write the answer in terms of pi

write the answer rounded to the nearest hundredths place

Answer:

Step-by-step explanation:

its a rectanlge

The null hypothesis is rejected at a level of significance of 0.05. This means that there is sufficient evidence to suggest that the early opening is increasing sales and the average daily sales are greater than $8000 per day.

To conduct the hypothesis test, we need to set up the null and alternative hypotheses:
Null hypothesis (H0): The early opening has no effect on the average daily sales and the mean remains at $8000 per day.
Alternative hypothesis (Ha): The early opening increases the average daily sales and the mean is greater than $8000 per day.
We will conduct a one-tailed z-test with a level of significance of 0.05.

The formula for the z-test statistic is:
z = (sample mean - population mean) / (standard deviation /[tex]\sqrt{sample size}[/tex])

Plugging in the values, we get:

z = (8200 - 8000) / (1500 /[tex]\sqrt{100}[/tex]) = 2.67

Looking up the z-score in a standard normal distribution table, we find that the corresponding p-value is 0.0038. Since the p-value is less than the level of significance, we reject the null hypothesis.

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If in a binomial situation, n = 4 and pi =.25. the mean of the distribution is 1.8 and the standard deviation is 0.84.

In a binomial situation where n = 4 and pi = 0.25, the probabilities of the following events using the binomial formula are:

a) P(x = 2) = (4 choose 2)(0.25)^2(0.75)^2 = 0.421875

b) P(x = 3) = (4 choose 3)(0.25)^3(0.75)^1 = 0.31640625

In a binomial situation where n = 5 and pi = 0.40, the probabilities of the following events using the binomial formula are:

a) P(x = 1) = (5 choose 1)(0.40)^1(0.60)^4 = 0.3456

b) P(x = 2) = (5 choose 2)(0.40)^2(0.60)^3 = 0.3456

In a binomial distribution where n = 3 and pi = 0.60, the probabilities for values of x from 0 to 3 can be calculated using the binomial formula:

P(x = 0) = (3 choose 0)(0.60)^0(0.40)^3 = 0.064

P(x = 1) = (3 choose 1)(0.60)^1(0.40)^2 = 0.288

P(x = 2) = (3 choose 2)(0.60)^2(0.40)^1 = 0.432

P(x = 3) = (3 choose 3)(0.60)^3(0.40)^0 = 0.216

To find the mean and standard deviation of the binomial distribution where n = 3 and pi = 0.60, we can use the following formulas:

Mean (μ) = n * pi = 3 * 0.60 = 1.8

Standard deviation (σ) = sqrt[n * pi * (1 - pi)] = sqrt[3 * 0.60 * (1 - 0.60)] = 0.84

Therefore, the mean of the distribution is 1.8 and the standard deviation is 0.84.

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Answer: no

Step-by-step explanation:

Based on the information provided, it appears that Erik is increasing the number of cars he sells each month by 8. If he continues this pattern, he will sell 54 cars in April, 62 in May, and so on. By December, he will have sold a total of 678 cars (30 + 38 + 46 + … + 126), which is less than his goal of 900 cars. So no, if Erik keeps this pattern, he will not reach his goal.Based on the information provided, it appears that Erik is increasing the number of cars he sells each month by 8. If he continues this pattern, he will sell 54 cars in April, 62 in May, and so on. By December, he will have sold a total of 678 cars (30 + 38 + 46 + … + 126), which is less than his goal of 900 cars. So no, if Erik keeps this pattern, he will not reach his goal.

Step-by-step explanation:

(x² /x² + 7x + 6)÷(9x - 9/x² - 1)

(x²/(x + 1)(x + 6))×((x + 1)(x - 1)/9(x - 1))

(x²/(x + 6))×1/9

x²/9(x + 6)

The Mean of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

On the off chance that all of the scores within the populace are changed into z-scores, at that point the coming about the conveyance of z-scores will have a cruel (mean) of and a standard deviation of 1.

Usually, since the change of a crude score x to a z-score is given by:

z = (x - μ) / σ

where μ is the populace Mean.

and σ is the populace standard deviation.

When all scores within the populace are changed to z-scores, the Mean of the coming about dispersion of z-scores will be:

( Mean of z-scores)

= [(Mean  of crude scores) - μ] / σ

= (μ - μ) / σ =

So also, the standard deviation of the dissemination of z-scores will be:

(standard deviation of z-scores) = (standard deviation of crude scores) / σ = σ / σ = 1

In this manner,

The cruel of the dispersion of z-scores will be 0, and the standard deviation will be 1. 

