g (x) = x2 + 12x-
35

The selection of the basketball players is an illustration of combination

The number of ways the basketball players can be chosen is  78

The given parameters are:

Number of players (n) =13

Players to select (r) = 2

The number of ways the players can be selected is calculated as:

[tex]^nC_r = \frac{n!}{(n -r)!r!}[/tex]

The equation becomes

[tex]^{13}C_2 = \frac{13!}{(13 -2)!2!}[/tex]

Evaluate the difference

[tex]^{13}C_2 = \frac{13!}{11!2!}[/tex]

Evaluate the factorials

[tex]^{13}C_2 = \frac{13 * 12 * 11!}{11! * 2}[/tex]

Evaluate the quotient

[tex]^{13}C_2 = 13 * 6[/tex]

Evaluate the product

[tex]^{13}C_2 = 78[/tex]

Hence, the number of ways the basketball players can be chosen is  78

Read more about permutation and combination at:

https://brainly.com/question/12468032

Answer/Step-by-step explanation:

Given:

Identify the fraction with the greater value in each pair and color it on the solution strip to solve the riddle.

Given fraction:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

[tex]\frac{1}{2}\;or\;\frac{2}{5}[/tex]

[tex]\frac{2}{6} \;or\;\frac{1}{4}[/tex]

[tex]\frac{1}{3}[/tex] [tex]or\frac{1}{5}[/tex]

[tex]\frac{2}{3}\;or\frac{2}{5}[/tex]

[tex]\frac{3}{5}\;or\frac{3}{7}[/tex]

[tex]\frac{5}7\;or\frac{6}8[/tex]

[tex]\frac{5}{5}\;or\frac{6}7[/tex]

[tex]\frac{1}6\;or\frac{2}7[/tex]

[tex]\frac{5}8\;or\frac{8}9[/tex]

[tex]\frac{1}6\;or\frac{3}{10}[/tex]

[tex]\frac{3}{10}\;or\frac{4}{12}[/tex]

[tex]\frac{2}{12}\;or\frac{4}{5}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve:

Finding greatest value for each;

Starting with [tex]\frac{1}{2}\;or\;\frac{2}{5}[/tex]

Turning both into decimal

1 ÷ 2 = 0.5

2 ÷ 5 = 0.4

Hence, [tex]\frac{1}{2}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{2}{6} \;or\;\frac{1}{4}[/tex]

2 ÷ 6 = 0.33333333333

1 ÷ 4 = 0.25

Hence, [tex]\frac{2}{6}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{1}{3}or\frac{1}{5}[/tex]

1 ÷ 3 = 0.33333333333

1 ÷ 5 = 0.20

Hence, [tex]\frac{1}{3}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{2}{3}\;or\frac{2}{5}[/tex]

2 ÷ 3 =0.66666666666

2 ÷ 5 = 0.4

Hence, [tex]\frac{2}{3}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{3}{5}\;or\frac{3}{7}[/tex]

3 ÷ 5 = 0.6

3 ÷ 7 = 0.42857142857

Hence, [tex]\frac{3}{5}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{5}7\;or\frac{6}8[/tex]

5 ÷  7 = 0.71428571428

6 ÷ 8 = 0.75

Hence, [tex]\frac{6}{8}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{5}{5}\;or\frac{6}7[/tex]

5 ÷ 5 = 1

6 ÷ 7 = 0.85714285714

Hence, [tex]\frac{5}{5}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{1}6\;or\frac{2}7[/tex]

1 ÷  6 = 0.16666666666

2 ÷  7 = 0.28571428571

Hence, [tex]\frac{2}{7}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{5}8\;or\frac{8}9[/tex]

5 ÷ 8 =0.625

8 ÷ 9 = 0.88888888888

Hence, [tex]\frac{8}9[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{1}6\;or\frac{3}{10}[/tex]

1 ÷  6 = 0.16666666666

3 ÷ 10 = 0.3

Hence, [tex]\frac{3}{10}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{3}{10}\;or\frac{4}{12}[/tex]

3 ÷ 10 = 0.3

4 ÷ 12 = 0.33333333333

Hence, [tex]\frac{4}{12}[/tex] is the greater value

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

[tex]\frac{2}{12}\;or\frac{4}{5}[/tex]

2 ÷ 12 = 0.16666666666

4 ÷ 5 = 0.8

Hence, [tex]\frac{4}{5}[/tex] is the greater value.

∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞

~Learn with Lenvy~

2/3 x 6 = (2x6) / 3 = 4

[tex] ln({x}^{3} - 4x) - ln(x {}^{2} - 2x ) [/tex]

can be written as;

[tex] ln( \frac{ {x}^{3} - 4x }{ {x}^2 - 2x } ) [/tex]

[tex] ln( \frac{x( {x}^{2 } - 4) }{x(x - 2)} ) = ln( \frac{x(x - 2)(x + 2)}{x(x - 2)} ) [/tex]

Now all you have to do, is divide the numerator and denominator by x and by (x-2)

to get,

[tex] ln( \frac{x(x - 2)(x + 2)}{x(x - 2)} ) = ln( \frac{x + 2}{1} ) = ln(x + 2) [/tex]

We proved that ln(x³-4x)-ln(x²-2) is equal to ln(x+2) :)

Answer:

y/2 = 9

In order to find the value of y, we must first isolate y by performing inverse operations.

Right now, y is being divided by 2, so the inverse operation of division is multiplication.

So we multiply by 2 on both sides:

y/2 = 9

*2     *2

2/2y = 18

y = 18

Answer:

First step : State the null and the alternative hypothesis

   The null hypothesis is  [tex]H_o : \mu = 3.5 \ hours[/tex]

    The alternative hypothesis is  [tex]H_a : \mu > 3.5 \ hours[/tex]

Second Step : Calculate the test statistics

   Generally the test statistics is mathematically represented as

             [tex]z = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

=>           [tex]z = \frac{3.75 - 3.5 }{\frac{0.7 }{\sqrt{45} } }[/tex]

=>           [tex]z  =  2.11[/tex]

Third Step  : Obtain the p-value

Generally from the z-table the probability of  z  =  2.11 is

    [tex] P(Z  >  2.11) =  0.0174[/tex]

Fourth Step : Compare the p-value with the level of significance and state the decision rule and the conclusion

From the obtained value  the [tex]p-value  <  \alpha[/tex] hence

 The decision rule is  

The null hypothesis is rejected

 The conclusion is

There is sufficient evidence to conclude that average of the laptop batteries is more than 3.5 hours of use per charge

Step-by-step explanation:

From the question we are told that

  The population mean is [tex]\mu = 3.5 \ hours[/tex]

   The sample size is  n =  45

   The standard deviation is  [tex]\sigma = 0.7 \ hours[/tex]

   The sample mean is  [tex]\= x = 3.75[/tex]

    The level of significance is  [tex]\alpha = 0.05[/tex]

First step : State the null and the alternative hypothesis

   The null hypothesis is  [tex]H_o : \mu = 3.5 \ hours[/tex]

    The alternative hypothesis is  [tex]H_a : \mu > 3.5 \ hours[/tex]

Second Step : Calculate the test statistics

   Generally the test statistics is mathematically represented as

             [tex]z = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

=>           [tex]z = \frac{3.75 - 3.5 }{\frac{0.7 }{\sqrt{45} } }[/tex]

=>           [tex]z  =  2.11[/tex]

Third Step  : Obtain the p-value

Generally from the z-table the probability of  z  =  2.11 is

    [tex] P(Z  >  2.11) =  0.0174[/tex]

Fourth Step : Compare the p-value with the level of significance and state the decision rule and the conclusion

From the obtained value  the [tex]p-value  <  \alpha[/tex] hence

 The decision rule is  

The null hypothesis is rejected

 The conclusion is

There is sufficient evidence to conclude that average of the laptop batteries is more than 3.5 hours of use per charge

Answer:

$13.23

Step-by-step explanation:

first, you divide 6 by $11.34 then you multiply 7 by $1.89 to get 13.23.

Check the picture below, so the parabola looks more or less like so, hmmm with a vertex at (-1 , -4), so, using those values from the table

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\stackrel{vertex}{\stackrel{h}{-1}~~,~~\stackrel{k}{-4}}\qquad \implies y=a[x-(-1)]^2-4\implies y=a(x+1)^2-4 \\\\\\ \textit{we also know that} \begin{cases} x=2\\ y=14 \end{cases}\implies 14=a(2+1)^2-4\implies 18=9a \\\\\\ \cfrac{18}{9}=a\implies 2=a~\hspace{10em}\boxed{y=2(x+1)^2-4}[/tex]

Answer:

Step-by-step explanation:

point form: (-2,4) (-5,1)

equation form: x= -2, y=4

                         x= -5, y=1

[tex]\huge \underline\frak \red{Answer}[/tex]

[tex]\small\mathbb\green{(-2;4) \: or \: (-5;1)}[/tex]

[tex]\small\mathbb\green{y=x+6}[/tex]

[tex]\small\mathbb\green{y=x²+8x+16}[/tex]

_____________________________________

[tex]\small\mathbb\green{x+6=x²+8x+16}[/tex]

[tex]\small\mathbb\green{x²+8x+16-x-6=0}[/tex]

[tex]\small\mathbb\green{x²+7x+10=0}[/tex]

[tex]\small\mathbb\green{x²+5x+2x+10=0}[/tex]

