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3 years ago

For a quadrilateral to be a rhombus, the diagonals and .

1 answer:

7 0

Blank 1= must be congruent
Blank2= must not be perpendicular

Also search up a quadrilateral rhombus see what it looks like then search up the definition of congruent and perpendicular and you’d be able to see for yourself

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The scores of students on the ACT college entrance exam in a recent year had the normal distribution with mean  =18.6 and stand

Maurinko [17]

Answer:

a) 33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) 0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

Step-by-step explanation:

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

Normal probability 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 $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 18.6, \sigma = 5.9$

a) What is the probability that a single student randomly chosen from all those taking the test scores 21 or higher?

This is 1 subtracted by the pvalue of Z when X = 21. So

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

$Z = \frac{21 - 18.6}{5.4}$

$Z = 0.44$

$Z = 0.44$ has a pvalue of 0.67

1 - 0.67 = 0.33

33% probability that a single student randomly chosen from all those taking the test scores 21 or higher.

b) The average score of the 76 students at Northside High who took the test was x =20.4. What is the probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher?

Now we have $n = 76, s = \frac{5.9}{\sqrt{76}} = 0.6768$

This probability is 1 subtracted by the pvalue of Z when X = 20.4. So

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

By the Central Limit Theorem

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

$Z = \frac{20.4 - 18.6}{0.6768}$

$Z = 2.66$

$Z = 2.66$ has a pvalue of 0.9961

1 - 0.9961 = 0.0039

0.39% probability that the mean score for 76 students randomly selected from all who took the test nationally is 20.4 or higher

4 0

3 years ago

A gardener has a container with 6 1/5 ounces of liquid plant fertilizer on Sunday the gardener uses 2 1/2 ounces on a flower gar

sergey [27]

Amount of liquid plant fertilizer in the container that the gardener has = 6 1/5 pounds
   = 31/5 pounds
We already know that 1 pound = 16 ounce
Then
Amount of liquid plant fertilizer in the
container that the gardener has = (31/5) * 16 ounce
= 496/5 pounds
Amount of liquid plant fertilizer that the gardener uses on Sunday = 2 1/2 ounces
   = 5/2 ounces
Then
The amount of liquid plant fertilizer that are left= (496/5) - (5/2) ounces
   = (992 - 25)/10 ounces
   = 967/10 ounces
   = 96.7 ounces
So the total amount of liquid plant fertilizer left is 96.7 ounces.

4 0

3 years ago

Tryson is building a rectangular garden platform with the short sides 10 feet and the long sides 15 feet.

lesya692 [45]

Answer:

50 ft

Step-by-step explanation:

For perimeter u add up all the sides and 15+15+10+10=50

8 0

3 years ago

Can any body help my son with this is very important please some body help him in tanks very much I hope some body help me

riadik2000 [5.3K]

The top box on the page explains the idea completely.
You need to read the top box several times, and understand it.
A ratio is a comparison of two quantities by division.

1). Days in May: 31
   Days in a year: 365
   Their ratio: 31/365 .

2). Sides of a triangle: 3
   Sides of a square: 4
   Their ratio: 3/4 .

The middle box explains how two ratios can be equal,
and it gives you a very detailed example. You should
read the middle box and understand it.
Ratios are fractions. They can be equal in just the same
way that any two fractions can be equal.
And you can simplify ratios in exactly the same way that
you simplify fractions ... divide top and bottom both by
the same number.

3). 8/12   Cook up three equal ratios.
   1. divide top and bottom by 2 . . . . . 4/6
   2. divide top and bottom by 4 . . . . . 2/3
   3. multiply top and bottom by 9 . . . . 72/108
   These are just some that I chose.
   There are millions of others.

4). 20/25 Cook up three equal ratios.
   1. divide top and bottom by 5 . . . . . 4/5
   2. multiply top and bottom by 4 . . . . 80/100
   3. multiply top and bottom by 3 . . . . 60/75
   These are just some that I chose.
   There are millions of others.

5). 5/6 Cook up three equal ratios.
   1. multiply top and bottom by 2 . . . . 10/12
   2. multiply top and bottom by 3 . . . .
   3. multiply top and bottom by 9 . . . . 45/54
   These are just some that I chose.
   There are millions of others.

6).   10/14 Cook up three equal ratios.
   1. divide top and bottom by 2 . . . . 5/7
   2. multiply top and bottom by 2 . . . .
   3. multiply top and bottom by (you choose) . . . .

5 0

3 years ago

An equation in point slope form that passes through (9, -2) and (-3, 2)

Harman [31]

Answer:

-----------

-3

Step-by-step explanation:

(9, -2) (-3, 2)

2- -2 4 1

--------------- = --------------- = ---------------

-3-9 -12 -3

(simplifyed)

7 0

3 years ago

For a quadrilateral to be a rhombus, the diagonals __ and __.

For a quadrilateral to be a rhombus, the diagonals and .