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Answer:

Inequality form : - 5 + squareroot13 / 2 < x < - 5- squareroot13 / 2 or x > 2

Step-by-step explanation: Solve the inequality by finding the roots and creating test intervals.

I hope this helps you out! :)

The solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].

The Interval Notation is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} , \dfrac{-5-\sqrt{13} }{2} \right ) \cup (2, \infty)[/tex].

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

The given inequality is;

[tex]\rm x^3 + 3x^2 > 7x + 6[/tex]

The solution to the inequality is determined in the following steps given below.

[tex]\rm x^3 + 3x^2 > 7x + 6\\\\\rm x^3 + 3x^2-7x-6 > 7x + 6-7x-6\\\\ x^3 + 3x^2-7x-6 > 0\\\rm \\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\ \rm x^3+5x^2+3x-2x^2-10x-6 > 0\\\\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\\rm (x-2)(x^2+5x+3) > 0[/tex]

Now finding the roots of the inequality;

[tex]\rm (x-2)(x^2+5x+3) > 0 \\\\(x-2) \left (\dfrac{-5\pm\sqrt{25-12} }{2} \right )\\\\(x-2)\left (\dfrac{-5+\sqrt{13} }{2} \right )\left (\dfrac{-5-\sqrt{13} }{2} \right )[/tex]

Hence, the solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].

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Answer:

18%:540 20%:600 22%:660

Step-by-step explanation:

18%:540 20%:600 22%:660

20-2=18 20+2=22

The required least to the greatest number of students their favorite color is red is 540 and 660 respectively.

Given that,
A group of students was asked about their favorite colors,
20% of the students said that their favorite color is red.
There are about 3000 students in the school.
The margin of error is ±2%,
To determine what is the range of the number of students who likely say that their favorite color is red

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Total number of students = 3000
Number of students like red color = 20% of 3000 = 0.20 * 3000 = 600
the margin of error ±2% of 3000 = ± 0.02 * 3000 = ± 60
Least number of students their favorite color is red = 600 - 60 = 540
Greatest  number of students their favorite color is red = 600 + 60 = 660

Thus, the required least to the greatest number of students whose favorite color is red is 540 and 660 respectively.

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answer

980

Step-by-step explanation:

7/9-1/3=480

4/9=480

9/9=?

Answer:

1080

Step-by-step explanation:

We take x to be the number of pennies in the bank at first which filled the bank by a ¹/3

¹/3=×

⁷/9=×+480

⅓ multiply by 3 with both the numerator and denominator to get 3/9

7/9-3/9=4/9

4/9=480

If 4/9=480 what of 9/9

9/9×480÷4/9

Reciprocate 4/9

9/9×480×9/4=1080

Answer:

3/6 can be simplified

Step-by-step explanation:

3 divided by 3

6 divided by 3

it comes out to be 1/2

Answer:

D

Step-by-step explanation:

Answer:

rawrrrrrr mannnnnn

Step-by-step explanation:

Answer:

Boo!

Step-by-step explanation:

Answer:

63(10)^4

Step-by-step explanation:

630 000= [tex]63(10)^4[/tex]

Answer: 60 rooms

Step-by-step explanation:

because in 30 rooms is 3 hour + other 3 hour are 60 rooms. =60 rooms

Answer:

14 boxes of candy would cost $35

Step-by-step explanation:

First find the unit price. It is $2.50 per box. Next multiply it by 14. It is $35 for 14 boxes of candy.

I hope this helped and have a great day.

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Answer:

any sum of the form m+n′, either n′ is equal to 0, in which case the first clause applies, and the sum can be evaluated immediately, or n′ is the successor s(n) of some natural number n, in which case the second clause applies, and we can compute the sum in terms of a strictly simpler sum.

Step-by-step explanation:

I hope that helps

Answer:

For me I think 216 diapers for 39.98 is the best option

Step-by-step explanation:

Get the price of one diaper in each offer

216 = $39.98

1= ?

1×39.98÷216=0.19

Option 2

88=24.99

1 =?

1×24.99÷88=0.28

So I prefer buying 1 diaper for$0.19 and get 216 of them for $39.98 rather than buying 1 diaper for $0.28 and get 88 of them for $24.99

Answer:

y =  b-rx+sx

Step-by-step explanation:

rx - sx + y = b

Subtract rx from each side

rx-rx - sx + y = b-rx

-sx +y = b-rx

Add sx to each side

sx - sx + y = b-rx+sx

y =  b-rx+sx

Answer:

3500cm^2

Step-by-step explanation:

Area of a triangle= bxh/2

10x10=100

7x10=70

100x70=7000

7000/2=3500

Answer:

  3500 cm²

Step-by-step explanation:

The given triangle has an area of ...

