use the distributive property to simplify the expression
1/2( 2n +4+6m)

The largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5

From the given information, we have 52 people in the room

Note that there are 12 months in a year

Let's divide the number by people by the months of the year

⇒ [tex]\frac{52}{12}[/tex]

⇒ 4 remaining 4

If 48 people are evenly distributed over twelve months, then there will be four people born in each month.

The remaining four people can be placed each in any of the twelve different months.

Hence, if 52 people are evenly distributed as possible, there will be eight months with four people and four months with five people.

Thus, the largest value of n such that the statement "at least n people in this room have birthdays falling in the same month" is always true is 5

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The slant height of the hexagonal pyramid is: B. 14 inches.

Area of a regular hexagon = 3√3/2(s²)

First, find the area of the regular hexagon:

Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².

Surface area is given as 420 + 150√3 in.².

Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3

Area of the 6 triangles = 420 in.²

Area of 1 triangle = 420/6 = 70 in.²

Use the area of a triangle to find the slant height (h):

70 = 1/2(10)(h)

2(70) = 10(h)

140/20 = h

h = 14 in.

The answer is B. 14 inches.

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Answer:

??

Step-by-step explanation:

Answer:

6.45

Step-by-step explanation:

I am not staring at zero.  I am starting at 6.4, so I take 6.4 and add that to half way between 6.5 and 6.4.

6.4 + 1/2(6.5-6.4)  Combine in the parentheses

6.4 + 1/2(.5)  Take half of .5

6.4 + .05  add

6.45

Answer:

1:216

Step-by-step explanation:

The probability of getting a 4 would be 1/6.  The probability of getting a 5 would be 1/6 and the probability of getting a 6 would be 1/6.  The bottom number is the total number of outcomes (1,2,3,4,5,6) and the top number is out of that set, how many do I want.  In the case of wanting a 4, I want 1 out of those 6 numbers and so on.

Now we multiple these together 1/6 x 1/6 x 1/6 and get  1/216 or another way to write this is 1:216

Answer:

look the answer is in the picture and don't forget to like and brainlest

Answer:

x = 90°

Step-by-step explanation:

The line that contains angle x and the 90° angle is a straight line.

A straight line measures as 180°.

So, subtracting the given 90° from the 180° line that the two angles share, we would get the measure of x.

[tex]180-90 =x[/tex]

Which means, [tex]x=90[/tex].

So the value of x is 90°.

The missing number for the subtraction of matrices is 4.

The subtraction of two matrices of the same size is really direct. You just need to subtract the elements that are in the same position, then:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] \\\\B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]\\\\A - B = \left[\begin{array}{ccc}a_{11} - b_{11}&a_{12}-b_{12}\\a_{21} - b_{21}&a_{22}-b_{22}\end{array}\right][/tex]

Then the missing therm will just be equal to the difference between the last two elements of each matrix:

-2 - (-6) = -2 + 6 = 4

The missing number is 4.

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The probability that a particular passenger chooses chips and soda as a snack is 0.25 or 25%.

In mathematics, probability is considered as the chances a specific situation or event occurs. For example, you can calculate the probability that it rains tomorrow based on general weather patterns.

Now, let's multiply these probabilities:

This means the  probability of a passenger choosing chips and soda as a snack is 0.25 or 25%.

Note: This question is incomplete; here is the missing section:

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The volume of the balloon is 1441.64cm³.

The radius of the balloon is given as 7cm. Also, the equation to calculate the volume is given as c³/6π²

The circumference c will be:

= 2πr = 2 × 22/7 × 7

= 44

The volume will be:

= c³/6π²

= 44³/(6 × 3.14²)

= 85284/(59.1576)

= 1441.64

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Answer:

[tex]x = \frac{n}{b - {t}^{2} } [/tex]

Step-by-step explanation:

I supposed that is a "n".

Steps as below:

[tex] {t}^{2} = b - \frac{n}{x} \\ b - \frac{n}{x} = {t}^{2} \\ - \frac{n}{x} = {t}^{2} - b \\ \frac{n}{x} = - ( {t}^{2} - b) \\ \frac{n}{x} = b - {t}^{2} \\ n = x(b - {t}^{2} ) \\ x(b - {t}^{2} ) = n \\ x = \frac{n}{b - {t}^{2} } [/tex]

Answer:

[tex]x = \frac{h}{b-t^2}[/tex]

Step-by-step explanation:

[tex]t^2 = b - \frac{h}{x}[/tex]

• First add  [tex]\frac{h}{x}[/tex]  to both sides:

⇒ [tex]\frac{h}{x} + t^2 = b[/tex]

• Now subtract  [tex]t^2[/tex]  from both sides:

⇒ [tex]\frac{h}{x} = b - t^2[/tex]

• Now multiply both sides by [tex]x[/tex] :

⇒ [tex]h = x(b - t^2)[/tex]

• Next divide both sides by  [tex](b - t^2)[/tex] :

⇒ [tex]\frac{h}{b-t^2} = x[/tex]

∴  [tex]\boxed{x = \frac{h}{b-t^2}}[/tex]  

The graph of Lin's distance as a function of time cannot be a straight line graph because of decrease in speed.

