Question
A local movie theater sells tickets at different prices for an adult and for a child. The price of an adult’s ticket is $10.50 and the price of a child’s ticket is $6.50 . If the theater sells a total of 65 tickets for a total price of $594.50 in an afternoon, how many child tickets did the theater sell?

The way that errors can be introduced are;

Giving the questionnaire to all participants when they arrive for their appointment does not follow the protocol;

The participant could fill out the questionnaire before experiencing the therapy session.

Statistical errors are defined as errors that describe the difference that exists between a value obtained from a data collection process and the 'true' value for the population. Thus, the greater the error, the less representative the data will be of the population.

There are two main errors in this case which are type I error and type II error.

A type I error is called false-positive and it occurs if an investigator rejects a null hypothesis that is actually true in the population.

A type II error is called false-negative and it occurs if the investigator fails to reject a null hypothesis that is actually false in the population.

Now, from the question, since the data collection protocol alls for a questionnaire to be administered to patients having knee replacement surgery after the third physical therapy appointment, then we can introduce an error by;

Giving the questionnaire to all participants when they arrive.

The participant could fill out the questionnaire before experiencing the therapy session.

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Giving a questionnaire to all par-ticipants follows the timing of theprotocol.

BReading the questionnaire to par-ticipants with poor reading skillsfollows the timing of the protocol.

CGiving the questionnaire to allparticipants when they arrive fortheir appointment does not fol-low the protocol; the participantcould fill out the questionnairebefore experiencing the therapysession.

DGiving the questionnaire to theparticipants after the appoint-ment to be completed while theyhave a snack follows the timingof the protocol.

Based on this output of multiple regression analysis, critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance is Approximately F = 2.50.

A single dependent variable and a number of independent variables can be analyzed using multiple regression, a statistical approach. Using independent variables whose values are known, multiple regression analysis aims to predict the value of the single dependent value.

When doing multiple regression, each independent variable's value is taken into account in order to predict the value of the single dependent variable. Example: A researcher chooses to examine student performance at a certain school over time.

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40/3 feet /second fast the top of the ladder sliding down the wall.

What is ladder?

A ladder is a piece of gear used for climbing up or down objects that consists of repeated bars or steps (rungs) between two upright lengths of metal, wood, or rope.

Typically, these ladders work best for outdoor tasks like roof access or exterior painting. A straight ladder's reach is typically two feet higher than its height.

Given:

A 10 foot ladder is leaning against a wall when the base begins to slide away from the wall. when the base is 8 feet from the wall, the base is moving at the rate of 4 feet per second.

We have dx/dt = 4 feet per second

We want to find dy/dt.

From given information,

x^2 + y^2 = 10^2         ..(1)

When x = 8

⇒ y = √(10^2 - 8^2)

y = √(100 - 64)

y = √36

y = 6 feet

Now differentiate equation (1) with respect to t

[tex]2x\frac{dx}{dt} +2y\frac{dy}{dt} = 0\\ x\frac{dx}{dt} + y\frac{dy}{dt} = 0\\ \frac{dy}{dt} = -\frac{x}{y} \frac{dx}{dt}[/tex]

Plug x = 8, y = 6 and dx/dt = 10

⇒

[tex]\frac{dy}{dt} = -\frac{8}{6}(10)\\ \frac{dy}{dt} = -\frac{40}{3}[/tex]

Hence, 40/3 feet /second fast the top of the ladder sliding down the wall.

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a) The area to the left of 25 is 0.63056

b) The area to the left of 16 is 0.12167

c) The area to the right of 22 is 0.56618

d) The area to the right of 28 is  0.20233

e) The area between 16 and 30 is  0.75666

Given,

The mean of the distribution = 23

Standard deviation  = 6

We have to find the following areas

(a) Entering the values

(b) Entering the values

(c) Entering the values

(d) Entering the value

(e) Entering the values

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According to the model, the kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.

From the question, we are to drag and drop the correct numbers to complete the given sentence.

The given sentence is

According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.

From the given information,

The equation that fits the model is

w = 0.45n + 0.12

By comparing with the slope-intercept form a line,

y = mx + c

Where m is the slope

and c is the y-intercept

m = 0.45

and c = 0.12

This means the kitten gained approximately 0.45 kilogram every month and the initial weight of the kitten is 0.12 kilogram

Hence,

The kitten gained approximately 0.45 kilograms every month and the kitten weighed approximately 0.12 kilograms when Jessica bought it from the store.

Here is the complete question:

Jessica bought a kitten from a pet store and recorded its weight at various times over a 6 month period.

She found the linear model that best fit the data was w = 0.45n + 0.12, where n is the number of months since Jessica bought the kitten and w is the kitten's weight in kilograms.

Drag and drop the correct numbers below to complete the sentence.

According to the model, the kitten gained approximately ____ kilograms every month and the kitten weighed approximately ____ kilograms when Jessica bought it from the store.

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answer:

I believe it's D

[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]

  = 0.108

pₐ = P( z < -0.108 ) = 0.4562

So the p-value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)

Data given and notation

n = 100 represent the random sample taken

X=8 represent the people with depression or a depressive illness

p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness

p₀ = 0.083  is the value that we want to test

α = 0.05 represent the significance level  assumed

Confidence = 83% or 0.83  assumed

z  would represent the statistic (variable of interest)

pₐ represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:  

Null hypothesis:  

p ≥ 0.083

Alternative hypothesis:  

p < 0.083

When we conduct a proportion test we need to use the z statistic, and the is given by:

[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex]                       ---------------------  (1)  

The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]

 =  - 0.083 / √ 0.0076

 = -0.083 / 0.028

 = -0.108

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

     pₐ = P( z < -0.108 ) = 0.4562

So the p value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).

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We concluded that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.

What is the growth factor?

The rate at which a quantity multiplies itself over time is known as its growth factor. A quantity's growth rate is the factor by which it grows (or shrinks) over time.

Here, we have

The required expression for y with respect to x is:

y = (1.7)ˣ.......(1)

Where, 1.7 = 1-unit growth factor

Now we check,

Whenever x changes by 1

x →x +1 .....(2)

Now we put Equation (2) in (1) and we get

y' = (1.7)ˣ⁺¹

y' = (1.7)ˣ (1.7).....(3)

Taking the ratio of equations 3 & 1, we get

y'/y =   (1.7)ˣ (1.7)/(1.7)ˣ

y' = 1.7y

Hence, we observe that whenever x changes by 1, the value of y  becomes 1.7 units larger than its previous value.

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The number of child ticket were sold on Wednesday is 236

The cost of child admission ticket = $6.10

The cost of adult admission ticket = $9.20

Consider the number of child ticket as x and the number of adult ticket as y

Twice times as many adult tickets as child tickets were sold

y = 2x

Then the equation will be

x + y = 707.70

Substitute the value of y in the equation

x + 2x = 707.70

Add the like terms

3x = 707.70

x = 707.70/3

Divide the terms

x = 235.9

x ≈ 236

Therefore, 236 child ticket were sold on that day

I have answered the question in general, as the given question is incomplete

The complete question is:

At the movie theatre, child admission is $6.10 and adult admission is $9.20 . On Wednesday, twice times as many adult tickets as child tickets were sold, for a total sales of $707.70 . How many child tickets were sold that day?

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The tottal number of ways to selct  15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15

C([tex]\frac{20}{12}[/tex]) = 15504

NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties

C([tex]\frac{19-k}{15-5}[/tex])

So for k=0, C1=3876

k=1, C2 =3060

k=2, C3=2380

So C =C1+C2+C3=9316.

So the number of ways 15504-9316= 6188.

Hence, The tottal number of ways to selct  15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.

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Recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

What do you mean by recursive realtion?

A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.

The recursive formula [tex]a_{n+1}=a_{n}[/tex] + d  can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.

It is given that cost of midisze car is $50.00

Rent per day = $19.99

We need to find the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on.

According to the question:

Cost become = 50.00 + 19.99n where n represents the number of days

Recursive formula become:

[tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]      where n>1

Therefore, recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

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The graph of the solution of the inequality is shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ x + 5 ≥ 2

Now,

Since, The inequality is,

⇒ x + 5 ≥ 2

Hence, Simplify the inequality as;

⇒ x + 5 ≥ 2

Subtract 5, we get;

⇒ x + 5 - 5 ≥ 2 - 5

⇒ x  ≥ - 3

Thus, The graph of the solution of the inequality is shown in figure.

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Answer:

A Acute angle (Give me pointssss)

Step-by-step explanation:

Its right bc im smart

Answer: 11 turkey burgers

Step-by-step explanation:

1/4 = 0.25
2.93 ÷ 0.25 = 11.72
You can't have a partial burger, so round down
He can make 11 turkey burgers

Answer:

12 burgers

Step-by-step explanation:

i just did this, you round up from the fraction you get

Initial and terminal points of the vector [tex]\vec{PQ}[/tex] of (3., 3) and (5, 7) , and the initial and final point of the vector [tex]\vec{RS}[/tex] of (4, -5), and (1, -5), indicate that  the the difference between the vectors is; 5·i + 5·j

A vector is a quantity that has both magnitude and direction.

The specified vectors are;

The initial and terminal point on vector [tex]\vec{PQ}[/tex] are; (3, 3) and (5, 7)
The initial and terminal point of vector  [tex]\vec{RS}[/tex] are  (4, -6), and (1, -5)

Therefore, the vector  [tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] is therefore;

The vector form of [tex]\vec{PQ}[/tex] = <5 - 3, 7 - 3> = <2, 4>

The vecror form of    [tex]\vec{RS}[/tex]  = <1-4, -5 - (-6)> = <-3, -1>

The difference  between the vectors is therefore;

The vectors are therefore;

[tex]\vec{PQ}[/tex] = 2·i + 4·j

[tex]\vec{RS}[/tex] = -3·i - j

The difference between the vectors is therefore;

[tex]\vec{PQ}[/tex] - [tex]\vec{RS}[/tex] = (2 - (-3))·i + (4 - (-1))·j = 5·i + 5·j

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In four digits number, if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.

In the given question, we have to find the value of underlined 5 in four digit numbers.

As we know that,

Place value labels like tens and ones notify us of a number appear digit's value. More than one digit can be used to create a number. As a result, to better understand the value of each digit, we employ place value labels such as ones, tens, hundreds, and thousands.

As we know that we count the numbers as ones, tens, hundreds and so on.

So if a 4 digit number is given and we have to find the value of underline 5, and then if 5 is ones place, then the value is 5. It 5 is on tens place then the value will be 50. If the 5 is on hundred places then value will be 500. If 5 are on thousand places then value will be 5000.

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The length of cable that is needed for the initial rise is; 41 feet.

The given parameters are as shown in the image of the triangle attached.

Where;

A = 28 , a = 25 ft, and b = 20 ft.

Now, if A is acute and a > b, it means that one solution exists. Using the

Law of Sines to find B;

a/sin A = b/sin B

Plugging in the relevant values gives;

25/sin 28 = 20/sin B

sin B = (20 sin 28)/25

sin B = 0.3756

B = sin⁻¹0.3756

B = 22.06°

Due to the fact that the two angles are now known, it means that the angle opposite x is 180 – (28 + 22.06 ) = 129.94 . Using the Law of Sines to find x;

a/sin A = x/sin X

25/sin 28 = = x/sin 129.94

solving fir x gives;

x = 40.83 ≈ 41 feet

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Answer: 2

Step-by-step explanation:

solve in parentesis than divide by 0.5 or 1/2 then 2^3= 4 so

that minus 4 equals 2

Answer:

5/2 or 2.5

Step-by-step explanation:

Slope is rise/run. We take the difference of the y-coordinates and divide it by the difference of the x-coordinates.

From this, we get [tex](7--3)/(5-1)[/tex], or [tex]10/4[/tex], which can be simplified to 5/2, or 2.5.

Answer: 14 Adult tickets

Step-by-step explanation:

The equation for the total number of tickets would be

x+y=18

5x+3y=82

y=18-x

5x+3(18-x)=82

2x=28

x=14

x= Number of adult tickets

The correct option is:

a. randomly generated from the specified probability distributions

Given,

In the question:

Values for the random variables or uncertain variable inputs to a simulation are:-

a. randomly generated from the specified probability distributions

b. equal to the most likely value

c. selected by the decision maker

d. calculated by fixed mathematical formulas

e. controlled by the decision maker

Choose the correct one.

Now, According to the question:

Let's Know:

How do you generate a random number from a probability distribution?

In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].

The correct option is:

a. randomly generated from the specified probability distributions

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With 95% of confidence interval for the time it takes salesperson to talk to a potential customer is (12.42 , 5.38).

A Random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected, minimizing the risk of selection bias.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by σ ² ,s² ,Var(X) , or V(X).

A confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used. The confidence level represents the long-run proportion of corresponding CIs that contain the true value of the parameter. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.

Given in the question:

n = 46

x = 8.90

σ = 6

α = 0.95

As we know that:

[tex]X[/tex] ±[tex]Z_{\alpha /2} * \frac{\beta }{\sqrt{n} }[/tex]

putting the values we get,

  8.90 ± Z (0.95/2) ×6/√46

Now, considering the positive sign, we get,

=  8.90 + 3.52

= 12.42

Now considering the negative sign,

8.90 ± Z (0.95/2) ×6/√46

= 8.90 - 3.52

= 5.38

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Answer: the last two situations

Step-by-step explanation:

there would be 0 students left in a school after 6 pm and the temperature in degrees fahrenheit has to be above 0 because it is a hot day and the oven is on

Alto earned $200 while Sheryl earned $300 over the summer.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider x represent the amount of money earned by Alto and y represent the amount of money earned by Sheryl

Together they earned a total of $500.

Hence the system of equations for the situation

x + y = 500 (1)

Sheryl earned $100 more than Alto:

y = x + 100

-x + y = 100(2)

Using Substitution to solve the system.

Solving equations 1 and 2 simultaneously gives:

x = 200 , y = 300

Therefore Alto earned $200 while Sheryl earned $300 over the summer.

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Answer: Brian payed $24.00

How u do it:

Discount= original price x discount%/100

Discount = 40 × 40%/100

Discount = 40 x 0.4 

You save = $16.00

Final Price = Original Price - Discount

Final Price = 40 - 16

Final Price = $24.00

The largest area is found to be 8702.5 [tex]ft^{2}[/tex].

We know that area of rectangle

A = xy ........ (1)

Perimeter of rectangle (given) = 590 ft

Using x and y as two variables ;

5x + 2y = 590

solve yb in term of x

y = -5/2 x + 295......(2)

Now we will get area only in one variable from (1) and (2)

A = x ((-5/2)x + 295)

A = -5/2 [tex]x^{2}[/tex] + 295x

differentiate it with respect gto x

A' = -5x + 295........ (3)

find the critical point to get your minima and maxima value.

Put A' = 0,  x = 295/5 = 59

x = 59

then , from (2)

y= (-5/2 × 59) + 295 = 147.5

y = 147.5

again differentiate (3)

A'' = -5 < 0. i.e critical point x = 59 is point of maxima.

So, maximum area = 59 × 147.5

Largest area = 8702.5 [tex]ft^{2}[/tex]

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Distributional semantics develops methods for measuring and classifying semantic similarity between language elements.

To quantify and classify semantic relatedness among linguistic items based on their distributional qualities in large samples of language data, distributional semantics is a field of study. The distributional hypothesis captures the fundamental principle of distributional semantics.

The semantic theory of language usage, states that terms used and occurring in comparable situations tend to have similar meanings is the basis for the distributional hypothesis in linguistics. For instance, the words "fire" and "dog" have very different meanings and aren't typically used together in a sentence. However, the terms "dog" and "cat" are occasionally used interchangeably, suggesting that they may have a similar connotation.

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Answer:

15. x = 4

16. x = 7

Step-by-step explanation:

15.

CD/ ED = DG / DF

48 / (5x - 2) = 40 / (2x + 7)

48 (2x + 7) = 40 (5x - 2)

96x + 336 = 200x - 80

200x - 96x = 336 + 80

104x = 416

x = 4

16.

ST / PL = TU / LM

(x + 1) / 72 = (2x - 3) / 99

99 (x + 1) = 72 (2x - 3)

99x + 99 = 144x - 216

144x - 99x = 99 + 216

45x = 315

x = 7