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4 years ago

Five times a number decreased by eight is at most ten or more than twice the number

1 answer:

3 0

Given:
five times a number = 5x
decreased by 8 = 5x - 8
is at most 10 = maximum is 10 so less than or equal to 10
more than twice the number = greater than 2x.

2x < 5x - 8 < 10

5x - 8 < 10
5x - 8 > 2x

****

5x - 8 < 10 if x = 3.60 then 2x < 5x-8 < 10
+ 8 +8 2(3.6) < 5(3.6) - 8 < 10
5x < 18 7.2 < 10 < 10
÷5 ÷5
 x < 3.60

5x - 8 > 2x x > 2.67; if x = 3
+8 + 8 2x < 5x - 8 < 10
5x > 2x + 8 2(3) < 5(3) - 8 < 10
-2x -2x 6 < 7 < 10
3x > 8
÷3 ÷3
x > 2.67

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Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are sum

s344n2d4d5 [400]

The contingency tables serve to record the frequencies with which an object appears according to the measured variables, in this case two variables, each with two scales, the scratch resistance and the shock resistance, both measured as high and low.

The information is organized in such a way that the value of each box represents the total number of objects that meet the characteristics measured for each variable, for example in this case we have 70 discs with high shock resistance and high scratch resistance, 9 with high scratch resistance and low shock resistance, 16 with high shock resistance and low scratch resistance and finally 5 discs with low scratch and shock resistance.

We complete the table like this to obtain other total values:

$\qquad\qquad\qquad\qquad\qquad\text{Shock resistance}\\\text{Scratch resistence}\left[\begin{array}{cccc}&\text{high}&\text{low}&\text{total}\\\text{high}&70&9&79\\\text{low}&16&5&21\\\text{total}&86&14&100\end{array}\right]$

With this information, and taking into account that the values presented are frequencies, to obtain the probability, each one must be divided into the total number of objects and multiply by 100, for this case as 100 objects, the frequency is the same percentage or probability .

Answer

a) The probability that, when selecting a random disk, its scratch resistance is high and its shock resistance is high is 70%, since this is the value that corresponds to the intersection of both variables in the table.

b) the probability that, when selecting a random disk, its resistance to scratches is high or that its resistance to impacts is high is 95% because the probability that its resistance to scratches is high is 79 % and the probability that its impact resistance is high is 86%, as one or the other requests, this is the sum of both minus the intersection, that is 79% + 86% -70% = 95%

c) the two events described are not mutually exclusive, that is, they cannot pass through, since the table informs us that of the analyzed discs 70, these two characteristics possessed, high shock resistance and high scratch resistance

8 0

3 years ago

Give the degree of the polynomial -3w+x^6y^5-2+5y^4w^3x^2

Jlenok [28]

Answer:

Here the degree of the polynomial is 11.

Step-by-step explanation:

To find the degree of the multivariate polynomials, we need to add up the powers of all the variables. So the total degree is given by the sum of all the powers of the highest powers terms.

Now in the given polynomial $-3w+x^6y^5-2+5y^4w^3x^2$

the term with the highest total powers is $x^6y^5$ and thus the total power is 6+5=11.

And hence the degree of this polynomial is 11.

5 0

3 years ago

the temper ire of chicken soup is 192.7 F as it cools the temperature of the soup decreases 2.3 what is the temperature of the s

ad-work [718]

The temperature of soup after 25 minutes is $135.2^{\circ}\ F$

Solution:

The temperature of chicken soup is 192.7°F

As it cools, the temperature of the soup decreases 2.3°F per minute

Let the initial temperature be $T_0$

Let "t" be the time for rate of decrease

Set up an equation

Temperature = Initial temperature - decrease in temperature

Decrease in temperature = rate of decrease x time

Therefore,

$T = T_0-2.3t$

To find the temperature of soup after 25 minutes, substitute t = 25

$T = 192.7 - 2.3 (25)\\\\T = 192.7 -57.5\\\\T = 135.2$

Thus the temperature of soup after 25 minutes is $135.2^{\circ}\ F$

5 0

3 years ago

Find the missing value when given the modulus.

kolbaska11 [484]

Solving the complex number, we get the value of the missing value that is ‘a’ = -6

We have been given the expression as

|a – i| = √37 (1)

Which is an expression of complex number. The general expression of complex number is given as

z = x + iy

where x is the real part and iy is the imaginary part

To find the modulus value, the formula is given by,

|z| = |x + iy|

|z| = √[(real part)2 + (imaginary part)2]

|z| = √(x2 + y2)

According to the question, |z| = √37 (2)

Equating equation (1) and (2), we get

√(a2 + 1) = √37

(a2 + 1) = 37

a2 = 37 – 1

a2 = 36

a = √36

a = ±6

Now value of a can be 6 or -6. We have been given that the modulus is in third quadrant.

Hence the value will be negative. Therefore, the missing value will be -6.

Learn more about complex number here : brainly.com/question/5564133

#SPJ9

3 0

2 years ago

Analyze the diagram below and complete the instructions that follow. Find a, b, and c.

ahrayia [7]

Answer:

The correct answer is the letter C.

Step-by-step explanation:

We can use the following trigonometric identity:

$cos(60)=\frac{6}{b}$ (1)

$cos(45)=\frac{c}{b}$ (2)

Solving each equation by b and equaling we have:

$\frac{6}{cos(60)}=\frac{c}{cos(45)}$

Let's recall that:

$cos(45)=\frac{1}{\sqrt{2}}$

$cos(60)=\frac{1}{2}$

Then we have:

$c=\frac{cos(45)*6}{cos(60)}$

$c=\frac{2*6}{\sqrt{2}}$

$c=\frac{12}{\sqrt{2}}$

$c=6\sqrt{2}$

Using equation (1) we can find b.

$cos(60)=\frac{6}{b}$

$b=12$

Finally, we can find a using the next equation:

$tan(60)=\frac{a}{6}$

$a=6*tan(60)$

$a=6\sqrt{3}$

Therefore, the correct answer is the letter C.

I hope it helps you!

5 0

3 years ago