Which type of graph is best for displaying the range of the data set above?
A. box-and-whisker plot

B. pie chart

C. bar graph

D. stem-and-leaf plot

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer: \(0.024\ \text{miles per sec}\)

Step-by-step explanation:

Given

Path is changing according to the function \(f(x)=0.03(10x-x^2)\)

Rate of change of the elevation is given by the derivative of the function

\(\Rightarrow f'(x)=0.03(10-2x)\)

At \(x=1\ f'(x) \ \text{is}\)

\(\Rightarrow f'(x=1)=0.03(10-2\times 1)\\\Rightarrow f'(x=1)=0.03(8)\\\Rightarrow f'(x=1)=0.24\ \text{miles per sec}\)

Using derivatives, it is found that the rate of change of elevation at x = 1 is of 0.24.

\(f^{\prime}(a)\)

In this problem, the function is:

\(f(x) = 0.03(10x - x^2)\)

Hence:

\(f^{\prime}(x) = 0.3 - 0.06x\)

At x = 1:

\(f^{\prime}(1) = 0.3 - 0.06(1) = 0.24\)

The rate of change of elevation at x = 1 is of 0.24.

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Answer:

The probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is 0.0885.

Step-by-step explanation:

We are given that the population of men at UMBC has a mean height of 69 inches with a standard deviation of 4 inches. The women at UMBC have a mean height of 65 inches with a standard deviation of 3 inches.

A sample of 50 men and 40 women is selected.

The z-score probability distribution for the two-sample normal distribution is given by;

                          Z  =  \(\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }\)  ~ N(0,1)

where, \(\mu_M\) = population mean height of men at UMBC = 69 inches

           \(\mu_W\) = population mean height of women at UMBC = 65 inches

           \(\sigma_M\) = standard deviation of men at UMBC = 4 inches

           \(\sigma_M\) = standard deviation of women at UMBC = 3 inches

           \(n_M\) = sample of men = 50

           \(n_W\) = sample of women = 40

Now, the probability that the sample mean of men heights is more than 5 inches greater than the sample mean of women heights is given by = P(\(\bar X_M-\bar X_W\) > 5 inches)

 P(\(\bar X_M-\bar X_W\) > 5 inches) = P( \(\frac{(\bar X_M-\bar X_W)-(\mu_M-\mu_W)}{\sqrt{\frac{\sigma_M^{2} }{n_M}+\frac{\sigma_W^{2} }{n_W} } }\) > \(\frac{(5)-(69-65)}{\sqrt{\frac{4^{2} }{50}+\frac{3^{2} }{40} } }\) ) = P(Z > 1.35)

                                         = 1 - P(Z \(\leq\) 1.35) = 1 - 0.9115 = 0.0885

The above probability is calculated by looking at the value of x = 1.35 in the z table which has an area of 0.9115.      

1) Let's begin by writing all the possible outcomes of those two dices between parentheses. The first number refers to the first dice, and the second one to the 2nd dice:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Note that there are 36 outcomes.

2) Now, let's focus on finding the number of favorable events:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

There are a total number of 10 favorable outcomes.

3) Therefore, we can write out the following probability:

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Therefore, the probability that the first number divided by the second number is greater than zero is 1/3.

In mathematics, probability is a measure of the likelihood or chance of an event occurring. It is a way of quantifying uncertainty and expressing how likely it is that a particular outcome will occur. Probability theory is used in a wide range of fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It is used to model and analyze random phenomena, make predictions, and estimate the likelihood of certain outcomes.

Here,

Since we are returning the first tile to the bag before selecting the second one, the two selections are independent of each other.

There are two cases to consider:

Case 1: We select a positive number on the first draw.

The probability of selecting a positive number on the first draw is 2/3, since there are two positive numbers (-12 and 1) out of a total of three tiles.

Regardless of what number we select on the first draw, there is only one negative number (-2) in the bag, so the probability of selecting a negative number on the second draw is 1/3.

Therefore, the probability of selecting a positive number on the first draw and a negative number on the second draw (which results in a quotient greater than zero) is:

(2/3) x (1/3) = 2/9

Case 2: We select the negative number (-2) on the first draw.

The probability of selecting the negative number (-2) on the first draw is 1/3.

In this case, we must select the positive number on the second draw in order for the quotient to be greater than zero. There is only one positive number (1) in the bag, so the probability of selecting it on the second draw is 1/3.

