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cricket20 [7]
3 years ago
13

Each pair of figures below is similar. Find the lengths of all unknown sides​

Mathematics
1 answer:
lions [1.4K]3 years ago
7 0

Answer:

  a) w = 8; y = 5.25

  b) x = 10; z = 7.2

Step-by-step explanation:

a) Dimensions on the smaller figure are FA/F'A' = 3/4 times those on the larger figure.

  6 = (3/4)w

  w = 24/3 = 8

  y = (3/4)·7 = 21/4 = 5.25

__

b) Dimensions on the smaller figure are ER/E'R' = 9/15 = 3/5 times those on the larger figure.

  6 = (3/5)x

  x = 30/3 = 10

  z = (3/5)12 = 36/5 = 7.2

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Shelia's measured glucose level one hour after a sugary drink varies according to the normal distribution with μ = 117 mg/dl and
TiliK225 [7]

Answer:

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

Step-by-step explanation:

To solve this problem, 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, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 117, \sigma = 10.6, n = 6, s = \frac{10.6}{\sqrt{6}} = 4.33

What is the level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L ?

This is the value of X when Z has a pvalue of 1-0.01 = 0.99. So X when Z = 2.33.

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

By the Central Limit Theorem

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

2.33 = \frac{X - 117}{4.33}

X - 117 = 2.33*4.33

X = 127.1

The level L such that there is probability only 0.01 that the mean glucose level of 6 test results falls above L is L = 127.1 mg/dl.

6 0
3 years ago
If Hector is 8 years old and Mary is 3 years old how old will Mary be when Hector is 16
IRINA_888 [86]
Okay so 8 (hector) - 3(Mary) = 5 years apart
So, 16 (hector) - 5 (years apart) = 11 (Mary’s age)
7 0
3 years ago
For each of the equations below, solve for y in terms of x. !<br> a. 2x – 3y = 12
ira [324]

Answer:

\large\boxed{y=\dfrac{2}{3}x-4}

Step-by-step explanation:

2x-3y=12\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\2x-2x-3y=12-2x\\\\-3y=12-2x\qquad\text{divide both sides by (-3)}\\\\\dfrac{-3y}{-3}=\dfrac{12}{-3}+\dfrac{-2x}{-3}\\\\y=-4+\dfrac{2}{3}x

7 0
3 years ago
Single Factor ANOVA is a method we use when we want to compare a quantitative variable among more than two categories.
Goryan [66]

Answer:

The given statement is "True".

Step-by-step explanation:

A statistical analytical technique that divides the perceived aggregate unpredictability present throughout an information source even further into 2 components.

  • Systemic components
  • Random components

If relevant information yet another category independent variable, as well as another quantifiable variable of interest, has been obtained, are using a single-way ANOVA.

Thus the above is the true answer.

3 0
3 years ago
Seven less than two times a number is 29.
Alexxx [7]
2x-7=29

"Seven less than" => minus 7.
"Two times <u>a number</u>" => 2x (x is the unknown number)
"is twenty-nine" => =29
Putting it all together, 

-7 + 2x = 29
or
2x-7=29
(if you were wondering x is equal to 18)
4 0
3 years ago
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