(d) The perimeter of the figure below is equal to 150 cm.
X
x+6
x+5
x+1
x+8
X+4
What is the length of the longest side of the polygon?
Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation.

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

[tex]\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }[/tex]

• Putting,

3rd term as 4 and the 4th term as 7.

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }[/tex]

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }[/tex]

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}[/tex]

[tex]\\[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\red{Solution:}}}}}[/tex]

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

[tex]\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term[/tex]

[tex]\\[/tex]

[tex] \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term[/tex]

• Putting,

4th term as 4.

[tex]\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}[/tex]

[tex]\\[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}[/tex]

[tex]\star\:{\underline{\underline{\sf{\green{Solution:}}}}}[/tex]

The frequency distribution table for calculations of mean :

[tex]\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} [/tex]

☆ Calculating the [tex]\sum f_{i}[/tex]

[tex] \implies 4 + 6 + 2 + 2 + 1 + 1[/tex]

[tex] \implies 16[/tex]

☆ Calculating the [tex]\sum f_{i}x_{i}[/tex]

[tex] \implies 12 + 6 + 14 + 8 + 6 + 2[/tex]

[tex]\implies 48[/tex]

As we know,

Mean by direct method :

[tex] \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}[/tex]

here,

• [tex]\sum f_{i}[/tex] = 16

• [tex]\sum f_{i}x_{i}[/tex] = 48

By putting the values we get,

[tex]\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}[/tex]

[tex]\sf \longrightarrow \overline{x} \: = \green{3}[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}[/tex]

• Swipe to see the full answer.

[tex]\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}[/tex]

The area of the plastic used to form the lampshade is 2021.25 square centimeters

The given parameters in the question are:

Outer radius, R = 28 cm

Inner radius, r = 7 cm

Angle, ∅ = 315

The area of the plastic used to form the lampshade is calculated using the following area  of sector formula

A = ∅/360 * π(R² - r²)

Substitute the known values in the above equation

A = 315/360 * 22/7 * (28² - 7²)

Evaluate the exponents

A = 315/360 * 22/7 * (784 - 49)

Evaluate the difference

A = 315/360 * 22/7 * 735

Evaluate the product

A = 2021.25

Hence, the area of the plastic used to form the lampshade is 2021.25 square centimeters

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Answer:

Tools used to construct a bisector are 1》pencil ,2》Eraser ,3》protector ,4》Compass ,5》Sharpner etc ....

The measures of the two different angles are 70° and 110°.

What is angle in parallelogram ?

Thus from the given question, we have:

(6n − 70)° + (2n + 10)° =  180°

8n - 60 =  180° + 60

8n = 240

n = 240/8

n = 30°

So that,

i. (6n − 70)° = (6[30] − 70)°

                    = 180 - 70

                     = 110°

ii. (2n + 10)° = (2[30] + 10)°

                   = 60 + 10

                   = 70°

Therefore, the measures of the two different angles are 70° and 110°.

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The sum of the equation is  = 5494000.

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

Distribute 2j to (j+3).

Rewrite the summation as the sum of two individual summations.

Evaluate each summation using properties or formulas from the lesson.

The lower index is 1, so any properties can be used.

The sum is 5,494,000.

[tex]\sum_{j=1}^{200} 2 j(j+3)[/tex]

simplifying them we get:

[tex]\sum_{j=1}^{200} 2 j^{2}+6 j[/tex]

Split the summation into smaller summations that fit the summation rules.

[tex]\sum_{j=1}^{200} 2 j^{2}+6 j=2 \sum_{j=1}^{200} j^{2}+6 \sum_{j=1}^{200} j[/tex]

[tex]\text { Evaluate } 2 \sum_{j=1}^{200} j^{2}[/tex]

The formula for the summation of a polynomial with degree 2

is:

[tex]\sum_{k=1}^{n} k^{2}=\frac{n(n+1)(2 n+1)}{6}[/tex]

Substitute the values into the formula and make sure to multiply by the front term.