Therefore, the probability of selecting the negative number (-2) on the first draw and the positive number on the second draw (which results in a quotient greater than zero) is:

(1/3) x (1/3) = 1/9

Since these are the only two cases that satisfy the condition, the overall probability is the sum of the probabilities of these two cases:

2/9 + 1/9 = 3/9 = 1/3

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Answer: 4000

Step-by-step explanation:

on the right side should have been added to

Answer:

The graph should have closed not open circles

Step-by-step explanation:

The denominator of the fraction at point Y is equal to 24.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Let the variable d represent the denominator of the fraction at point Y and since point Y is the same distance from 0 as point X, which is at 2/3 on a number line, this can be modeled by this mathematical expression:

8/d = 1 - 2/3

8/d = 1/3

Cross-multiplying, we have:

d = 8 × 3

d = 24.

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The fourth term  of the progression is 24 and sixth term of the progression is 96.

Given,

In the question:

The first term of the geometric progression is 3 and the common ratio is 2.

To find the fourth term and sixth term of the progression.

Now, According to the question:

The Geometric Progression is:

\(a_{1}=3\) and r = 2

To solve for n = 4

The formula is :

\(a_{n} = ar^n^-^1\)

Put all the values in above formula :

\(a_{4} = 3(2)^4^-^1\) = 3(2)^3 = 24

To solve for n = 6

The formula is :

\(a_{n} = ar^n^-^1\)

Put all the values in above formula :

\(a_{6} = 3(2)^6^-^1\) = 3(2)^5 = 96

Hence, the fourth term  of the progression is 24 and sixth term of the progression is 96.

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Answer:

12.5

Step-by-step explanation:

3 scoops = 1 cup

6 scoops = 2 cups

9 scoops = 3 cups

12 scoops = 4 cups

Answer:

1) Parallel line:  y = 4x + 1

4) Perpendicular line:  y = -5x + 9

6) Perpendicular line: y = 3x + 2

Step-by-step explanation:

I will only provide solutions to question 1, 4, and 6, in accordance with Brainly's guidelines. Since the given problem essentially involves the same type of questions, the solutions that I will provide should allow you to apply the same techniques in solving for the remainder of the questions.

Parallel lines have the same slope.

Perpendicular lines have negative reciprocal slopes. This means that when you multiply the slopes of two lines that are perpendicular from each other will result in a product of - 1.

In other words, if the slope of a line is m₁, and the slope of the other line is  m₂, then it means that they are perpendicular from each other if:  m₁ × m₂ = - 1

According to the definitions provided on parallel lines, since the given linear equation has a slope, m = 4, then it means that the other line parallel to it must have the same slope.

Given the y-intercept of the other line as b = 1, and its slope, m = 4, then the equation of the line parallel to y = 4x + 3 is:

Equation of Parallel line:  y = 4x + 1.

Given the linear equation, y = ⅕x + 4, where its slope,  m₁ = ⅕

Then it means that the negative reciprocal of  ⅕ must be ⇒   \(\large\mathsf{-\frac{5}{1}\:\:or\:\:-5}\)

Because:  m₁ × m₂ = - 1

                 ⅕ × -5 = -1

Therefore, if the y-intercept of the other line is b = 9, and its slope is m₂ = -5, then the equation of the line perpendicular to y = ⅕x + 4 is:

Perpendicular line:  y = -5x + 9.

Given the equation of the first line, y = -⅓x - 8, where its slope, m₁ = -⅓.

Then it means that the slope of the other line must be m₂ = \(\large\mathsf{\frac{3}{1}\:\:or\:\:3}\)  because:                

       m₁ × m₂ = - 1

       -⅓ ×  3 =  -1

Next, substitute the slope of the other line, m₂ = 3, and the values of the given point, (2, 8) into the slope-intercept form, y = mx + b, in order to solve for the y-intercept of the other line.

y = mx + b

8 = 3(2) + b

8 = 6 + b

Subtract 6 from both sides to isolate b:

8 - 6 = 6 - 6 + b

2 = b

Therefore, the equation of the line perpendicular to y = - ⅓x - 8 is:

Perpendicular line: y = 3x + 2.

\((2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}\)

The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.

On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

this question is related to probability.

mutually exclusive

Mutually exclusive events are those events that do not occur at the same time.

For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.

probability

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

42°

Step-by-step explanation:

This is right triangle and sum of 2 angles is 90°:

y+48°=90°

so y= 90°- 48°= 42°

\(\dfrac 28 x + \dfrac 38 (x-1) = 4\\\\\implies \dfrac 18(2x + 3x -3) = 4\\\\\implies 5x -3 = 32\\\\\implies 5x = 32 +3 \\\\\implies 5x = 35\\\\\implies x = \dfrac{35}5\\\\\implies x = 7\)

Answer:

The value of x is 7.

