Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
2 – 3 = -3 + 2

Answer:

D

2+3 is not a ratio it equals to 5

The required Poisson distribution used to model the elapsed time between the occurrence of successive events for a poisson random variable

We have to find distribution model used to model elapse the time between the occurrence of successive events for Poisson random variable.

we know that, Poisson distribution

P(x=x) = e^-λ(λ)^x/x!

Time between succeess,

P(y>x) = e^-λy

and, P(y<x) = 1- e^-λy

They are exponential distribution.

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The 99% confidence interval for the population mean is (29.25, 41.05) months.

To calculate the confidence interval, we can use the formula:

Confidence interval = sample mean ± (critical value * standard deviation / square root of sample size)

Given that the sample mean is 35.15, the critical value for a 99% confidence level can be found using a standard normal distribution table, which is approximately 2.576. The standard deviation is known to be 20 months, and the sample size is 31.

Substituting these values into the formula, we get:

Confidence interval = 35.15 ± (2.576 * 20 / √31) ≈ (29.25, 41.05) months.

This means we can be 99% confident that the true population mean falls within this range.

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Answer:

57)  \(\sqrt[4]{1}\) = 1            

58)  \(\sqrt[5]{1}\) = 1

59) \(\sqrt[4]{16}\) = 2

60) \(\sqrt[4]{81}\) = 3  

61) \(-\sqrt[4]{16}\) = -2

62) \(-\sqrt[4]{81}\) = -3

63) \(\sqrt[4]{-16}\) = \(2\sqrt[4]{-1}\)

64) \(\sqrt[4]{-81}\) = \(3\sqrt[4]{-1}\)

65) \(\sqrt[5]{-1}\) = -1

66) \(\sqrt[7]{-1}\) = -1

67) \(\sqrt[6]{-1}\) =  \(i\)

68) \(\sqrt[8]{-1} = \sqrt[8]{-1}\)

69)  \(-\sqrt[4]{256}\) = -4

70) \(-\sqrt[4]{10,000}\) = -10

71) \(\sqrt[6]{64}\) = 2

72) \(\sqrt[5]{32}\) = 2

73) \(-\sqrt[5]{32}\) = -2

74) \(-\sqrt[6]{64}\) = -2

The percentage of the group that is between 62 and 65 inches tall is 47.725%

The given parameters are:

Calculate the z-scores for x = 62 and x = 65 using:

z = (x - μ)/σ

So, we have:

z = (62 - 62)/1.5 = 0

z = (65 - 62)/1.5 = 2

The percentage is then represented as:

P(62 < x < 65) = P(0 < z < 2)

Rewrite as:

P(62 < x < 65) = P(z < 2) - P(z < 0)

Evaluate

P(62 < x < 65) = 0.47725

Express as percentage

P(62 < x < 65) = 47.725%

Hence, the percentage of the group that is between 62 and 65 inches tall is 47.725%

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0.17

Explanation

Step 1

the percentage is a ratio , between a number and 100

for example:

if you know that 56 % of the students are boys, it means that 56 of every 100 students are boys.

then.

Step 2

I hope this helps you

Answer:

1) Pr(all three) = 0.064

2) Pr(none) = 0.216

3) Independent event

Step-by-step explanation:

Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)

Where Pr = probability

This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure

Where p = success, q = failure

For n trials,

Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)

Pr (security) = 40% = 0.4

p = 0.4

q = 1-p = 1-0.4 = 0.6

Numbers selected at random = n = 3

See attachment for more details on the workings.

1) Probability all three of the selected homes have a security system = Pr(all three)

Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³

= 0.4×0.4×0.4

Pr(all three) = 0.064

2) Probability none of the three selected homes have a security system

= Pr(none)

Pr(none) = 1 × (0.4)^0 × (0.6)³

= 0.6³ = 0.6×0.6×0.6

Pr(none) = 0.216

3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.

Answer:

16537.5

Step-by-step explanation:

4.5% of 13500 = 607.5

607.5 x 5 = 3037.5

3037.5 + 13500 = 16537.5

฿₤₦

To translate the given English statements into logical expressions using the provided predicates, here are the translations:

1. Everyone who was well went to work yesterday.

  - ∀x [(W(x) ∧ ¬P(x)) → W(x)]

2. Someone who was sick yesterday did not go to work yesterday.

  - ∃x (P(x) ∧ ¬W(x))

3. Someone who missed work was neither sick nor on vacation.

  - ∃x (¬(P(x) ∨ Q(x)) ∧ ¬W(x))

4. Joshua was on vacation yesterday and he did not go to work.

  - Q(Joshua) ∧ ¬W(Joshua)

5. Everyone was well and went to work yesterday.

  - ∀x (W(x) → W(x) ∧ ¬P(x))

Please note that these translations assume that the domain consists of all employees of the company, including Joshua. Also, the logical expressions are based on the provided predicates and their interpretations.

