As each person entered a movie theater, Aaron counted how many of the 105 people had popcorn and how many had a drink. He found that out of 84 people that had popcorn, only 10 did not have a drink. Six people walked in without popcorn or a drink. Construct a two-way table to show this data.

Answer:

I believe its C i saw this yesterday somewhere not 100% sure

Step-by-step explanation:

The answer for it is diagram B because it does not cross or have parallel lines

The inverse οf the given functiοn is  (5x+1)/2.

An inverse functiοn is a functiοn that undοes the resuIts οf anοther functiοn. A functiοn g is the inverse οf a functiοn f when x=g(y) and y=f(x). In οther wοrds, appIying f and then g is the same as dοing nοthing. In terms οf the cοnnectiοn between f and g, this can be written as g(f(x))=x.

Here, we have

Given: f(x) = (2x-1)/5

We have tο find the inverse οf the given functiοn.

f(x) = (2x-1)/5

y = (2x-1)/5

Interchange the variabIes.

x =  (2y-1)/5

SοIve fοr y

5x + 1 = 2y

y = (5x+1)/2

RepIace y with f⁻¹(x) tο shοw the finaI answer.

f⁻¹(x) = (5x+1)/2

Hence, the inverse οf the given functiοn is  (5x+1)/2.

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Answer:

18

Step-by-step explanation:

I would say 18 because the triangles are similar. 20x1.5 is 30. So if you multiply 12x1.5, you get 18.

Hope it helps!

Answer:

  7. P(q) = 60 -0.03(x -80)²

  8. P(q) = -0.03x² +4.8x -132

  9. q = 35 balloons

  10. see attached

Step-by-step explanation:

You want the profit equation, break-even sales, and a graph for a party supply company that makes a maximum profit of $60 when they sell 80 balloons, and a profit of $33 when they sell 50 balloons.

If the profit is described by a quadratic equation with a maximum at (quantity, dollars) = (80, 60), and a point on the curve of (50, 33), we can write the equation in two steps.

The vertex-form equation will look like ...

  P(q) = 60 -a(q -80)² . . . . . for some scale factor 'a'

We want P(50) = 33, so we have ...

  P(50) = 33 = 60 -a(50 -80)²

  33 = 60 -900a

  a = (60 -33)/900 = 3/100 = 0.03

The profit equation is ...

  P(q) = 60 -0.03(q -80)²

Expanding the equation gives ...

  P(q) = 60 -0.03(q² -160q +6400)

  P(q) = -0.03q² +4.8q -132

The profit is zero at ...

  P(q) = 0 = 60 -0.03(q -80)²

  0.03(q -80)² = 60

  (q -80)² = 2000 . . . . . . . . divide by 0.03

  q = 80 ±20√5 = 35.3 or 124.7 . . . . . take the square root, add 80

The store will no longer make a profit when sales drops to 35 balloons.

The attachment shows a graph of the profit function.

__

Additional comment

You can find where the profit goes to zero using the graph, the quadratic formula, or by solving it using vertex form, as above. The graph is quick and easy; using the vertex form equation works nicely.

Selling 36 balloons will result in a profit of $1.92.

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Answer:

3.25

Step-by-step explanation:

thats how absolute value works

Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

Step-by-step explanation:

N = 50 000   and  N = 1000 * 2^t

so

50 000 = 1000 2^t      divide both sides of the equation by 1000

50 = 2^t      LOG both sides

log 50 = t log 2

log 50 / log 2 = t = 5.64 hours

the following instructional adjustments or educational adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers : Asking multiple students to share and defend their solutions before acknowledging the correct answer.

The discussion allows the teacher to observe how students solve the problems that involves multiplying two-digit numbers. It will also allow students to express themselves before they realize their answer is incorrect.

Educational Adjustments to teaching could be described as the continuing adjustments that teachers develop to adjust teaching and learning based on research in order to enhance students' attainment of intended instructional aims.

Educational Adjustments are steps or changes that facilitate students to receive educational content and results on a comparable level to facilitate students to receive educational content and results on a comparable level as their peers.

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Complete question :

Which of the following instructional adjustments can the teacher make to best assess all of the students' understanding of multiplying two-digit numbers?

1. Allowing students to write their answers on paper, then collecting the papers at the end of the lesson

2. Asking multiple students to share and defend their solutions before acknowledging the correct answer

3. Asking students who did not hold up their thumbs to share their answer and explain

4. Having Billy work the problem out on the board in front of the class

Answer:

Total area of pyramid = 113.57 sq units

Step-by-step explanation:

Given that

Pyramid has a regular hexagonal with side, a = 4 units

Slant height = 6 units

To find: Total Area of pyramid = ?

Solution:

Total area of pyramid = Area of hexagon + Area of each triangular face

Area of hexagon is given as:

\(A = 6 \times \dfrac{\sqrt3}{4}a^2\\\Rightarrow A = 6 \times \dfrac{\sqrt3}{4}4^2\\\\\Rightarrow A = 41.57\ sq\ units\)

There are 6 triangular faces with base = 4 units and height as 6 units.

