = 800

n - 2 = 800/180

n - 2 = 40/9

n = 40/9 + 2

n = 58/9 = 6.44

As number of sides should always be in integer form, it is not possible to have the sum of all the interior angles of the polygon to be 800 degrees.

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8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, the letters that can be used to create the required three letter word in question: a, b, c, d, e.
Total number of letters that can be used = 5
Total number of vowels in the available letters to be used = 2 ('a' and 'e')
Total number of consonants in the available letters to be used = 3 ('b', 'c' and 'd')
Case 1: A three letter word having all vowels where letters can be repeated
Here, since two letters are to put in three empty positions, the total number of ways to form this word = 2³ = 2 × 2 × 2 = 8
Case 2: A three letter word having all consonants where letters can be repeated
Here, since three letters are to put in three empty positions, the total number of ways to form this word = 3³ = 3 × 3 × 3 = 27
Thus, 8 strings can be formed with all vowels from a, b, c, d, e and 27 strings can be formed with all consonants from a, b, c, d and e.

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The number of sodas sold is 168

The number of hot dogs sold is 56

Total of sodas and hot dogs=224

Let the number of sodas sold be s, and the number of hot dogs sold be s

So we have the following:

s=3h.................i

s+h=224..........ii

we solve the two equation to find the value of s and h,

From equation ii, s=224-h, replacing this in equation i, we have:

224-h=3h

224=4h

h=56

Now, s=3*56

          =168

s=168

Number of sodas=168

Number of hot dog sold=56

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The complete question is given below;

A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Answer:

  a(n) = 10 -3n

Step-by-step explanation:

You want the explicit formula for the sequence recursively defined by a(1)=7, a(n)=a(n-1) -3.

The recursion relation tells you that each term is 3 less than the one before. That is, the common difference between terms is -3.

A sequence with a common difference is an arithmetic sequence. The formula for the n-th term is ...

  a(n) = a(1) +d(n -1)

where a(1) is the first term and d is the common difference.

The first term is given by the recursive definition as 7. Then the explicit formula is ...

  a(n) = 7 -3(n -1)

This can be simplified to ...

  a(n) = 10 -3n

We are going to use these properties :

1. (a^m)^n = a^mn
2. a^m x a^n = a^(m+n)
3. a^m : a^n = a^(m-n)

Using the first property, (3^6)^5 = 3^(6x5) = 3^30

Using the second property :
9 = 3^2
-> 9 x 3^7 = 3^2 x 3^7 = 3^(2+7) = 3^9

Therefore, it is simplified down to 3^30 : 3^9

Finally, we will use the third property :
3^30 : 3^9 = 3^(30-9) = 3^21

The probability that exactly one of the accessories, be 0.678

The probability that exactly two of the accessories, be 0.11

The probability that at least one of the accessories, be 0.884

The probability that at least two accessories, be 0.206

The probability that at most one of the accessories, be 0.794

The probability that at most two of the accessories, be 0.904

The probability that a case or a warranty, but not both be, 0.726

The probability that a case but neither of the other two accessories be, 0.634

The probability that a warranty and a dock but not a case be, 0.018

Given, a computer store compiled data that 500 purchasers of new tablets bought at the same time they bought the tablet.

Let A be the set of purchasers we bought cases,

B be the set of purchasers we bought extended warranty,

C be the set of purchasers we bought dock,

Now, A = 411 , B = 82 , C = 100

also, A∩B = 65 , B∩C = 57 , A∩C = 77 and A∩B∩C = 48 , A'∩B'∩C' = 58

(a) the probability that exactly one of the accessories, be

P(A)-P(A∩B)-P(A∩C)+P(A∩B∩C) + P(B)-P(A∩B)-P(B∩C)+P(A∩B∩C) + P(C)-P(C∩B)-P(A∩C)+P(A∩B∩C) = 411-65-77+48+82-57-65+48+100-57-77+48

= 339/500

= 0.678

(b) the probability that exactly two of the accessories, be

P(A∩B)+P(B∩C)+P(A∩C)-3P(A∩B∩C) = 65+57+77-48-48-48

= 55/500

= 0.11

(c) the probability that at least one of the accessories, be

who bought 1 or 2 or all 3 accessories be,

= 0.678 + 0.11 + 0.096

= 0.884

(d) the probability that at least two accessories, be

who bought 2 or all 3 accessories be,

= 0.11 + 0.096

= 0.206

(e)  the probability that at most one of the accessories, be

who bought nothing or one accessories be,

= 0.116 + 0.678

= 0.794

(f) the probability that at most two of the accessories, be

who bought nothing or 1 or 2 accessories be,

= 0.116 + 0.678 + 0.11

= 0.904

(g) the probability that a case or a warranty, but not both

= 0.822 + 0.164 - 0.26

= 0.726

(h) the probability that a case but neither of the other two accessories

=  0.634

(i) the probability that a warranty and a dock but not a case

= 0.018

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The total amount paid in dollars per hour is $19.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.

