Simplify the expression 5(x-3)(x^2+4x+1)

Anna plants peas in 3/8 of her garden and herbs in 1/8 of it. she divides the rest of the garden into 6 sections. what fraction

Scrat [10]

To find this answer you will first subtract the two fractions from the original size of one whole garden. After that take the remaining amount and break it into six sections. This answer would represent the fraction of the original garden that is in each section. Here are the steps:
1. Add the two fractions together to get 4/8 or 1/2. This means that half of it is left.

2. Take the 1/2 that remains and divide it by 6 (1/2 divided by 6 = 1/2 x 1/6). The answer is 1/12.

3. 1/12 of the original garden is in each section.

5 0

3 years ago

Are rectangular garden has a perimeter of 280 feet the north side of the garden is 90 feet what is the length of the inside of t

attashe74 [19]

The length of the inside of the garden is<u> 50 feet.</u>

What is perimeter ?

A perimeter is a closed path that covers, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter.

There are various practical applications for calculating the perimeter. A calculated perimeter is the length of fencing needed to completely encircle a yard or garden. The perimeter (circumference) of a wheel/circle describes how far it will roll in one revolution. Similarly, the amount of string wrapped around a spool is proportional to the spool's perimeter; if the string length were correct, it would equal the perimeter.

Given :

The rectangular garden has a perimeter of 280 feet

breadth = 90 feet

Let the length be x.

Therefore according to the question,

2( 90 + x ) = 280

=> 90+ x = 140

=> x = 50

To learn more about perimeter click on the link below:

brainly.com/question/397857

#SPJ10

6 0

2 years ago

1) Write the equation of the line parallel to = 2 + 4 and passes through the point (6, −2). Show all work

worty [1.4K]

I think I understand 3 but not the rest of them

4 0

3 years ago

Read 2 more answers

Does anyone know this?

goldenfox [79]

Answer:

x¹=-6 x²=0

Step-by-step explanation:

Substitute y =0

Swap sides

Factor expression

Split into possible cases

Solve equation

5 0

4 years ago

Each year about 1500 students take the introductory statistics course at a large university. This year scores on the nal exam ar

nikitadnepr [17]

Answer:

a) Left-skewed

b) We should expect most students to have scored above 70.

c) The scores are skewed, so we cannot calculate any probability for a single student.

d) 0.08% probability that the average score for a random sample of 40 students is above 75

e) If the sample size is cut in half, the standard error of the mean would increase fro 1.58 to 2.24.

Step-by-step explanation:

To solve this question, we need to understand skewness,the normal probability distribution and the central limit theorem.

Skewness:

To undertand skewness, it is important to understand the concept of the median.

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

If the median is larger than the mean, the distribution is left-skewed.

If the mean is larger than the median, the distribution is right skewed.

Normal probabilty distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation, also called standard error of the mean $s = \frac{\sigma}{\sqrt{n}}$

(a) Is the distribution of scores on this nal exam symmetric, right skewed, or left skewed?

Mean = 70, median = 74. So the distribution is left-skewed.

(b) Would you expect most students to have scored above or below 70 points?

70 is below the median, which is 74.

50% score above the median, and 50% below. So 50% score above 74.

This means that we should expect most students to have scored above 70.

(c) Can we calculate the probability that a randomly chosen student scored above 75 using the normal distribution?

The scores are skewed, so we cannot calculate any probability for a single student.

(d) What is the probability that the average score for a random sample of 40 students is above 75?

Now we can apply the central limit theorem.

$\mu = 70, \sigma = 10, n = 40, s = \frac{10}{\sqrt{40}} = 1.58$

This probability is 1 subtracted by the pvalue of Z when X = 75. So

$Z = \frac{X - \mu}{\sigma}$

By the Central limit theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{75 - 70}{1.58}$

$Z = 3.16$

$Z = 3.16$ has a pvalue of 0.9992

1 - 0.9992 = 0.0008

0.08% probability that the average score for a random sample of 40 students is above 75

(e) How would cutting the sample size in half aect the standard error of the mean?

n = 40

$s = \frac{10}{\sqrt{40}} = 1.58$

n = 20

$s = \frac{10}{\sqrt{20}} = 2.24$

If the sample size is cut in half, the standard error of the mean would increase fro 1.58 to 2.24.

4 0

3 years ago