Area of 6 triangular faces:

\(6 \times \dfrac{1}{2} \times Base\times Height\\\Rightarrow 6 \times \dfrac{1}{2} \times 4\times 6\\\\\Rightarrow 72\ sq\ units\)

Total area of pyramid = 41.57 + 72 = 113.57 sq units

The equation of the axis of symmetry of the parabola is equal to x = 4.

In this problem we find the representation of a parabola whose axis of symmetry is parallel with y-axis. The axis of symmetry passes through the vertex of the parabola. The definitions of the vertex and the axis of symmetry are, respectively:

Vertex

(x, y) = (h, k)

Axis of symmetry

x = h

If we know that h = - 4, then the equation of axis of symmetry is x = 4.

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Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

the variance will be 0.6217.

What is frequency distribution?

The gathered data is arranged in tables based on frequency distribution. The information could consist of test results, local weather information, volleyball match results, student grades, etc. Data must be presented meaningfully for understanding after data gathering. A frequency distribution graph is a different approach to displaying data that has been represented graphically.

A small data analysis class has six computer science majors among the fourteen total students.

Three people are chosen at random to form a group.

here this is hypergeometric distribution with parameter n=sample size =3 ; N =population size =14

and k=computer sience major =6

a) E(X) =nk/N =3*6/14 =18/14 =9/7 =1.2857

b)|varaince =σ²=(nk/N)*(1-k/N)*(N-n)/(N-1)) =(3*6/14)(1-6/14)*(14-3)/(14-1)= 0.6217

Hence, the variance will be 0.6217.

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If each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

Given that Nicole‘s mother put tiles on a section of the kitchen floor.

The section included 5 rows with 13 tiles in each row

Each tile cost $2.

To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles

Number of tiles =5×13

=65 tiles

Now let us find the amount

Total amount on tiles = 2×65

=$130

Hence, if each tile cost $2 then the amount spend by  Nicole’s mother on tiles is $130

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Answer: 2.72 i guess

Step-by-step explanation:

blue line = x

12c-8-2c+10-4=10c-x

(12-2)c+(10-4-8)=10c-x

10c-2=10c-x

=> x=2

Answer: 78

Step-by-step explanation: multiply 13 x 30 which gives you 390 then divide that by 5 giving you 78 minutes.

Ages of children falls in the Ratio of the variable . Ages of children: 4 years, 5 years, 6 years, 7 years, and 8 years

What level of measurement is the ages of children?

Technically, age is a continuum and a ratio. The age of a person does, after all, have a meaningful zero point (birth), and if you measure it well enough, it is continuous.

Age is what kind of variable and what scale of measurement?

The quick response is that age is taken into account a ratio variable because it has a "true zero" value.

                         The age of a person can be zero (a baby), and we can claim that the age difference between 0 and 10 years is equal to the age difference between 10 and 20 years.

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Step-by-step explanation:

Let m and c be the slope and y-intercept respectively,

(y-3)/(x-9) = m

y-3 = mx-9m

y= mx - 9m+3

y = mx + 3(1-3m)

Answer:

d

Step-by-step explanation:

The correct order, from least to greatest, is: 2, 1, 3, 4.

Answer:

11 and 14cm

Step-by-step explanation:

11 squared = 121

14 squared = 196

121+196 = 317!

The numbers that opposite 1/15 and 1/16 are -1/15 and -1/16

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

Numbers = 1/15 and 1/16

The opposite of numbers is the negative equivalent of the number

Take for instance, we have a number x

The opposite of x is -x

Using the above as a guide, we have the following representation

Numbers = 1/15 and 1/16

This means that, the opposite numbers can be represented as

Opposite numbers = -1/15 and -1/16

Hence, the opposite numbers are -1/15 and -1/16

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The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Considering the expression of a line, the price of the guitar in 2011 is $354.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points, the value of the ordinate to the origin b can be obtained.

Being:

the slope can be calculated as:

m= (300 - 246)÷ (2008 - 2005)

m= 54÷ 3

m= 18

Considering point 2 and the slope m, you obtain:

300= 18×2008 + b

300= 36,144 + b

300- 36,144 = b

-35,844 = b

Finally, the equation of the line is Price= 18×Year - 35,844

Now, you want to know the price of the guitar in 2011. Replacing in the linear equation, you get:

Price= 18×2011 - 35,844

Solving:

Price= 36,198- 35,844

Price= 354

In summary, the price of the guitar by 2011 is $354.

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To solve for x you can first divide by 12 into both sides of the equation, like this

Now, you can add 2.3 from both sides of the equation

Therefore, the value of x that satisfies the equation is

Finally, to check that this value satisfies the given equation, just plug x = 3.6 into the equation and see that a true proposition is reached. So, you have

Answer:

Step-by-step explanation:

Hello There!

Because this is a right triangle we can use the Pythagorean theorem

When solving for missing leg we use this equation

\(c^2-b^2=a^2\)

where c = hypotenuse and b = given leg and a = missing side length

now we plug in the given values into the formula

\(45^2-3^2=a^2\)

\(45^2=2025\)

\(3^2=9\)

\(2025-9=2016\)

\(a^2=2016\)

\(\sqrt{a^2}=a\)

\(\sqrt{2016}=44.89988864\)

final step: round to the nearest tenth

so we can conclude that the missing angle is equal to 44.9

Notes: