Valley playhouse receives 2884 by selling 430 tickets to the opening night of the musical. if the full price of a ticket is 8 and discount tickets are 4 how many discount tickets were sold

Answer:A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Step-by-step explanation:

A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Answer:

A cafe makes ten 8-ounce fruit smoothies. Each smoothie is made with 4 ounces of soy milk and 1.3 ounces of banana flavoring. the rest is blueberry juice. How much of each ingredient will be necessary to make the 10 smoothies?

Step-by-step explanation:

(a) Construct confidence intervals are : 90%: [428.95, 444.05], 95%: [427.13, 445.87], 99%: [423.67, 449.33].

(b) The 99% confidence interval has the widest interval.

(a) To construct confidence intervals for the mean breaking strength of the wool fibers, we shall use the given formula:

Confidence interval = sample mean ± (critical value * standard error)

The critical value here will depends on the level of confidence. For a 90% confidence level, the critical value is 1.645 (from the standard normal distribution). For a 95% confidence level, the critical value is 1.96, and for a 99% confidence level, the critical value is 2.576.

Standard error is obtained by dividing the sample standard deviation by the square root of the sample size.

Plugging in the values, we can calculate the confidence intervals:

90% confidence interval:

Lower bound = 436.5 - (1.645 * (11.9 / √20))

Upper bound = 436.5 + (1.645 * (11.9 / √20))

95% confidence interval:

Lower bound = 436.5 - (1.96 * (11.9 / √20))

Upper bound = 436.5 + (1.96 * (11.9 / √20))

99% confidence interval:

Lower bound = 436.5 - (2.576 * (11.9 / √20))

Upper bound = 436.5 + (2.576 * (11.9 / √20))

(b) The width of a confidence interval depends on both the critical value and the standard error. When aiming for a higher level of confidence, the interval becomes wider as it requires a larger critical value. Consequently, it can be concluded that among the given confidence intervals, the one with a 99% confidence level will have the broadest range.

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The given statement is FALSE.

If one or more data items are much greater than the other items, the median, rather than the mean, is more representative of the data.

When one or more data items are much greater than the other items, these extreme values can greatly influence the mean.

When you have a skewed distribution, the median is a better measure of central tendency than the mean

The median and mean can only have one value for a given data set. The mode can have more than one value

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To determine the exponential equation that best fits the data below:

Inorder to convert the exponential to linear, use logarithm

To estimate the value of y using the above exponential equation when x= 6

Hence the estimate the value of y ≈ 100

Therefore the correct answer is Option D

the absolute extrema of the linear equation f(x) =  12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

What are the absolute extrema of a linear equation within a closed interval?

According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:

Absolute maximum

f(- 8) =   12x^2 -11x +2

f(- 8) = 27

Absolute minimum

f(4) = - 3 · 4 + 3

f(4) = - 9

By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2  are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer:

If the door was at the right angle then that means it is not an optical illusion, but if the door is straight then that means the door is not at a right angle so it's an optical illusion.

Step-by-step explanation:

Maybe if the door was straight, but you saw it at a right angle then maybe you      were laying down, you were sick, seeing things or you drank a lot of alcohol that day. If it was a right angle on that day then it was not an optical illusion.

Proved that f is pose a continuous function on R. If each of the functions fn is bounded, is  necessarily true that f is bounded.

Given:

Let {fn} be a sequence of continuous functions defined on R, and that fn + f uniformly on every finite interval [a, b]. Prove that f is pose a continuous function on R.

Denote by fn(x) any continuous function such that fn(x)=f(x) if x∈[−n,n], and fn(x)=0 if x∈(−∞,−n−1)∪(n+1,+∞). It is easy to see that such a function exists, and is bounded.

Now, using the fact that every interval [a,b] is contained in a interval [−N,N], you can check easily that (fn) converges to f uniformly on every [a,b] (actually, fn|[a,b] is constant equal to f|[a,b] for n sufficiently large).

No, because this would not give a continuous function. Define fn equal to f on [−n,n], and equal to zero on (−∞,−n−1)∪(n+1,+∞), and complete it as you want and the intervals [−n−1,n) and (n,n+1] to get a continuous function.

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Step-by-step explanation:

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in

At Game 7, the attendance for the basketball team had declined by 5% x 6 games = 30% and This means that the attendance at Game 7 was 23,500 x (1 - 0.3) = 16,450 people.