Step-by-step explanation:

Question :

\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)

Solution :

\({\implies{\sf{\dfrac{2}{8} x + \dfrac{3}{8}(x - 1) = 4}}}\)

\({\implies{\sf{\dfrac{2}{8} \times x + \dfrac{3}{8}(x - 1) = 4}}}\)

\({\implies{\sf{\dfrac{2 \times x}{8} + \dfrac{3(x - 1)}{8} = 4}}}\)

\({\implies{\sf{\dfrac{2x}{8} + \dfrac{3x - 3}{8} = 4}}}\)

\({\implies{\sf{\dfrac{2x + 3x - 3}{8} = 4}}}\)

\({\implies{\sf{\dfrac{5x - 3}{8} = 4}}}\)

\({\implies{\sf{{5x - 3} = 4 \times 8}}}\)

\({\implies{\sf{{5x - 3} =32}}}\)

\({\implies{\sf{5x = 32 + 3}}}\)

\({\implies{\sf{5x = 35}}}\)

\({\implies{\sf{x = 35 \div 5}}}\)

\({\implies{\sf{x = \dfrac{35}{5}}}}\)

\({\implies{\sf{x = \cancel{\dfrac{35}{5}}}}}\)

\({\implies{\sf{x = 7}}}\)

\(\star{\underline{\boxed{\sf{\pink{x = 7}}}}}\)

Hence, the value of x is 7.

\(\rule{300}{1.5}\)

Step-by-step explanation:

Answer:

$330

Step-by-step explanation:

\(\frac{24}{198} =\frac{40}{x}\)

Cross multiply:

24x= 198(40)

to get x=330

Answer:

73.4 degrees

Step-by-step explanation:

Answer:625

Step-by-step explanation:(2+3)^4

5^4

In the equation y = 10 - 0.1x, the coefficient 0.1 represents the slope of the line.

it represents the rate of change of y with respect to x, which is the amount by which y changes for every unit increase in x.

In this case, the slope is negative (-0.1), which means that as the number of minutes on hold (x) increases by 1 unit, the level of satisfaction (y) decreases by 0.1 units.

In other words, the longer a customer spends on hold, the lower their level of satisfaction is likely to be. The slope is a key parameter in the equation and provides valuable information about the relationship between the two variables.

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The polynomial of degree 4, P(x), can be written as a product of linear factors in the form of P(x) = a(x-4)²(x-0)(x+4) where a is a constant.

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

To find the value of a, we can use the point (5,18) which is given. Since P(5) = 18, we can substitute 5 for x in the equation and solve for a. This gives us a (5-4)²(5-0)(5+4) = 18, and we can solve for a = 18/120 = 0.15. Therefore, the formula for P(x) is P(x) = 0.15(x-4)²(x-0)(x+4).

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Answer:

f5= 5

Step-by-step explanation:

The value of F₅ in the given Fibonacci sequence is 5, i.e. option A is the correct answer.

Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones.

i.e.

\(F_n = F_{n-1} + F_{n-2}\)

We have,

Fibonacci sequence {0, 1, 1, 2, 3, 5, 8, ...}

i.e.

F₁ = 0, F₁ = 1, F₂ = 1, F₃ = 2, F₄ = 3, F₅ = 5, F₆ = 8

Now,

We have to find the value of F₅,

Here, for n = 5,

i.e.

\(F_5 = F_{5-1} + F_{5-2}\)

i.e.

F₅ = F₄ + F₃

So,

F₅ = 3 + 2

So,

We get,

F₅ = 5

So, the value of  F₅ for the given sequence is  F₅.

Hence, we can say that the value of F₅ in the given Fibonacci sequence is 5, i.e. option A is the correct answer.

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Answer:

11880 ways

Step-by-step explanation:

We can solve this problem in two ways. I'm going to show you how to do both.

We have 12 persons and are to choose a chairperson, a vice chairperson, secretary and a treasurer. So we are picking 4 members our of 12 persons.

From this 12, when we pick out one member, we are left with 11members. From 11, if we pick out another one, we have 10 left. From 10, if we pick out another member we have 9 left.

Such that

12 x11 x10x 9= 11880

These are the total different leadership structures possible.

Another way to solve this is by permutation method.

nPr

12!/(12-4)!

= 12!/8!

= 11880 ways

Answer:

211410

Step-by-step explanation:

234900x.10

23490

234900-23490

211410

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

Answer:

18 + m = 49 or 49 = 18 + m

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

The statements that can be used to compare the characteristics of the functions are:

1. g(x) has the greatest maximum value.

2. All three functions share the same domain.

Explanation:

- The table shows the values of three functions - f(x), g(x), and h(x) - evaluated at different values of x.

- We cannot determine the domain of f(x) or h(x) from the given table but we can see that g(x) has a domain of all real numbers.

- We can see that g(x) has the highest maximum value among the three functions, which is 8.

- We cannot determine the range of f(x) or g(x) from the given table but we can see that h(x) has a range of all negative numbers.

- We cannot say anything about the domain or range of f(x) based on the given table.

- Therefore, the two statements that can be used to compare the characteristics of the functions are: g(x) has the greatest maximum value and all three functions share the same domain.