Three friends decide to go out to eat, and then go shopping. if there are 5 local restaurants and 4 good stores for shopping, how many possibilities are there for their big night out

Answer:

x = 6

Step-by-step explanation:

First we divide both sides by 3 :

x² = 108 ÷ 3

x² = 36

Now we square root both sides :

x = √36

x = 6

Hope this helped and have a good day

Answer:

     x = ± 6

Step-by-step explanation:

Quick steps

[tex]3x^{2} =108[/tex]

[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]

[tex]x=[/tex] ±6

A (positive) number has two square roots; one positive and one negative

Hope this helps

The first five terms of the sequence with the given n-th term [tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0

For given question,

We have been given the n-th term of the sequence [tex]a_n = cos(\frac{n\pi}{2} )[/tex]

We need to find the first five terms of the sequence.

For n = 1

[tex]\Rightarrow a_1 = cos(\frac{1\pi}{2} )\\\\\Rightarrow a_1=0[/tex]

For n = 2,

[tex]\Rightarrow a_2 = cos(\frac{2\pi}{2} )\\\\\Rightarrow a_2=cos(\pi)\\\\\Rightarrow a_2=-1[/tex]

For n = 3,

[tex]\Rightarrow a_3= cos(\frac{3\pi}{2} )\\\\\Rightarrow a_3=0[/tex]

For n = 4,

[tex]\Rightarrow a_4 = cos(\frac{4\pi}{2} )\\\\\Rightarrow a_4=cos(2\pi)\\\\\Rightarrow a_4=1[/tex]

For n = 5,

[tex]\Rightarrow a_5 = cos(\frac{5\pi}{2} )\\\\\Rightarrow a_5=0[/tex]

Therefore, the first five terms of the sequence with the given n-th term[tex]a_n = cos(\frac{n\pi}{2} )[/tex] are : 0, -1, 0, 1, 0

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Answer:

4) 7a+20

5) 14+2b

6) 25c² - 15

Step-by-step explanation:

4) 9a+7-2a+13= 9a-2a+7+13 = 7a+20

5) 21-3b+5b-7= 21-7+5b-3b = 14+2b

6) (3c)² + (8c)² - 15 = 9c² + 16c² - 15 = 25c² - 15

Answer:9

Step-by-step explanation:

The statement that <A > <C and <B > <D has been proved

In geometry, the side length opposite the largest angle is the longest side.

Similarly, the side length opposite the smallest angle is the shortest side.

From the given figure of quadrilateral, we have the following sides in increasing order:

The angles opposite the side lengths are:

This means that:

<A > <C and <B > <D

Hence, the statement that <A > <C and <B > <D has been proved

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Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:

1/5.

A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.

In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:

p = 2/10 = 1/5.

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Answer: third store

Step-by-step explanation:

1

First store: 95

Second store: 0.8*115=92

Third store: 0.9*105=94.5

The maximum value of c=4x+2y subject to the constraints is 14

The objective function is given as:

c = 4x+2y

The constraints are given as:

x≥0 y≥0

2x+2y≤10

3x+y≤9

Rewrite 2x+2y≤10 and 3x+y≤9 as equations

2x+2y = 10

3x+y = 9

Divide 2x+2y = 10  through by 2

x+y = 5

Subtract x+y = 5 from 3x+y = 9

3x - x + y - y = 9 - 5

Evaluate the difference

2x = 4

Divide by 2

x = 2

Substitute x = 2 in x+y = 5

2+y = 5

Solve for y

y = 3

So, we have

(x, y) = (2, 3)

Substitute (x, y) = (2, 3) in c = 4x+2y

c = 4 * 2 + 2 * 3

Evaluate

c = 14

Hence, the maximum value of c=4x+2y subject to the constraints is 14

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Answer:

See the attached picture.

Step-by-step explanation:

The equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

Myra is 5 years younger than her sister Talat

Myra age is represented by m while Talat age is represented by t.

Hence,

m = age of Myra

t = age of Talat

Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.