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If all of the scores in the population are transformed into z-scores, the values for the mean and standard deviation for the complete set of z-scores will be a mean of 0 and a standard deviation of 1.

This is because the process of transforming scores into z-scores involves subtracting the mean of the population and dividing by the standard deviation, which effectively standardizes the data to have a mean of 0 and a standard deviation of 1. When all the scores in a population are transformed into z-scores, the mean of the complete set of z-scores will be 0 and the standard deviation will be 1. This is because z-scores represent the number of standard deviations a value is from the mean, and the transformation standardizes the distribution.

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The points on the surface z² = xy + 16 closest to the origin are: (-4,4,0) and (4, -4, 0)

We know that the distance between an arbitrary point on the surface and the origin is d(x, y, z) = √(x² + y² + z²)

Using Lagrange multipliers,

L(x, y, z, λ) = x² + y² + z² + λ(z² - xy - 16)

We have partial derivatives.

[tex]L_x[/tex] = 2x - λy

[tex]L_y[/tex] = 2y - λx

[tex]L_z[/tex] = 2z + 2zλ

[tex]L_\lambda[/tex] = z² - xy - 16

Now we set each partial derivative to zero to find critical points.

[tex]L_x[/tex] = 0

2x - λy = 0

[tex]L_y[/tex] = 0

2y - λx = 0

After solving above equations simultaneously we get (x + y)(x - y) = 0

i.e., x = -y   OR   x = y

[tex]L_z[/tex] = 0

2z + 2zλ = 0

z = 0  OR  λ = 0

Consider [tex]L_\lambda[/tex] = 0

z² - xy - 16 = 0

-xy = 16                  ............(as z = 0)

when x = y then -y² = 16 which is not true.

So, consider x = -y

-(-y)y = 16

y² = 16

y = ±4

when y = 4 then we get x = -4

and when y = -4 then we get x = 4

Therefore, the closest points are:(-4,4,0) and (4, -4, 0)

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Answer:

x>14

Step-by-step explanation:

since 14/4 = 3.5 your X value should be greater than 14. You would graph the point anywhere to the right of 14

Answer: x>14

Step-by-step explanation:

isolate x

3.5<x/4

14<x

x>14

open circle x>14

Answer:

---------------------------

Use the identity for the square of a sum:

Comparing with the given we see that:

Then find b:

To complete the square we need to add b² = (-3)² = 9 to both sides:

The correct answer is option b. Burger Quick, because it has a larger mean.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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To make the expression a perfect square trinomial, we need to add and subtract the square of half of the coefficient of k. In this case, the coefficient of k is -3. Half of -3 is -3/2. The square of -3/2 is 9/4. Therefore, we can add and subtract 9/4 to the expression as follows:

Now we can write this as a perfect square trinomial:

Answer:

It should be the first one

Step-by-step explanation:

3x2=6

3x3=9

Answer:

k = - 8

Step-by-step explanation:

given that (x - a) is a factor of f(x) , then f(a) = 0

given

(x - 1) is a factor of f(x) then f(1) = 0 , that is

3(1)³ + 5(1) + k = 0

3(1) + 5 + k = 0

3 + 5 + k = 0

8 + k = 0 ( subtract 8 from both sides )

k = - 8

Answer:

  (-5x +y +1)(5x -y +1)

Step-by-step explanation:

You want the factored form of 1-25x²+10xy-y².

We recognize the last three terms as those of a perfect square trinomial:

  25x² -10xy +y² = (5x -y)²

Using this form for the last three terms, we see the given expression is the difference of squares. It can be factored as such.

  1 -(5x -y)² = (1 -(5x -y)(1 +5x -y)

  = (-5x +y +1)(5x -y +1)

__

Additional comment

The forms we used here are ...

  (a -b)² = a² -2ab +b²

  a² -b² = (a -b)(a +b)

<95141404393>

Answer:

below

Step-by-step explanation:

26. yes because a straight line is formed

27. domain - -2 to 2

range -2 to 1

Answer:

Yes, the graph is a linear function.

Domain: x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Step-by-step explanation:

A linear function is an expression that will form a straight line when graphed (or a graph that forms a straight line). These points form a straight line, so the function is linear.