[tex]\small\mathbb\green{x(x+5)+2(x+5)=0}[/tex]

[tex]\mathbb\green{(x+2) (x+5) = 0}[/tex]

[tex]\small\mathbb\green{x+2=0 \: ➢ \: x¹ = -2}[/tex]

[tex]\small\mathbb\green{x+5=0 \: ➢ \: x² = -5}[/tex]

_______________________________________

[tex]\small\mathbb\green{y¹ = -2+6 \: ➢ \: y¹ = 4}[/tex]

[tex]\small\mathbb\green{y² = -5+6 \: ➢ \: y² = 1}[/tex]

_______________________________________

[tex]\small\frak\pink{Hope \: its \: helpful \: to \: you}[/tex]

Answer:

no solution

Step-by-step explanation:

1

Since 12=-4112=−41 is false, there is no solution.

Answer:

The base is 14 and the height is 8

Step-by-step explanation:

8 times 14 is 112. 112 divided by 2 is 56.

[tex]Hello[/tex] [tex]There![/tex]

Let's do this step-by-step explanation!

[tex]\frac{2}{3}[/tex] × [tex]7 \frac{2}{6}[/tex]

Convert mixed numbers to improper fractions: [tex]7 \frac{2}{6} =\frac{44}{6}[/tex]

[tex]=\frac{2}{3}[/tex] × [tex]\frac{44}{6}[/tex]

Cancel: [tex]\frac{44}{6} :\frac{22}{3}[/tex]

[tex]=\frac{2}{3}[/tex] × [tex]\frac{22}{3}[/tex]

Apply the fraction rule:

[tex]2[/tex] × [tex]22[/tex]

[tex]3[/tex] × [tex]3[/tex]

Mutiply the numbers: [tex]2[/tex] × [tex]22[/tex] [tex]=44[/tex]

[tex]44[/tex]

-----

[tex]3[/tex] × [tex]3[/tex]

Mutiply  the numbers: [tex]3[/tex] × [tex]3=9[/tex]

[tex]=\frac{44}{9}[/tex]

Convert the fractions into mixed numbers: [tex]=\frac{44}{9} = 4\frac{8}{9}[/tex]

[tex]=4\frac{8}{9}[/tex]

Answer:

[tex]4\frac{8}{9}[/tex]

Hopefully, this helps you!!

[tex]SokkaBanned[/tex]

Answer:

try 28.8

Step-by-step explanation:

This word problem is another way of saying

How many times can 6/14 go into 49/14

To find this out we divide

(49/14)/(6/14)

We also know that dividing by a fraction is the same as multiplying

=(49/14)(14/6)

=49/6

≈8.16

As we just want how many segments of 6/14 feet rope, we can ignore the decimals/round down getting the answer

Eight pieces of rope can be made our of 49/14 piece of rope.

Answer:

d = 4 miles

Step-by-step explanation:

combined speed = 7 + 9 = 16 mph

s = d/t

d = st

d = 16 miles/hr × 0.25 hr

d = 4 miles

Please mark me as brainliest

a^-7

Step-by-step explanation:

When you divide numbers with exponents, essentially you are subtracting the exponents. So, -13 - -6 is equivalent to -7.

The probability of randomly selecting a can between 205cm to 210cm is 0.8765

Data;

To solve this problem, we can simply use the formula of probability and substitute the value.

[tex]p\frac{(205-108.5)}{2..5} < \frac{x - 208.5}{2.5} < \frac{210 - 205.5}{2.5}\\p(-1.4 < z < 1.8)[/tex]

Rearranging the equation and solving for the z-values;

[tex]p(z < 1.8-p < z < -1.4)[/tex]

This becomes

[tex]p = 0.9641 - 0.0876 = 0.8765[/tex]

The probability of randomly selecting a can between 205cm to 210cm is 0.8765

Learn more on normal distribution here;

https://brainly.com/question/4079902

Now

Coterminal angle:-

Option C is correct

Answer:

x − 4x + 6y + (14x − 5y) ⇔ 11x+y

(5x − 3y) − x + 3x − 5y ⇔ 7x-8y

5(x + y) + 6(x − y) ⇔ 11x-y

3x + 3y + 2(2x − y)  ⇔  7x+y

Step-by-step explanation:

Solve the following;

3x + 3y + 2(2x − y)

4(x + y) − 3(x + y)

x − 4x + 6y + (14x − 5y)

(5x − 3y) − x + 3x − 5y

5(x + y) + 6(x − y)

Solve:

3x + 3y + 2(2x − y)

[tex]=3x+3y+4x-2y[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=3x+4x+3y-2y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:3x+4x=7x[/tex]

[tex]=7x+3y-2y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:3y-2y=y[/tex]