Therefore, the equation that represents the  Myra's age given Talat age is as follows:

t = m + 5

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Answer:

Step-by-step explanation:

Using the normal distribution, the probability that x is less than 110 is:

A. 0.975.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 98, \sigma = 6[/tex]

The probability is the p-value of Z when X = 110, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 98}{6}[/tex]

Z = 2

Z = 2 has a p-value of 0.975.

Hence option A is correct.

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Answer:

6 1/10

Step-by-step explanation:

In order to add fractions, we have to make the denominators equal.  we can multiply 1/2 by 5/5 and get 5/10, and multiply 3/5 by 2/2 and get 6/10, to make the denominator equal. Now we add the fractions. 4 5/10 + 1 6/10 = 5 11/10 = 6 1/10

Answer:

When the eqn cuts the x-axis , y=0

3x=12

x=12/3

x=4

So,at x=4 is the point at which the linear equation cuts the x-axis

Answer:

collect like terms

12xy=12

xy=1

Answer:

Step-by-step explanation:

Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM.  9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM.  60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.

Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.

Answer: 21[tex]x^{2}[/tex] - 52x - 48

Step-by-step explanation:

Using the expanding rule we get

5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)

15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48

21[tex]x^{2}[/tex] - 52x - 48

Answer:

21x^2-52x-48

Step-by-step explanation:

5x(3x-10) + (2x-6)(3x+8)

Distribute

5x^2 -50x+6x^2-2x-48

Combine like terms

21x^2-50x-2x-48

21x^2-52x-48

Answer:

g(x) = log(x + 1) + 4

Step-by-step explanation:

The graph of g(x) is shifted 1 unit left and 4 units right from its parent function.

Answer:

y = 4x + 3

Step-by-step explanation:

as the line is parallel to the given equation, the gradient (4x) must stay the same, and as it must pass through the point (-2, -5), we can solve for the y intercept:

to calculate for the y intercept, it is best to express the equation in slope intercept form:

y = mx + b

in this equation, mx stands for the gradient, which ive already highlighted remains 4x, and b stands for the y intercept (which we don't know yet).

y = 4x + b

what we have been given instead is the coordinates for the point this line crosses through (-2,-5) meaning when x = -2, y = -5.

Using this information, we can replace x and y in the equation:

-5 = 4(-2) + b

with consideration to the order of operations, it is important to solve the brackets first

-5 = -8 + b

now to get b by itself add 8 to both sides of the equation:

-5 + 8 = -8 + 8 + b

3 = b

now we remember from the slope intercept equation, b = the y intercept, so we can now solve the equation.

y = 4x + b  

replace b with the number we solved for (3).

y = 4x + 3

this is the equation of the line that is parallel to y = 4x + 1, and passes through the point (-2, -5)

hope this helps :)

Answer:

[tex]154 $\ m^2[/tex]

Step-by-step explanation:

If 88 m of long rope is wrapped twice around the base of the drum, the circumference of the drum is 44m. We can use this information to find the radius of the base.

The equation for circumference is [tex]C=2\pi r[/tex]. We can substitute the value we found for circumference into the equation:

[tex]44=2\pi r[/tex]

Divide both sides by 2

[tex]22=\pi r[/tex]

Divide both sides by π

[tex]r=\frac{22}{\pi}[/tex]

The area of a circle is [tex]A=\pi r^2[/tex]. We can substitute the value we found for the radius into the equation:

[tex]A=\pi (\frac{22}{\pi})^2\\[/tex]

[tex]A=\pi (\frac{22}{\pi})(\frac{22}{\pi})[/tex]

[tex]A=22*\frac{22}{\pi}[/tex]

[tex]A=\frac{484}{\pi}[/tex]

[tex]A\approx154[/tex]

The difference of the means of the two data sets is = 4.57

The mean absolute deviation of the roller coaster speeds in North America is 13.3

The mean absolute deviation of the roller coaster speeds in Asia is 16.8

First we have to start with the data for North America

128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77

To get the mean you have to sum up the values and divide through by the total number 10

937.8/10

Mean = 93.78

Mean Absolute Deviation  = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10

133.32/10 = 13.3

For Asia, we have the data as

149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4

Mean for Asia = 892.1/10

= 89.21

Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10

= 168.32/10

16.8

The difference in the means = 93.78 -89.21

=  4.57

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Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

Given: 4x - 8y = 9 ............(1)

8x - 7y = 9 ............(2)

To be the same line, the equations have to be multiples of each other.