The domain of the function is everything that x can be equal to. We can see here that the ordered points are:

(-2, -1.5), (-1.5, -1), (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), (1.5, 2)

So, the domain of the function is all of the x values of the ordered pairs, or:

x∈[-2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5]

(the symbol next to the x means "belongs to.")

As for the range, it is everything that y can be equal to. Let us look once again at the ordered pairs. The range of the function is equal to the y coordinates of these ordered pairs, or:

Range: y∈[-1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2]

Keep in mind that if the function contains more than one value for x or y, it is listed ONLY ONCE in the domain/range.

The function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

When f(x) is divided by 3x + 1, the quotient is 3x² - 4x - 1 and the remainder is -10. We can use polynomial long division to write f(x) in the form:

f(x) = (3x² - 4x - 1)(3x + 1) - 10

Multiplying out the right side gives:

f(x) = 9x³ - 7x² - 13x - 11

Therefore, the function f(x) is f(x) = 9x³ - 7x² - 13x - 11 written in standard form.

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The option that linear optimization outcome is not possible is option (d) there is an unbounded solution

In linear optimization, a problem is said to be unbounded if there exists at least one feasible solution with an objective value that can be made infinitely large (or small) by increasing (or decreasing) the value of one or more decision variables without violating any of the problem's constraints. An unbounded solution is not a feasible or practical solution since it implies that there is no limit to how much the objective function can be improved.

On the other hand, it is possible to have multiple optimal solutions (a), a unique optimal solution (b), or have the solver request a change in a constraint (c) in linear optimization, depending on the specific problem and constraints.

Therefore, the correct option is (d) there is an unbounded solution

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According to unitary method, there are 10 30¢ cards and 8 35¢ cards in the box, which adds up to a total of $5.80.

Let's start by defining our units. In this case, our units are the number of 30¢ cards and the number of 35¢ cards. We know that the box of cards is being sold for $5.80, which means the total value of all the cards in the box is $5.80. We can use this information to set up an equation:

0.30x + 0.35y = 5.80

where x is the number of 30¢ cards and y is the number of 35¢ cards.

Next, we are given the information that the number of 30¢ cards is six more than one half the number of 35¢ cards. Using the unitary method, we can set up an equation that relates the number of 30¢ cards to the number of 35¢ cards:

x = 0.5y + 6

Now we can use this equation to eliminate x from our first equation:

0.30(0.5y + 6) + 0.35y = 5.80

Simplifying this equation gives:

0.15y + 1.80 + 0.35y = 5.80

0.50y = 4.00

y = 8

So there are 8 35¢ cards in the box. We can use the unitary method again to find the number of 30¢ cards:

x = 0.5y + 6

x = 0.5(8) + 6

x = 10

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Answer: 25% chance

Step-by-step explanation: the chance is 25 % because theirs 3 coins each equaling 25 So, all 3 added will equal 75 %  and then, if the 1 coin landed on heads while the other 2 coins lands on heads that would minus 25% and 50% and get 25%.                                                                          

hopefully u consider me as a giga chad  :)

There are 19 people who own a cat or a dog.

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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The value of x for the given chords is 23.

A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the centre of the circle. In the illustration below, a circle and its chord are shown. At the circle's centre, chords with identical lengths subtend equal angles.

We know that, the product of the lengths of the segments of one chord, when two chords cross inside a circle, equals the product of the lengths of the segments of the other chord.

Thus,

(18)(10) = (9)(x - 3)

180 = 9x - 27

9x = 207

x = 23

Hence, the value of x for the given chords is 23.

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The value of x to the nearest hundredth is 14.12.

Similar triangles are triangles that have the same shape, but their sizes may vary. The ratio of the corresponding sides of similar triangles are equal.

Also for two angles to be similar, the corresponding angles must be equal.

Triangle ABC and BCD are similar. Therefore ;

30/34 = x/16

34x = 30×16

34x = 480

divide both sides by 34

x = 480/34

x = 14.12( nearest hundredth)

therefore the value of x is 14.12.

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If some students checked 6 bags of Doritos marked with a "net-weight" of 28.3 grams, then these data satisfies all the three assumptions for inference (random condition, independent condition and normal condition.

To determine whether weight of bag satisfy the assumptions for inference, we need to consider the assumptions of statistical inference.

The assumptions are :

(i) Random Sampling: The data should be collected from a random sample, where each bag of Doritos has an equal chance of being selected.

This assumption is satisfied, because we assume that the "6-bags" are randomly selected.