[tex](2)$$\left(\frac{200(200+1)(2 \cdot 200+1)}{6}\right)$$[/tex]

we get: 5373400

Evaluating same as above : [tex]6 \sum_{j=1}^{200} j[/tex]

we get: 120600

Add the results of the summations.

5373400 + 120600

= 5494000

The sum of the equation is  = 5494000.

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72 grams tea is needed to prepare 288 fluid ounces of tea.

According to the statement

we have given that the yvette uses 6 grams of tea leaves to make 24 fluid ounces of tea.

And we have to find that the how much grams of tea uses to make 288 fluid ounces of tea.

So, For this purpose,

the given terms are:

6 grams tea = 24 fluid ounces of tea

Now, we use division method

1 gram of tea = 4 fluid ounces of tea

It means

4 fluid ounces of tea prepared by 1 gram of tea.

then

288 fluid tea prepared = ?

So,

288 fluid tea prepared by grams of tea = 288/4

288 fluid tea prepared by grams of tea = 72.

So, 72 grams tea is needed.

So, 72 grams tea is needed to prepare 288 fluid ounces of tea.

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The measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

Given four measurements:

We are required to choose one measurement which would most likely to have a negative exponent in scientific notation.

A negative exponent is defined as the multiplicative inverse of the base,raised to the power which is of the opposite sign of tthe given power.It is expressed as [tex]e^{-x}[/tex].

We know that exponent shows continuous growth or continuous decay.

Among all the measurement the measurement which is most likely to have a negative exponent in scientific notation is the length of an amoeba in meters because among all the option amoeba can grow continously or decay continuously.

Hence the measurements which would most likely to have a negative exponent in scientific notation is the length of an amoeba in meters.

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Answer:

graph C

Step-by-step explanation:

when X= 0

Y ---> -5

so , answer is graph C

Answer:

c

Step-by-step explanation:

the graph of | x | has its vertex at the origin and has shape V

the graph of | x | - 5 is the graph of | x | translated 5 units vertically down.

That is graph c represents | x | - 5

Three students want to estimate the mean backpack weight of their schoolmates. To do this, they each randomly chose 8 schoolmates and weighed their backpacks. Then as per the given sample data,

(a) The sample means of the backpacks are: 6.375,6.375,6.625

(b) Range of sample means: 0.25

(c)The true statement is: The closer the range of the sample means is to 0, the less confident they can be in their estimate.

For the first sample, mean= 6.375

For the second sample, mean= 6.375

For the third sample, mean= 6.625

Range of sample means=Maximum Mean- Minimum Mean

                                        = 6.625 - 6.375

                                        = 0.25

The students will estimate the average backpack weight of their classmates using sample means, the true statement is:

The closer the range of the sample means is to 0, the more confident they can be in their estimate.

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The average mean cost used for the condominium on maui is 132.5

According to the statement

we have given that the some data values and we have to find the mean of the data and tell the how much expensive is condominium on maui.

So, The given data set is

89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120

So, For this purpose we know that the

Average Mean is a middle point or something (as a place, time, number, or rate) that falls at or near a middle point

Formula to calculate mean is sum of terms / total number of terms.

So,

Mean = 89+ 50+ 68+ 60+ 375+ 55+ 500+ 60+ 50+ 250+ 45+ 45+ 125+ 235+ 1+ 40+ 350+ 65+ 60+ 120 / 20

Mean = 2643 / 20

Mean = 132.5

So, The average mean cost used for the condominium on maui is 132.5

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Maui Vacation How expensive is Maui? If you want a vacation rental condominium

(up to four people), visit a Maui tourism web site. The Maui News gave the following costs in dollars per day for a random sample of condominiums located throughout the island of Maui.

89 50 68 60 375 55 500 60 50 250 45 45 125 235 1 40 350 65 60 120

what average mean would you use?

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Answer:

perimeter = 24

Step-by-step explanation:

formula:

In an equilateral triangle with sides of lengths ‘a’

The height of the triangle is equal to :

[tex]= \frac{\sqrt{3} }{2} a[/tex]

……………………………………………

Calculating ‘a’ :

We have to solve the equation:

[tex]4\sqrt{3} =\frac{\sqrt{3} }{2} a[/tex]

[tex]\Longleftrightarrow 4=\frac{1 }{2} a[/tex]

[tex]\Longleftrightarrow a = 8[/tex]

Calculating the perimeter:

= 3a

= 3 × 8

= 24

we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.

