Solve the equation9x² – 29x – 28 = 0
Give your answers to 2 decimal places when appropriate

Answers

Answer 1

Answer:

Final answer:

The roots of the equation 9x² - 29x - 28 = 0 are x = 4 and x = -0.78.

Explanation:

The equation given is a quadratic equation. To solve it, we can use the quadratic formula: x = [-b ± sqrt(b²-4ac)] / (2a), where a, b, and c are coefficients of the quadratic equation. In your equation, a=9, b=-29, and c=-28.

So now, we substitute these values into the quadratic formula:
x = [29 ± sqrt((-29)²-4*9*(-28))] / (2*9)
Solving inside the square root first, we get:
x = [29 ± sqrt(841+1008)] / 18
x = [29 ± sqrt(1849)] / 18
Continue to simplify and you get:
x = [29 ± 43] / 18, which gives us two possible solutions:
x = 72 / 18 = 4
and
x = -14 / 18 = -0.78 (to two decimal places).

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Answer 2

Answer:

Answer:

x = 4 or x = 0.78

Step-by-step explanation:

9x² – 29x – 28 = 0

2 roots: x = ((-(-29) ± √(-29)² - 4 x 9 x (-28)) / (2 x 9)

= (29 ± √841 + 1008) / 18

= (29 ± 43) /18

x = 72 /18 = 4 or

x = -14 /18 = - 0.78

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Please help me with number 7 and 8 and explain both of them how you got it. Will mark the brainliest!

Answers

7. No this isnt possible only a irregular shape, a square or a rectangle.
8. True. it has 4 equal sides and 4 equal angles.

Find the y-intercept and x-intercept of the line -x+2y=4

Answers

Answer:

The y-intercept and x-intercept of the line are 2 and -4 respectively.

Step-by-step explanation:

Given equation of line -x + 2y = 4

We have to find the y-intercept and x-intercept of the line.

Consider the given equation of line -x + 2y = 4

the y-intercept of line is the point where the line touches y axis and we know at y axis the coordinate of x is 0.

Thus, putting x = 0 in line equation , we get,

-(0) + 2y = 4

⇒ y = $(4)/(2)$

⇒ y = 2

the x-intercept of line is the point where the line touches x axis and we know at x axis the coordinate of y is 0.

-x + 2(0) = 4

⇒ x = - 4

Thus, the y-intercept and x-intercept of the line are 2 and -4 respectively.

Answer:

y-intercept is 2 and x-intercept is -4

Step-by-step explanation:

The first step is to re-write the equation of the line in slope-intercept form; $y=mx+c$ where m is the slope and c the y-intercept. In this case we have; $y=(1)/(2) x+2$ . To determine the y-intercept we set the x to be equal to zero; $y=(1)/(2)(0)+2=2$ and the y-intercept is thus 2. To determine the x-intercept we set y to be equal to zero and solve for x; $0=(1)/(2)x+2$ . Solving for x yields -4.

Central limit theorem Imagine that you are doing an exhaustive study on the children in all of the elementary schools in your school district. You are particularly interested in how much time children spend doing active play on weekends. You find that for this population of 2,431 children, the average number of minutes spent doing active play on weekends is μ = 87.85, with a standard deviation of σ = 118.1. You select a random sample of 25 children of elementary school age in this same school district. In this sample, you find that the average number of minutes the children spend doing active play on weekends is M = 79.07, with a standard deviation of s = 129.91.The difference between M and 1.1 is due to the :_______

Answers

Answer:

Sampling error

Step-by-step explanation:

The answer is sampling error.

The sampling error occurs when the sample does not represent the full population and the result from the sample is not a representation of the results from full sample.

From information given

Population mean = 87.85

Population standard deviation = 118.1

n = 25

Sample mean = 79.07

Sample standard deviation = 129.91

118.2/√25

= 23.62

The standard deviation of the distribution is what is referred to as standard error of m = 23.62

Final answer:

The difference between the population mean and sample mean is likely due to sampling variability, a concept related to the Central Limit Theorem. Given the small sample size in this case, it's not unusual to see this difference.

Explanation:

The difference between the mean of the population (μ) and the mean of the sample (M) is likely attributable to the phenomenon known as sampling variability. This is a concept central to the Central Limit Theorem, which states that when enough random samples are taken from a population, the distribution of the means of these samples will approximate a normal distribution, even if the original population distribution is not normal. The mean of this distribution will be equal to the populating mean, and its standard deviation will be the standard deviation of the population, divided by the square root of the sample size (n).

In this specific case, you've taken a relatively small sample (n=25) from a larger population (N=2,431). Consequently, it is not unexpected that there is some difference between the population mean (μ = 87.85) and the sample mean (M = 79.07). However, as you increase the number of samples you are drawing, according to the Central Limit Theorem, the average of these sample means should converge on the population mean.

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How many groups of 7 are in 21?

Answers

There are 3 groups of 7 in 21.

To find that divide 7 from 21

3. You would divide 7 by 21 and get 3

For each of the following four statements, indicate whether it is possible or not according to probability theory. Explain your answer. (1) The probability that a customer will buy 5 items in a single purchase is 30% ___________________________ (2) The probability that a customer will buy 3 items in a single purchase is 101% ___________________________ (3) The probability that a customer will buy 3 items in a single purchase is 99% ___________________________ (4) The probability that a customer will buy 8 item

Answers

Answer:

a) According to probability theory, the following are possible:

(1) The probability that a customer will buy 5 items in a single purchase is 30%. This represents a 0.30 chance of the customer buying 5 items.

(3) The probability that a customer will buy 3 items in a single purchase is 99% This means that there a 0.99 chance that the customer will buy 3 items.

b) According to probability theory, the following are not possible:

2) The probability that a customer will buy 3 items in a single purchase is 101%. Probability is always equal to 1 or 100%. It cannot exceed 100%.

(4) The probability that a customer will buy 8 item. This part lacks the necessary information to solve the problem.

Step-by-step explanation:

Probability describes the likelihood or chance of an event happening out of the many possible events that can take place. The sum of all probabilities for a particular event is always equal to 1. This shows that probability does not exceed 100%.

Blood potassium level, continued. Judy’s measured potassium level varies according to the Normal distribution with with μ=3.8 and σ=0.2mmol/l. Let’s consider what could happen if we took 4 separate measurements from Judy. What is the blood potassium level L such that the probability is only 0.05 that the average of 4 measurements is less than L? (Hint: This requires a backward Normal calculation.)the book says about 3.64 but i got 3.28