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ABCD can be square if the distance between all four points is the same.

A square is a two-dimensional closed shape with four equal sides and four corners. The opposite sides of the square are parallel to each other. A square is also a rectangle with equal length and width. A square is an equilateral quadrilateral with all four equal sides and all four equal angles. Square angles are right angles or 90 degrees. Also, the diagonals of the square are equal and bisect at 90 degrees. A square is just a quadrilateral with four equal sides. There are many rectangular objects around us.

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Answer:

V=14

Step-by-step explanation:

3v=42 divide both sides by 3. getting v=14

Step-by-step explanation:

Principal = 250,000

Rate = 4%

Simple interest = 850,000

Time = ?

\(t = \frac{100 \times interest}{principal \times rate} \\ t = \frac{100 \times 850000}{250000 \times 4} \\ t = \frac{100 \times 85}{25 \times 4} \\ t = \frac{8500}{100} \\ t = 85years\)

Answer:

The radius of the Hemisphere is 15.8 cm.

Explanation:

The formula for the volume of an hemisphere can be written as;

Given that the volume of the hemisphere is;

We can get the radius of the hemisphere using the formula above.

Firstly let us make r the subject of formula;

Lastly let us substitute the given volume V into the derived formula for radius r.

Therefore, the radius of the Hemisphere is 15.8 cm.

Answer:

The answer is 3/8 Step-by-step explanation: apex

Solution :

Let \($v_0$\) be the unit vector in the direction parallel to the plane and let \($F_1$\) be the component of F in the direction of \(v_0\) and \(F_2\) be the component normal to \(v_0\).

Since, \(|v_0| = 1,\)

\($(v_0)_x=\cos 60^\circ= \frac{1}{2}$\)

\($(v_0)_y=\sin 60^\circ= \frac{\sqrt 3}{2}$\)

Therefore, \(v_0 = \left<\frac{1}{2},\frac{\sqrt 3}{2}\right>\)

From figure,

\(|F_1|= |F| \cos 30^\circ = 10 \times \frac{\sqrt 3}{2} = 5 \sqrt3\)

We know that the direction of \(F_1\) is opposite of the direction of \(v_0\), so we have

\($F_1 = -5\sqrt3 v_0$\)

    \($=-5\sqrt3 \left<\frac{1}{2},\frac{\sqrt3}{2} \right>$\)

    \($= \left<-\frac{5 \sqrt3}{2},-\frac{15}{2} \right>$\)

The unit vector in the direction normal to the plane, \(v_1\) has components :

\($(v_1)_x= \cos 30^\circ = \frac{\sqrt3}{2}$\)

\($(v_1)_y= -\sin 30^\circ =- \frac{1}{2}$\)

Therefore, \($v_1=\left< \frac{\sqrt3}{2}, -\frac{1}{2} \right>$\)

From figure,

\(|F_2 | = |F| \sin 30^\circ = 10 \times \frac{1}{2} = 5\)

∴  \(F_2 = 5v_1 = 5 \left< \frac{\sqrt3}{2}, - \frac{1}{2} \right>\)

                   \($=\left<\frac{5 \sqrt3}{2},-\frac{5}{2} \right>$\)

Therefore,

\($F_1+F_2 = \left< -\frac{5\sqrt3}{2}, -\frac{15}{2} \right> + \left< \frac{5 \sqrt3}{2}, -\frac{5}{2} \right>$\)

           \($=<0,- 10> = F$\)

Answer:

Mean - 17.222222222222

Median - 17

Mode - 12

Step-by-step explanation:

lets arrange this is least to greatest.

2, 4, 12, 12, 17, 18, 28, 29, 33

to find the mean(even though you dont need it), you add all the numbers up and devide by the amount of numbers.

so -> 2 + 4 + 12 + 12 + 17 + 18 + 28 + 29 + 33 = 155

and there are 9 numbers, so 155 / 9 = 17.2 and a lot more 2s

to find the median, you arrange from least to greatest vice versa, then find the middle number.