  A = (1/2)bh = (1/2)(10 cm)(7 cm) = 35 cm²

The area of the enlarged triangle will be 10² = 100 times that, or 3500 cm².

__

You can see this if you use the enlarged dimensions in the area formula:

  A = (1/2)bh = (1/2)(10·10 cm)(10·7 cm) = 100·35 cm² = 3500 cm

Answer:

$100 each.

Step-by-step explanation:

500 divided by 5 = 100

Answer:

208 - 0.7a < 180

Step-by-step explanation:

Answer:

7/8

Step-by-step explanation:

Odds against are the ratio between losses and wins.

odds against = L / W

Probability of winning is the ratio between wins and all games.

probability = W / games

probability = W / (W + L)

The odds against are 1 to 7.

1/7 = L / W

W = 7 L

The probability is therefore:

P = (7 L) / (7 L + L)

P = 7/8

Answer:

160

Step-by-step explanation:

8(4)(2)=      64

4(4)(2)=    +32

8(4)(2)=      64

               ______

                160

Answer:

Step-by-step explanation:

Answer: 0.05

Step-by-step explanation:

Let M = Event of getting an A in Marketing class.

S = Event of getting an A in Spanish class,

i.e. P(M) = 0.80 , P(S) = 0.60 and P(M∩S)=0.45

Required probability = P(neither M nor S)

= P(M'∩S')

= P(M∪S)'                                 [∵P(A'∩B')=P(A∪B)']

=1- P(M∪S)                               [∵P(A')=1-P(A)]

= 1- (P(M)+P(S)- P(M∩S))   [∵P(A∪B)=P(A)+P(B)-P(A∩B)]

= 1- (0.80+0.60-0.45)

= 1- 0.95

= 0.05

hence, the probability that Helen does not get an A in either class= 0.05

Answer:

please give brainlist

Rounding to a certain number of decimal places

If we want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places).

hope this helped

Answer:

[tex]w=1\text{ or } w=-3[/tex]

Step-by-step explanation:

So we have the equation:

[tex]5-3|2+2w|=-7[/tex]

First, subtract 5 from both sides:

[tex]-3|2+2w|=-12[/tex]

Divide both sides by -3:

[tex]|2+2w|=4[/tex]

Definition of Absolute Value:

[tex]2+2w=4\text{ or } 2+2w=-4[/tex]

Divide both sides of the equation by 2 for both equations:

[tex]1+w=2\text{ or } 1+w=-2[/tex]

Subtract 1 from both sides:

[tex]w=1\text{ or } w=-3[/tex]

And we're done!

To check:

[tex]5-3|2+2(1)|=-7[/tex]

Multiply:

[tex]5-3|2+2|=-7[/tex]

Add:

[tex]5-3|4|=-7[/tex]

Multiply:

[tex]5-12=-7[/tex]

Subtract:

[tex]-7\stackrel{\checkmark}{=}-7[/tex]

And:

[tex]5-3|2+2(-3)|=-7[/tex]

Multiply:

[tex]5-3|2-6|=-7[/tex]

Subtract:

[tex]5-3|-4|=-7[/tex]

Absolute Value:

[tex]5-3(4)=-7[/tex]

Multiply:

[tex]5-12=-7[/tex]

Subtract:

[tex]-7\stackrel{\checkmark}{=}-7[/tex]

Answer:

4x+14

Step-by-step explanation:

In order to find the perimeter of an triangle you need to add up all the sides of the triangle.

3x-5+19-x+2x --->  3x+14-x+2x --> 4x+14

The average of anything can be calculated by adding up all the terms and dividing by the number of terms.

In this case,

the number of terms = 3

x = the missing test score.

(91 + 72 + x) / 3 = 80

Let's multiply both sides by 3

91 + 72 + x = 240

Combine like terms.

163 + x = 240

Subtract 163 from both sides

x = 77

Carlos scored a 77 on his third test.

Answer:

Jacob's age is 42

Jasmine's age is 24

Step-by-step explanation:

Let Jacob's age be x

Let Jasmine's age be y

x + y = 66

x - 6 = 2(y - 6)

x - 6 = 2y - 12

x - 2y = -12 + 6

x - 2y = -6

x + y = 66 ------- (1)

x - 2y = -6 ------- (2)

From (1),

x = 66 - y -------- (3)

Substitute the value of x in (2)

x - 2y = -6

66 - y - 2y = -6

-3y = -6 - 66

-3y = -72

y = -72/-3

y = 24

Solve for x in (1)

x + y = 66

x + 24 = 66

x = 66 - 24 = 42

x = 42, y = 24