The attendance for a basketball team declined at a rate of 5% per game throughout a losing season. This means that for every game, the attendance dropped by 5% in comparison to the attendance of the game before it.

15 games were played in the season and 23,500 people were at the first game. To calculate the attendance at Game 7, we first need to calculate the total amount that the attendance had declined by by the 7th game.

This can be done by multiplying the rate of decline (5%) by the number of games that had passed (6 games). This gives us a total decline of 30%. We then need to calculate the attendance at Game 7 by subtracting the total decline from the initial attendance.

This can be done by multiplying the initial attendance (23,500) by (1 - 0.3), which gives us 16,450 people. Therefore, the attendance at Game 7 was 16,450 people.

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Answer:

It's asking you to add right? if it's not tell me what it's asking and i'll re-do it

if so your answer should be: x3 + 39

Answer:

A grizzly bear's normal heart rate when not hibernating is about 50 beats per minute.

Step-by-step explanation:

10÷50=.20

Answer:

To find the derivative of the function y = x^2 - x + 3 using the first principle, we start by applying the definition of the derivative:

f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h

where f(x) = x^2 - x + 3.

Now we substitute the function into the equation and simplify:

f'(x) = lim (h -> 0) [(x+h)^2 - (x+h) + 3 - (x^2 - x + 3)] / h

f'(x) = lim (h -> 0) [(x^2 + 2xh + h^2 - x - h + 3) - (x^2 - x + 3)] / h

f'(x) = lim (h -> 0) [2xh + h^2 - h] / h

Now we can cancel out the h in the numerator and denominator, leaving:

f'(x) = lim (h -> 0) [2x + h - 1]

Finally, we take the limit as h approaches 0:

f'(x) = 2x - 1

Therefore, the derivative of y = x^2 - x + 3 with respect to x is f'(x) = 2x - 1.

Step-by-step explanation:

Answer:

\(\dfrac{\text{d}y}{\text{d}x}=2x-1\)

Step-by-step explanation:

Differentiating from First Principles is a technique to find an algebraic expression for the gradient at a particular point on the curve.

\(\boxed{\begin{minipage}{5.6 cm}\underline{Differentiating from First Principles}\\\\\\$\text{f}\:'(x)=\displaystyle \lim_{h \to 0} \left[\dfrac{\text{f}(x+h)-\text{f}(x)}{(x+h)-x}\right]$\\\\\end{minipage}}\)

The point (x + h, f(x + h)) is a small distance along the curve from (x, f(x)). As h gets smaller, the distance between the two points gets smaller. The closer the points, the closer the line joining them will be to the tangent line.

To differentiate y = x² - x + 3 using first principles, substitute f(x + h) and f(x) into the formula:

\(\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{(x+h)^2-(x+h)+3-(x^2-x+3)}{(x+h)-x}\right]\)

Simplify the numerator:

\(\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{x^2+2hx+h^2-x-h+3-x^2+x-3)}{x+h-x}\right]\)

\(\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx+h^2-h}{h}\right]\)

Separate into three fractions:

\(\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\dfrac{2hx}{h}+\dfrac{h^2}{h}-\dfrac{h}{h}\right]\)

Cancel the common factor, h:

\(\implies \displaystyle \dfrac{\text{d}y}{\text{d}x}=\lim_{h \to 0} \left[\:2x+h-1\:\right]\)

As h → 0, the second term → 0:

\(\implies \dfrac{\text{d}y}{\text{d}x}=2x-1\)

There are 22 people who sent the chain letter, and 189 people did not continue the chain.

We know that the chain started with one person who sent it to 7 others, so that makes a total of 8 people in the first round. In the second round, each of those 7 people could either send it to 7 more people or ignore it, so there are two possibilities for each of those 7 people: they either continue the chain or they don't.

Therefore, there are 2⁷ = 128 possible outcomes for the second round.

If we assume that everyone who received the letter in the second round sent it to 7 more people, then there would be 7 x 128 = 896 people in the third round.

Continuing this pattern, we can see that the number of people in each round is given by the formula of combination 8 x 7ⁿ⁻¹, where n is the round number (starting with n = 1 for the first round).