Then we have the product:

P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now, notice that there is a 20 there.

Any number times 20 will end with a zero, then:

P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.

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Answer:

1.187991

Step-by-step explanation:

sin^2(225)−(cos(330))(cos(240))

=(−0.930095)2−(cos(330))(cos(240))

=0.865076−(cos(330))(cos(240))

=0.865076−−0.991199(cos(240))

=0.865076−(−0.991199)(0.325781)

=0.865076−(−0.322914)

=1.187991

Answer:

○ [tex]F = \frac{S + 24}{3}[/tex]

Step-by-step explanation:

We know that:

[tex]S = 3F -24[/tex],

where F is the length of the foot of a person, and S is their shoe size.

To solve for the length of a person's foot, we have to rearrange the given equation to make F the subject:

[tex]S = 3F -24[/tex]

⇒ [tex]S + 24 = 3F[/tex]     [adding 24 to both sides]

⇒ [tex]\frac{S + 24}{3} = F[/tex]          [dividing both sides by3]

⇒ [tex]F = \frac{S + 24}{3}[/tex]          [swapping the sides]

Hi there,

please see below for solution steps :

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

First let us revise the rounding rules before getting down to the process of rounding :

[tex]\sf{763.9 \ to \ the \ nearest \ whole \ number :}\\\hfill\stackrel{\small\text{add 1 }}{3^{+1}}.\\\hfill\stackrel{\small\text{drop it}}{9}}[/tex]

[tex]\sf{763.9\approx764}[/tex]

‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗

f(x) = 3^x

f(4) = 3^4

f(4) = 3 * 3 * 3 * 3

f(4) = 9 * 9

f(4) = 81

Hope this helps!

Answer:

315 students

Step-by-step explanation:

Based on the question, we can deduce:

[tex] \frac{4}{5} = 80percent \: passing \: rate[/tex]

Next we can find out the total number of students who sat for the examination.

80% = 252

[tex]1percent \: = \frac{252}{80} \\ 100 \: percent = \frac{252}{80} \times 100 = 315 \: students [/tex]

Answer: 40 inches

Step-by-step explanation: If the 20 points on the line were spaced 1 inch apart, the result would be 20 inches. Each point you're going to is 1 inch in spacing and there is only going to be 20 inches of spacing (1 inch per point.)

For 2 inches spaced apart, the result would be simply 40 inches. You just need to add the distance of 20 more to the already distance of 20 points, since if 2 were to be divided, it would be 1, which is 20 inches in distance as stated. Another 20 points would be another inch in distance, and adding them gives you 2 inches in distance or 40 inches all together.

I apologize if I wasn't clear enough, I couldn't find a way to explain it as good as I thought it was in my mind.

Hope it helped though!

Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

The amount of money she should deposit is 6131.14 dollars.

The amount she should deposit can be found as follows:

[tex]p = \frac{A}{(1+\frac{r}{n} )^{nt} }[/tex]

where

Therefore,

p = [tex]\frac{20000}{(1+\frac{0.12}{4}{} )^{40} }[/tex]

[tex]p=\frac{20000}{(1+0.03)^{40} }[/tex]

[tex]p = \frac{20000}{1.03^{40} }[/tex]

[tex]p=\frac{20000}{3.262037792}[/tex]

Hence,

p = $6,131.14

Therefore, she should deposit 6131.14 dollars.

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The limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

According to the given question.

We have to find the limit of [tex]\lim_{x \to \infty} 5x - lnx[/tex]

As we know that L'hospital rule is a theorem which provides a technique to evaluate limits of indeterminate forms.

And the formual for L'hospital rule is

[tex]\lim_{x \to \ c} \frac{f_{x} }{g_{x} } = \lim_{x \to \ c} \frac{f^{'}( x)}{g^{'} (x)}[/tex]

[tex]\lim_{x \to \infty} 5x - lnx[/tex]  can be written as

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

If we put the value of limit in lnx/x we get an indeterminate form ∞/∞.