2, 4, 12, 12, 17, 18, 28, 29, 33

the middle number is 17, so the mean is 17

to find the mode, you have to find the number that is most repeated.

2, 4, 12, 12, 17, 18, 28, 29, 33

the number that is repeated the most is 12, so your mode is 12.

Hope this helped!!!

To determine whether to reject or fail to reject the null hypothesis, we typically rely on statistical hypothesis testing. After conducting a hypothesis test, we consider the test statistic and the corresponding p-value.

When the p-value is less than or equal to the predetermined significance level (usually denoted as α), we reject the null hypothesis. This indicates that the observed data provides sufficient evidence to support the alternative hypothesis. Conversely, when the p-value is greater than the significance level, we fail to reject the null hypothesis. In this case, we do not have enough evidence to support the alternative hypothesis.

The significance level α is predetermined and represents the probability of making a Type I error, which is the rejection of the null hypothesis when it is actually true. Commonly used significance levels include 0.05 (5%) and 0.01 (1%). The choice of the significance level depends on the specific research context and the consequences of making a Type I error.

It is important to note that failing to reject the null hypothesis does not necessarily mean that the null hypothesis is true. It simply means that the observed data does not provide enough evidence to support the alternative hypothesis. There could still be other factors or limitations in the study that contribute to the lack of significant results.

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Gulls managed to eat scallops in the novel "Island of the Blue Dolphins" through their adaptive feeding behaviors and opportunistic nature.

In the novel "Island of the Blue Dolphins" by Scott O'Dell, gulls are depicted as opportunistic feeders that have adapted their feeding behaviors to consume scallops. The island where the story takes place is abundant with scallops, which serve as a vital food source for the gulls.

Gulls are skilled at detecting and locating food sources, including scallops. They have keen eyesight and the ability to spot scallops in the water or on the shore. Gulls use their sharp beaks to pry open the shells of the scallops, accessing the nutritious flesh inside.

They are known to scavenge and steal food from other animals, including smaller birds or marine creatures. In the case of scallops, gulls may compete with other predators, such as otters or crabs, to obtain these shellfish for their own sustenance.

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Answer: 3

Step-by-step explanation: (2x2 + 5x - 7) + ( 3 - 4x2 + 6x)= -8+11x=3

Protractor postulate: given any angle, we can express its measure as a unique real number from 0 to 180 degrees.

The protractor postulate is a fundamental concept in geometry that establishes a way to measure angles using a protractor. According to this postulate, every angle can be uniquely represented by a real number between 0 and 180 degrees.

A protractor is a geometric tool with a semicircular shape and marked degrees along its edge. To measure an angle using a protractor, we align the center of the protractor with the vertex of the angle and the baseline of the protractor with one side of the angle. We then read the degree measure where the other side of the angle intersects the protractor.

The protractor is divided into 180 degrees, with 0 degrees being the starting point at the baseline of the protractor, and 180 degrees being at the opposite end of the baseline. By aligning the protractor with an angle, we can determine its measure as a real number within this range.

For example, if we measure an angle using a protractor and find that the other side intersects the protractor at 45 degrees, we can express the measure of the angle as 45 degrees. Similarly, if the intersection point is at 90 degrees, the angle measure would be 90 degrees. The protractor postulate guarantees that these angle measures are unique within the range of 0 to 180 degrees.

It is important to note that the protractor postulate assumes that angles can be measured using a protractor and that the measurement is accurate and reliable. The postulate provides a consistent and standardized way to assign a numerical value to an angle, allowing for precise communication and comparison of angles in geometric contexts.

In summary, the protractor postulate establishes that the measure of any angle can be expressed as a unique real number between 0 and 180 degrees. This concept is fundamental in geometry and allows for the measurement, comparison, and communication of angles using a protractor.

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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I cannot tell if that is an multiply sign or a x

Step-by-step explanation:

Answer:

0.18

Step-by-step explanation:

Maths big brain

Answer:

k=5

Step-by-step explanation:

for every one unit on the x, the y goes up five. So, the ratio is 5:1 or five.

Answer:

1/3 is the experimental probability of rolling 6

Explanation:

Given, a die roll 10 times in which we get 6 three times. Total no. of  possible outcomes = 10 and number of favorable outcomes = 3

Therefore, the probability of getting 6 =  1/3.

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

45

Step-by-step explanation:

x+5 =50

x=45