We want to find the round number such that the total number of people in the chain is 211. Setting the formula above equal to 211 and solving for n gives

8 x 7ⁿ⁻¹ = 211

7ⁿ⁻¹ = 26.375

n - 1 = log_7(26.375)

n = 2.78 (rounded to two decimal places)

Since we can't have a fractional round number, we can assume that the chain ended after the second round (since the third round would have too many people). Therefore, the total number of people who sent the letter is

8 + 7(2) = 22

To find the number of people who did not continue the chain, we can subtract the number of people who sent the letter from the total number of people in the chain

211 - 22 = 189

Therefore, 189 people did not continue the chain.

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Answer:

Step-by-step explanation:

its 45 cm due too

There are 72 multiples of 9³ that are greater than \(9^4\) and less than \(9^5\).

We have,

The values of 9³, \(9^4\), and \(9^5\):

9³ = 729

\(9^4\) = 6561

\(9^5\) = 59049

Now,

The multiples of 729 that fall within the range (6561, 59049).

The number of multiples can be calculated as follows:

Multiples = (Highest value ÷ Divisor) - (Lowest value ÷ Divisor)

= (59049 ÷ 729) - (6561 ÷ 729)

= 81 - 9

= 72

Therefore,

There are 72 multiples of 9³ that are greater than \(9^4\) and less than \(9^5\).

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Answer: x=6 y=3

Step-by-step explanation:

12/2 = 6

1 pizza is 6 dollars

6/2=3

1 soda is 3 dollars

3*4=12

6*3=18

18+12=30

Answer: You could do 7x+5 over 5, like a fraction. Or you could do 5/7 (x+5). I take the slash as a fraction so..

Hope it helps

Recall that:

Then, if:

Now, notice that:

Therefore:

Answer: True.

The table has a constant of proportionality of 0.322

The table that completes the question is added as an attachment

On the table, we have the following points

(x, y) = (9.3, 3)

To determine the constant of proportionality, remove the origin

So, we have

(x, y) = (9.3, 3)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have

k = 3/9.3

Evaluate the quotient

So, we have

k = 0.322

Hence, the constant of proportionality of the table is 0.322

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Answer:

3/2 x + 5/3

Step-by-step explanation:

1/4x + 1 + 3/4x + (2/3) + (1/2x) =

= 1/4 x + 3/4 x + 1/2 x + 1 + 2/3

= 1/4 x + 3/4 x + 2/4 x + 3/3 + 2/3

= 6/4 x + 5/3

= 3/2 x + 5/3

The least-squares regression line is used to predict the values of one variable based on the values of the other variable. In this case, the Verbal score can be predicted from the Math score.

The formula for the least-squares regression line is: Verbal = a + b * Math, where a is the intercept and b is the slope. The least-squares regression line for predicting Verbal score from Math score can be determined using a calculator or a statistical software package.

Once the least-squares regression line has been determined, it can be used to make predictions about the Verbal score for a given Math score. For example, if a student scores 600 on the Math portion of the SAT, the least-squares regression line can be used to predict their Verbal score.

The least-squares regression line is a useful tool for analyzing the relationship between two variables. It can be used to identify patterns and trends, and to make predictions about future values.

However, it is important to remember that correlation does not equal causation, and that other factors may be influencing the relationship between the two variables. The least-squares regression line should be used as a starting point for further analysis, rather than as a definitive answer.

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Part A:

If a quadratic has only one x-intercept, then that is where the vertex lies. being that the vertex is the highest or lowest point in the quadratic. To sketch, it will open downwards with a single x-cept

Part B:

The graph will be above the x-axis. And having the vertex being at (0,1) as it says its the minimum value. All the minimum means is that its the lowest value of this given parabola.

Part C:

Plot the points of the y-intercept and z-intercepts. Then plot the maximum value is. Connect the dots.

The complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

In this question, we have been given some information about lines a, b, k and m.

We need use this information and determine which lines in the figure are parallel.

We have been given angle 2 is supplementary to angle 3.

We know that, the sum of the angles on the same side of the transversal which are inside the two parallel lines is always 180°

Also, supplementary angles are the angles whose sum is 180°

i.e., ∠2 + ∠3 = 180°

From above we conclude that, the lines and b are parallel and line k would be the transversal.

Therefore, the complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

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