Multiplying (1) by 2, we get

2(4x - 8y = 9) = 8x - 16y = 18

From (1) solve the value of y, we get

4x - 8y = 9 ............(1)

-8y = -4x + 9

The value of y = (1/2)x - 9/8

From (2),

8x - 7y = 9

solve the value of y, we get

-7y = -8x + 9

The value of y = (8/7)x - 9/7

To be the exact line, the equations would be exact. Parallel lines maintain the exact slope but different y-intercepts. Perpendicular lines have to oppose, reciprocal slopes like 1/2 and -2 or 8/7 and -7/8.

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The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First

First gives;

y = -2·x + 34 = 18

Second gives;

y = -x/3 - 10 = -38/3

Third gives;

= -24

Fourth gives;

y = (x - 2)² = 36

We have after several iterations;

Third gives,

= -24

Next we input into the second to get,

y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2

Next we input into the fourth to get,

y = ((-2) - 2)² =  (-4)² = 16

Next we input into the first to get,

y = -2×16 + 34 = -32 + 34 = 2

Which gives the order as follows;

Third → Second → Fourth → First

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Answer:

Round the decimal values however needed.

Step-by-step explanation:

The uppercase letters represent the angles, while the lowercase counterparts are the side lengths opposite said angle. For example, side b is opposite angle B.

Angle B is 41 and angle C is 90 because of the square marker. The remaining angle A is...

A+B+C = 180

A+41+90 = 180

A+131 = 180

A = 180-131

A = 49

Or note that

A = 90 - B = 90 - 41 = 49

This shortcut works since we have a right triangle.

---------

That takes care of the angles. Now onto the sides.

We'll need to use trig ratios to determine the missing sides. There are a few approaches, but this is one you could take

tan(angle) = opposite/adjacent

tan(A) = a/b

tan(49) = a/15

a = 15*tan(49)

a = 17.255526 approximately

Furthermore,

sin(angle) = opposite/hypotenuse

sin(B) = b/c

sin(41) = 15/c

c*sin(41) = 15

c = 15/sin(41)

c = 22.863796 approximately

There is another trig function (cosine) that you could use. Also, you could use the pythagorean theorem once you know two sides of the right triangle.

The pythagorean theorem is a^2+b^2 = c^2

The answers have been confirmed with GeoGebra which is a useful geometry app.

[tex](x-5)(x+5)-(x+1)^2\\=x^2 -25-(x^2+2x +1)\\=x^2 -25-x^2-2x -1\\=-2x-26[/tex]

ANSWER: -2x -26

Ok done. Thank to me :3

Answer:

I think its -10 or -8

Step-by-step explanation:

Answer:

12√2.

Step-by-step explanation:

You can do this by the Pythagoras theorem:

20^2 = x^2 + (4sqrt7)^2    where  x is the distance required.

x^2 = 20^2 - (4sqrt7)^2

      = 400 - 112

      =  288

x  = √288

   =  √144 *√2

   =   12√2.

Taking into account the definition of a system of linear equations, the value of x is -4.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, the system of equations to be solved is

[tex]\left \{ {{3x+4y=-16} \atop {x=4y}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×4y +4y= -16

Solving:

12y +4y= -16

16y= -16

y= (-16)÷ 16

y= -1

Remembering that x=4y, then x= 4×(-1)= -4.

Finally, the value of x is -4.

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The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

The expression is given as:

(2x+1)/(x²-3)

The above expression is a fraction and the numerator has 2 terms

For a fraction

A + B)/x

The fraction can be split as

A/x + B/x

Using the above as a guide, we have:

(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)

Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)

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