Dexter is in charge of ticket sales at his town’s water park. He has to report to his boss how many tickets he sells and how much money the water park makes in ticket sales each day - adult tickets ($7), child tickets ($5). Today, Dexter has sold 100 adult and 125 child tickets. Yesterday, he sold 120 adult and 120 child tickets. Can Dexter write an expression to figure out today’s ticket sales, and use this to compare today’s sales to yesterday’s?

Dexter needs to write an expression to figure out the total money made from the 100 adult and 125 child tickets he sold today, compared to the 120 adult and 120 child tickets he sold yesterday. The adult tickets cost $7 and the child tickets cost $5

Answer:

3

Step-by-step explanation:

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

Using the formula for a z-distribution confidence interval of proportions, he also needs to know the confidence level.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

Of these 3 itens, the problem states that he knows the sample size and the sample proportion, hence he needs to know z to determine the confidence interval. z depends on the confidence level, which is the remaining parameter.

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Answer:

Hey! I'm gonna go ahead and give ya the "meaning" of the fundamental theorem of algebra but not the answer to the A. B. and C.

Step-by-step explanation:

fundamental theorem of algebra, theorem of equations proved by Carl Friedrich Gauss in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers. The roots can have a multiplicity greater than zero.

[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]

Answer:

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

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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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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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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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]

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

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

The probability of correctly picking the two numbers is 2/10.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

The probability of correctly picking the two numbers = (numbers that have to be selected to win / total numbers)

2/10

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Answer:

75%

Step-by-step explanation:

3/4 ie 75/100. .........edge

Answer:

6.5%

Step-by-step explanation:

I = prt

5616 = 7200 × r × 12

r = 5616/(7200 × 12)

r = 0.065

r = 6.5%

Answer:

figure A = 3 units

figure B = 9 x 3 = 27 units

scale factor =

[tex] \frac{3}{27 } = \frac{1}{9} [/tex]

so the scale factor = 9

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: $4.50

Step-by-step explanation:

Original Price: $6

Discount: 25%

Discounted Price: 6*25%= $1.5

                              $6-$1.5= $4.5

The statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

For a data distribution that is displayed by a box plot, the measure of variation that can be used to describe the data distribution is the interquartile range.

Interquartile range, which is a measure of variation can be determined from a box plot by finding the value of the third quartile and first quartile, the finding their difference. The difference is the interquartile range.

Interquartile range = third quartile - first quartile.

Interquartile range for crackers = 85 - 75

Interquartile range for crackers = 10

Interquartile range for trail mix = 105 - 90

Interquartile range for trail mix = 15.

The bigger the value of the interquartile range, the more variation there is that exist in a data distribution.

Interquartile range for trial mix is the largest, therefore, the statement that is true about the box plots is: D. The number of calories in the packs of trail mix have a greater variation than the number of calories in the packs of crackers.

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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:

$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 corresponding angles are ∠2 and ∠6 i.e., ∠2≅∠6 according to the corresponding angles theorem. So, option 2 is correct.

The theorem states that,

The lines 'AB' and 'CD' are parallel and cut by a transverse 'EF' if and only if their corresponding angles are congruent.

The corresponding angles are those which lie on the same side of the transverse one is interior and the other is an exterior angle.

From the diagram,

Lines 'AB' and 'CD' are parallel and line 'EF' cuts these parallel lines.

So, the corresponding angles formed are:

(∠1, ∠5), (∠2, ∠6), (∠3, ∠7), and (∠4, ∠8)

According to the theorem, they are congruent. I.e.,

∠1 ≅ ∠5

∠2 ≅ ∠6

∠3 ≅ ∠7

∠4 ≅ ∠8

So, option 2 is correct.

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Disclaimer: The given question is incorrect. Here is the correct question.

Question: Lines 'c' and 'd' are parallel lines cut by the transversal 'p'. Which must be true by the corresponding angles theorem?

1) ∠1 = ∠7

2) ∠2 = ∠6

3) ∠3 = ∠5

4) ∠5 = ∠7

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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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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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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Answer: A. V: x = –4; H: y = 4

Step-by-step explanation:

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:

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]

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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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

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