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3 years ago

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Determine whether the following statement is true or false. If true, prove the statement directly from definitions. If false, gi

ve a counterexample. For all integers a and b, if a|b then a 2 |b 2 . g

1 answer:

Alenkasestr [34]3 years ago

7 0

Explanation is in the file

tinyurl.com/wtjfavyw

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Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.43cm and a standard deviation

malfutka [58]

Answer:

Approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.43cm, standard deviation of 0.35cm.

What percentage of the apples have diameters that are between 7.08cm and 7.78cm?

7.43 - 0.35 = 7.08 cm.

7.43 + 0.35 = 7.778 cm.

Within 1 standard deviation of the mean, so approximately 68% of the apples have diameters that are between 7.08cm and 7.78cm.

5 0

3 years ago

Triangle F G E is shown. Angle F E G is a right angle. The length of hypotenuse F G is 15.2 meters and the length of F E is 9 me

kkurt [141]

The anser is on that guys link bbg

8 0

3 years ago

Read 2 more answers

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

3 years ago

Select the correct answer from each drop-down menu.

Annette [7]

All of given options contain quadratic functions. One way to determine the extreme value is squaring the expression with variable x.

Option B contain the expression where you can see perfect square. Thus, equation $\bf{y=-(x-2)^2+5}$ (choice B) reveals its extreme value without needing to be altered.

To determine the extreme value of this equation, you should substitute x=2 (x-value that makes expression in brackets equal to zero) into the function notation:

$y=-(2-2)^2+5=5.$

The extreme value of this equation has a minimum at the point (2,5).

7 0

3 years ago

Read 2 more answers

Hi :) I need help with the question in the screenshot if anybody knows it can you plz help I will give you brainliest, thanks an

amm1812

This question is difficult to give a definite answer to because it's an approximation, but I estimate the solutions to be around x = 2.6 and x = -2.6.

When they ask for solutions of the graphed function they are asking for an approximation of where the graph intercepts the x-axis, and we can see it kind of intercepts in the middle of 2 and 3, except slightly closer to 3, which is why I estimated 2.6.

The graph also appears to be symmetrical, which means the solutions will be the same except one would be negative and one would be positive, which means the second solution would be -2.6.

I hope this helps! Let me know if you have any questions :)

6 0

3 years ago