Therefore, [tex]\lim_{x \to \infty} \frac{lnx}{x} = \frac{\frac{1}{x} }{1}[/tex]

[tex]\implies \lim_{x \to \infty} \frac{1}{x} = 0[/tex]   (as x tends to infinity 1/x tends to 0)

So,

[tex]\lim_{x \to \infty} 5x - lnx\\= \lim_{x \to \infty} x(5 - \frac{lnx}{x})[/tex]

[tex]= \lim_{x \to \infty}x(5 -0)[/tex]

[tex]= \lim_{n \to \infty} 5x \\= \infty[/tex](as x tends to ∞ 5x also tends to infinity)

Therefore, the limit of lim x→[infinity] (5x − ln(x)) by using L'hospital rule is ∞.

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area is 1/2 times base times height

triangle A

1/2 times 7 times 9

answer 31.5

Triangle B

1/2 times 7 times 5

answer 17.5

The value of each variable in the two-way table is:

a = 7

b = 31

c = 28

d = 13

e = 65

A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.

The following have to be established:

a player can either be male or female

a player favors either the left or the right

a = females that favor the left. Looking at the Venn diagram, this number is 7.

b = total number of females : 24 + 7 = 31

c = males that favor the right = total number of males - males that favor the left

34 - 6 = 28

d = Total number of people who favor the left = 7 + 6 = 13

Total number of baseball players = 65

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[tex]1.2 \: degrees \: drop \: a \: day \\ 14 \: days \: in \: two \: weeks \\ net \: change = 14 \times 1.2 = 16.8 \: deg[/tex]

Answer:

3

Step-by-step explanation:

[tex]6=2 \times 3 \\ \\ 12=3 \times 2^2 \\ \\ 21=3 \times 7[/tex]

Answer:

$40/unit?

Step-by-step explanation:

I'll assume the the fixed and variable costs are for 2000 units.

Fixed Costs = $35,000

Variable Costs = $45,000

Tota Costs = $80,000

The selling price can be anything. Free and we lose $80,000; $40 each, net profit of $0; $100 each for a net profit of $120,000.

In the absence of any infoprmation regarding selling price (e.g., 50% profit margin), I'd select the $40/unit selling price since that is breakeven.

The approximate solution of this system of equations is

(x,y)=(-0.25,1.25)

Equation is defined as the state of being equal and is often shown as a math expression with equal values on either side, or refers to a problem where many things need to be taken into account.

Given that,

y = |x − 1| and y = 3x+2

 y = |x − 1|

    = (x-1) ,    for  (x-1)>0 or x>1

and

y = -(x-1)  ,    for(x-1)<0  or x<1

y  = -x+1      

Now,   For x>1

y = x-1    ......(1)

y = 3x+2   ......(2)

Solving for x by equaliting's method:

 3x+2 = x-1

→ 3x-x = -1-2

→ 2x = -3

→ x = -3/2

→ x = -1.5 which is <1.

For x<1

y = -x+1    ......(1)

y = 3x+2   ......(2)

Solving for x by equaliting's method:

 3x+2 = -x+1

→ 3x+x = 1-2

→ 4x = -1

→ x = -1/4

→ x= -0.25 which is <1.

substitute the value of x = -0.25 in equation 1 for x<1.

y = -x+1

  = -(-0.25)+1

y  = 1.25

Hence, The approximate solution of this system of equations is

(x,y)=(-1/4,5/4)=(-0.25,1.25).

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Answer:

30%

Step-by-step explanation:

1) Based on the given conditions, formulate:

30 meters/100 meters

2) Calculate 30 meters/100 meters:

3/10

3) Convert to percentage:

- 3/10 x 10/10

- 3x10/10x10

30/100

30/100 = 30%

You’re done!

Also, if you could label this brainliest that would be a great help!

Thanks xx

-Dante

Answer:

12:1

Step-by-step explanation:

each pack contains 12 eggs

108/9 = 12

Hope this helps

[tex] \sqrt[4]{ - 8} [/tex]