We have to find the amount paid per hour.

Total amount given = $133

Number of hour Barn work = 7 hours

Amount paid per hour = 133/ 7

= $ 19

Therefore the amount paid per hour is $19.

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Answer:

A. [tex]y=-3x+16[/tex]

B. [tex]y=3x+5[/tex]

C. [tex]y=\frac{1}{3}x+1[/tex]

Step-by-step explanation:

A.

[tex]y-10=-3(x-2)[/tex]

[tex]y-10=-3x+6[/tex]

[tex]y=-3x+16[/tex]

B.

[tex]y-2=3(x+1)[/tex]

[tex]y-2=3x+3[/tex]

[tex]y=3x+5[/tex]

C.

[tex]y-2=\frac{1}{3}(x-3)[/tex]

[tex]y-2=\frac{1}{3}x-1[/tex]

[tex]y=\frac{1}{3}x+1[/tex]

The simplified expression of the radical expression given as 5√7/√35 is 7

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

5√7/√35

The above expression is a fraction and at the same time it is a radical expression

The denominator of the fraction is √35

So, we start by rationalizing the expression by the fraction

This is represented as

5√7/√35 = 5√7/√35 * √35/√35

Evaluate the products of the numerator

So, we have the following representation

5√7/√35 = 5√245/√35 * 1/√35

Evaluate the products of the denominator

So, we have the following representation

5√7/√35 = 5√245/35

Simplify the fraction

This gives

5√7/√35 = √245/7

Simplify the fraction

5√7/√35 = 7√5/7

So, we have

5√7/√35 = 7

Hence, the simplified expression is 7

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The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.

The Maclaurin series for e^z is:

e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...

The Maclaurin series for 1/1-z is:

1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...

Multiplying these two series together gives:

e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)

= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...

= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...

This series converges for |z| < 1

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Step-by-step explanation:

we have a basic fee of $40 just for renting the car.

and we rent it for 2 days for $30 per day.

so, this costs

40 × 2×30 = 40 + 60 = $100

well, 61.53 is really 10 + 10 + 10 + 10 + 10 + 10 + 1.53.

well, 1.53 doesn't really come nowhere near close to round up to 10, so it boils down to 0, so 61.53 will just be 10 + 10 + 10 + 10 + 10 + 10 + 0 or just 60 once rounded up, now, what's 15% of 60?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 60}}{\left( \cfrac{15}{100} \right)60}\implies 9[/tex]

well, we can get the 15% of 61.53 by just (15/100) * 61.53

however, the exercise is asking on rounding it up to "tens" first

61.53 has "10" six times plus 1.53, the rounding happens with the "surplus"

in this case the surplus is 1.53.

now, for rounding anything the tipover point is at the half, for $10 the half is $5, so if the amount is $5 or more, rounds up to $10, if less than that goes to 0.

1.53 is nowhere near 5, which is the halfpoint or tipover point, because of that, it rounds up to 0, so 61.53 rounded up to "tens" only will be "six tens" only, or 60.

Answer:

7^{2} + x^{2} = 16^{2}

49+x^2=256

x^2=207

x=14.387=14

Answer:

14 units

Step-by-step explanation:

To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.  

Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:

[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).

Answer:

domain: [tex](-\infty, \infty)[/tex]

range: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]

24 groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Given that;

How many groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Every participant in an experiment is exposed to every treatment or condition in a within-subject design, sometimes referred to as a repeated measures design.

The term "between-subjects design" is comparable to this within-subjects design. People are solely assigned to one treatment in a between-subjects design. As a result, one therapy would be given to one group of volunteers, while a different treatment would be given to another group. After that, the variations between the two groups would be contrasted.

24 groups would be required for a perfectly counterbalanced design for even four treatment conditions. This would obviously be impracticable because a large enough sample size would be required to conduct such an experiment.

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Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.

As here we have scale factor=3>1.

Hence, the dilation  changes the original will expand the original figure.

Hence, each of the coordinate of a figure get multiplied by 3.