[tex]=7x+y[/tex]

Hence, this tiles will  be used.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

4(x + y) − 3(x + y)

[tex]\mathrm{Add\:similar\:elements:}\:4\left(x+y\right)-3\left(x+y\right)=\left(x+y\right)[/tex]

[tex]=x+y[/tex]

Thus, this tiles will not be used.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

x − 4x + 6y + (14x − 5y)

[tex]\mathrm{Apply\:rule}:\quad \:a+\left(b+c\right)=a+b+c[/tex]

[tex]6y+\left(14x-5y\right)=6y+14x-5y[/tex]

[tex]=x-4x+6y+14x-5y[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=x-4x+14x+6y-5y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:x-4x+14x=11x[/tex]

[tex]=11x+6y-5y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:6y-5y=y[/tex]

[tex]=11x+y[/tex]

Thus, this tiles will be used

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

(5x − 3y) − x + 3x − 5y

[tex]\mathrm{Apply\:rule}:\quad \left(a\right)=a[/tex]

[tex]\left(5x-3y\right)=5x-3y[/tex]

[tex]=5x-3y-x+3x-5y[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=5x-x+3x-3y-5y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:5x-x+3x=7x[/tex]

[tex]=7x-3y-5y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-3y-5y=-8y[/tex]

[tex]=7x-8y[/tex]

Hence, this tiles will be used

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5(x + y) + 6(x − y)

[tex]=5x+5y+6\left(x-y\right)[/tex]

[tex]=5x+5y+6x-6y[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=5x+6x+5y-6y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:5x+6x=11x[/tex]

[tex]=11x+5y-6y[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:5y-6y=-y[/tex]

[tex]=11x-y[/tex]

Hence, this tiles will be used

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~Learn with lenvy~

Answer: 198cm

Step-by-step explanation:

We are given the dimensions of a rectangular prism;

3cm 9cm and 6cm

We are required to determine its surface area;

We need to know that;

Surface area of a rectangular prism is given by;

A = 2(WL+HL+WH)

Where L, W and H are length , width and height respectively;

Assuming;

Width is 3 cm

Length is 9 cm, and

Height is 6 cm

Then;

Area = 2 ( (3×9) + (6×9) + (3×6))

       = 2(99)

      = 198 cm²

Therefore, the area of the rectangular prism is 198 cm²

Answer: 346.2yd³

Step-by-step explanation:

Volume = Area of Base x Height

Volume = πr² x 9

Volume = π(3.5)² x 9

Volume = 38.465 x 9

Volume = 346.184 ≅ 346.2yd³

To solve linear equations, we must perform inverse operations on both sides of the equal sign to cancel values out.

We perform inverse operations to combine like terms. This means to get x to one side and everything else on the other.

[tex]5x+7=15[/tex]

Because 7 is being added to x, subtract it from both sides:

[tex]5x+7-7=15-7\\5x=8[/tex]

Because x is being multiplied by 5, divide both sides by 5:

[tex]\dfrac{5x}{5}=\dfrac{8}{5}\\\\x=\dfrac{8}{5}[/tex]

Therefore. [tex]x=\dfrac{8}{5}[/tex].

[tex]7x+4=5x-18[/tex]

Here, we can group all the x values on the left side of the equation. Subtract 5x from both sides:

[tex]7x+4-5x=5x-18-5x\\2x+4=-18[/tex]

To isolate x, subtract 4 from both sides:

[tex]2x+4-4=-18-4\\2x=-22[/tex]

Divide both sides by 2:

[tex]\dfrac{2x}{2}=\dfrac{-22}{2}\\\\x=-11[/tex]

Therefore, [tex]x=-11[/tex].

Step-by-step explanation:

When written in standard form, yout can just look at the first term

If the first term is positive it opens upwards

if the first term is negative, it opens downwards

Answer:

3484 ft²

explanation:

area of parallelogram is base * height

given:

using the formula:

base * height

67 * 52

3484 ft²

Answer:

are congruent

Step-by-step explanation:

The speed of the jet is 1302 miles per hour.

Since a private jet can fly 1134.6 miles against a 27-mph headwind in the same amount of time it can fly 1469.4 miles with a 27-mph tailwind, to find the speed of the jet you must perform the following calculation:

Therefore, the speed of the jet is 1302 miles per hour.

Learn more about speed determination in https://brainly.com/question/15191306

Answer:

the square root of 2 is approximately 1.41

Step-by-step explanation:

Hope that helps!

Answer:

The answer is 1.41421356237...

Step-by-step explanation:

the square root of 2=2^1/2

2=2^1/2

2^12=1.41421356237...

The square root of 2=1.41421356237...

1.41421356237...

Answer:

40.32

Step-by-step explanation:

I hopped I helped! <3