(ii) Independence: The data points should be independent of each other, meaning that the weight of one bag of Doritos should not depend on the weight of another bag.

This assumption is satisfied as, bags were weighed separately and their weights were recorded without any influence from other bags.

(iii) Normality: The distribution of the data should be approximately normal.

This assumption is also satisfied , because histogram shows that there are "No-Outliers" and normal "quantile-plot" is linear.

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The length of L of one "arch" of the cycloid that is the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire is 8R.

The parametric equations of cycloid are,

x(t) = R (t - sint)

y(t) = R (1 - cost)

Now differentiating the equations with respect to 't' we get,

x'(t) = R (1 - cost)

y'(t) = R sint

The length L of one arch of the cycloid is given by,

L = [tex]\int_a^b{\sqrt{(x'(t))^2+(y'(t))^2}}dt[/tex]

Here since the curve is cycloid so a = 0 and b = [tex]2\pi[/tex].

So,

L = [tex]\int_0^{2\pi}{\sqrt{(R(1-\cos t))^2+(R\sin t)^2}dt}[/tex]

  = [tex]\int_0^{2\pi}{\sqrt{R^2(1-\cos t)^2+R^2\sin^2t}dt}[/tex]

  = [tex]R\int_0^{2\pi}{\sqrt{1-2\cos t+\cos^2t+\sin^2t}dt}[/tex]

  = [tex]R\int_0^{2\pi}{\sqrt{2-2\cos t}dt}~~~[\because \cos^2t+\sin^2t=1][/tex]

  = [tex]R\int_0^{2\pi}{\sqrt{2(1-\cos t)}dt}=R\int_0^{2\pi}{\sqrt{4\sin^2 \frac{t}{2}}dt}[/tex]

  = [tex]2R\int_0^{2\pi}{\sin \frac{t}{2} dt}[/tex]

  [tex]=2R\frac{[-\cos \frac{t}{2}]_0^{2\pi}}{\frac{1}{2}}=4R[-\cos\pi+\cos0]=8R[/tex]

Hence the length L of an "arch" of the cycloid, that is, the distance traveled by a small stone stuck in the tread of a tire of radius R during one revolution of the rolling tire is 8R.

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As per the data mentioned in the table, Jade's mom is 0.7 ft or 1 ft taller than jade.

Mixed numbers represent whole numbers and proper fractions together. Usually represents a number between any two integers. Hybrid numbers are made by combining three parts:

An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number.

Height of jade's mom = 5⁵/₈ ft

Jade's height = 4⁵/₆

The difference in their heights is:

= (45/8) - (29/6)

= (270 - 232)/48

= 38/48

= 0.7 ft

0.7 ft ≈ 1 ft

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The correct option is C, the skews are different.

We have two dot plots and we want to see which statement is the best suported by these.

The right one is better distributed, so we can conclude that the correct statement is that the data have different skews.

The ranges may seem also to be different, but are the same ones, in the first one is:

20 - 12 = 8

In the second it is:

19 - 11 = 8

so the correct option is C.

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We get a probability of 3/8 or 0.375.

To find the probability of two successes (i.e., drawing two red balls) out of three draws from an urn containing 14 balls (7 of which are red), we can use the binomial probability formula:

[tex]P(X = 2) = (n\ choose\ x) * p^x * (1-p)^{(n-x)[/tex]

where

n is the total number of draws (3 in this case),

x is the number of successes (2 in this case),

p is the probability of a success on any given draw (7/14 or 1/2 in this case),

and (n choose x) is the number of ways to choose x items out of n items.

Plugging in the values, we get:

[tex]P(X = 2) = (3\ choose\ 2) * (1/2)^2 * (1/2)^{(3-2)} = 3/8[/tex]

Therefore, the probability of getting two red balls out of three draws is 3/8 or 0.375.

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The smallest positive integer value of n for which 225n is a multiple of 540 is 8.

To determine the smallest positive integer value of n for which 225n is a multiple of 540, we need to find the least common multiple (LCM) of 225 and 540 and then divide it by 225.

To find the LCM of 225 and 540, we can factor both numbers into primes:

225 = 3^2 x 5^2

540 = 2^2 x 3^3 x 5

The LCM will be the product of the highest powers of each prime factor:

LCM = 2^2 x 3^3 x 5^2 = 1800

Now, we divide the LCM by 225:

1800 / 225 = 8

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