Hence, the co

ordinates of the image are given as:

i.e. A(0,0) → A'(0,0)

B(2,3) → B'(6,9)

C(1,-2) → C'(3,-6)

D(-3,-3) → D'(-9,-9)

Step-by-step explanation:

Answer: 1 11/20

hope this helps :)

The maximum area that the material would cover is 640, 000 square yards

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then

rate of change = change in y / change in x

if 3200 yards was used for fencing, then 3200 yards is perimeter

and perimeter of a rectangle = 2( L + B)

so that,

2(L + B) = 3200

L + B = 1600

express L in terms of B

L = 1600 - B

Area(A) = L X B

A = L X B

substitute L = 1600 -B

A = (1600 - B) x B

multiply out

A = 1600B - [tex]B^{2}[/tex]

for maximum area,

[tex]\frac{dA}{dB}[/tex] = 0

But dA / dB = 1600 - 2B

1600 - 2B = 0

2B =1600

B = 1600/2

B = 800 yards

L = 1600 - B

L = 1600 - 800

L = 800 yards

Area = L X B

A = 800 x 800

A = 640,000 square yards

In conclusion, he maximum area is  640,000 square yards and the dimensions are 800 yards by 800 yards

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The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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Answer:

First option

Step-by-step explanation:

→ Define domain

The set of x values a function can take

→ Identify

2 to negative infinity

Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.

We have following information,

total number of seniors in math club = 15

total number of juniors in math club = 11

total number of students in math club = 26

A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .

Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485

Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462

Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors

= 485 × 462 = 2,24,070

Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..

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Answer:

  600

Step-by-step explanation:

You want to use distributive property to answer (15x6) + (85x6).

The distributive property shows you what you can do with a common factor:

  (15×6) + (85×6) = (15 +85)×6 . . . . . . apply the distributive property

  = 100 × 6 . . . . . . evaluate the sum in parentheses

  = 600 . . . . . . perform the multiplication

Using distributive property, the simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

In the given question we have to solve the given expression.

The given expression is (5x - 7)(4x + 1).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

(5x - 7)(4x + 1)=5x(4x + 1) - 7(4x + 1)

(5x - 7)(4x + 1)=(5x*4x + 5x*1) - (7*4x + 7*1)

(5x - 7)(4x + 1)=(20x^2 + 5x) - (28x + 7)

Simplifying

(5x - 7)(4x + 1)=20x^2+5x -28x - 7

(5x - 7)(4x + 1)=20x^2- 23x - 7

The simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

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Answer:

the domain is the x values: -5,-4,-2,0,1

The range is the y values: -1, 1, 3, 4

Step-by-step explanation:

The solution set for the pair of inequalities as given in the task content is; (-∞, -4) U (11, ∞).

It follows from the task content that the solution set of the pair of inequalities is to be determined.

Therefore, each inequality can be solved as follows;

-13 > 2x - 5;

-13 + 5 > 2x

-8 > 2x

-4 > x.

Also, the inequality 2x - 5 > 17 can be solved as follows;

2x > 17 + 5

2x > 22

x > 11.

Therefore, the solution set of the inequalities as given in the task content in interval notation is;

(-∞, -4) U (11, ∞).

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The distance covered by the car is 264cm.

Here we have to find the distance covered by the car.

Information provided:

Diameter (d) = 5.6cm

radius(r) = 5.6/2

             = 2.8cm

Rotation = 15 times

Formula to find the circumference of the tire:

Circumference = 2πr

                        = 2 × 22/7 × 2.8

                        = 17.6cm

This is the distance covered by the tire in one rotation.

Distance covered after 15 rotations = 15× 17.6

                                                         = 264 cm

Therefore distance covered is 264 cm.

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Answer: To find the vertex: use formula x= -b/2a.

plug x into the given equation to find y value.

now you have (h,k)

find a point on the graph and plug in to the vertex form equation to find "a"

Step-by-step explanation:

Answer:

0, 6 * 0,6 = 0.36

Step-by-step explanation:

Keyword is AND.First AND second matches both. It means you need to use *.

The probability of winning both matches is 0.36 or 36%.

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

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Since the outcome of each match is independent, we can use the multiplication rule of probability to find the probability of winning the next two matches:

P(win both matches) = P(win first match) x P(win second match)

The probability of winning a single match is given as 0.6.

Therefore, the probability of winning the first match is 0.6.

Now, assuming you won the first match, you still have a probability of 0.6 of winning the second match.

Therefore, the probability of winning both matches is:

P(win both matches) = P(win first match) * P(win second match)

= 0.6 x 0.6

= 0.36

Therefore,

The probability of winning both matches is 0.36 or 36%.

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The quantity of sugar Isabelle would need to make 4 1/5 batches of cookies is 21 cups of sugar

From the question, we are to determine the quantity of sugar that Isabelle would need to make the given number of batches. The number of batches Isabelle wants to make is 4 1/5 batches.

From the given information, Isabelle's lemon cookie recipe calls for 5 cups of sugar. If 1 batch of the lemon cookie calls for 5 cups of sugar

Then, 4 1/5 batches of the lemon cookie will call for 5 × 4 1/5 cups of sugar 5 × 4 1/5

= 5 × 21/5= 21

Hence, Isabelle will need 21 cups of sugar

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