Given that Lin walks half a mile at a constant rate i.e. Lin velocity is constant.

If the speed is low then the time will be high. If speed is high then the time will be low because of the following rule:

Speed=Distance/ time.

For the first five minutes the graph will be upward sloping because he was sprinting and his speed was high so he will cover much more distance.

But after five minutes the graph will be downward sloping as the speed becomes low and he willcover less distance.

Hence the graph of Line's distance will not look like linear curve.

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The probability that the cab was really yellow given that it was reported as being yellow is 0.32.

Given that there are 80% black taxis and 20% yellow taxis, witness is 80% accurate.

Probability is the chance of happening an event among all the events possible. It lies between 0 and 1. The value of probability can be calculated through the following formula:

Probability=Number of items/ total items.

Black taxis=80%

Yellow taxs=20%

Eyewitness is accurate=80%

Probability that the cab was really yellow=

P(X=Yellow)P(Witness is correct)+P(X=Black)P(Witness is incorrect)

Probability that car is black=0.8

Probability that car is yellow=0.2

Probability that witness is correct=0.8

Probability that witness is incorrect=1-0.8

=0.2

We have to just put the values in the formula given above.

Required probability=0.2*0.8+0.8*0.2

=0.16+0.16

=0.32

Hence the probability that the cab is really yellow is 0.32.

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Answer:

64

Step-by-step explanation:

2x-4y=3

x= (3 +4y)/2

substitute into the main equation

y= 0

x= 3/2

16^x /256^y

16^3/2 ÷ 256^0

√16^3 ÷1

= 64

Answer:

64

Step-by-step explanation:

2x - 4y = 3

2x = 4y + 3

x = 2y + 1.5

[tex] \dfrac{16^x}{256^y} = [/tex]

[tex] = \dfrac{16^{2y + 1.5}}{256^y} [/tex]

[tex] = \dfrac{16^{2y + 1.5}}{16^{2y}} [/tex]

[tex] = 16^{2y + 1.5 - 2y} [/tex]

[tex] = 16^\frac{3}{2} [/tex]

[tex] = 4^3 [/tex]

[tex] = 64 [/tex]

Rule 1: Multiply by 2 then add 1 starting

( n x 2 +1) => 2n + 1

n is the position of our terms, so I substitute 1 because you're told to start from 1 which becomes our first term

2n + 1

2 x 1 + 1 =3

2 x 2 + 1 = 5

2 x 3 + 1 = 7

2 x 4 + 1 = 9

3,5,7,9....

(you can clearly see the sequence increasing by 2 each time, not following Multiply by 2 then add 1)

However, if we were to do add one each time, you'll add one to your pervious answer. So, this time I'll substitute the pervious answer

2 x 1 + 1 =3

2 x 3 + 1 = 7

2 x 7 + 1 = 15

2 x 15 + 1 = 31

3,7,15,31....

(from 3 to 7, you clearly see its multiplied by 2, then +1 & that's our sequence, this method apply to the second rule too of using previous)

Rule 2: Divide by 2 then add 4

(n ÷ 2 + 4) => n/2 + 4

n/2 + 4

(starting from 40.)

40/2 + 4 = 24

24/2 + 4 = 16

16/2 + 4 = 12

12/2 + 4 = 10

24,16,12,10.....

Answer: (started off with the number it asked of)

R 1 -

1,3,7,15,31....

(1 x 2 +1 does give 3)

R 2 -

40, 24,16,12,10.....

(40÷2 = 20, then + 4, gives 24)

Hope this helps!

To get 14 liters of antifreeze solution, add 14 - x liters of the solution

From the question, we are to determine how many liters should be added to the solution

From the given information,

We are to get 14 liters of antifreeze solution,

and

we already have x liters of the solution

To get 14 liters of antifreeze solution, we will add 14 - x liters of the solution

Hence, to get 14 liters of antifreeze solution, add 14 - x liters of the solution

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Using proportions, it is found that 66 men can leave so there will still be enough food.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Considering the situation described, the rule of three is given as follows:

4200 men - 32 days - 12 hectogram per person.

x men - 42 days - 16 hectogram per person.

Considering that the amount per person and the number of people is inverse proportional, we have that:

[tex]\frac{4200}{x} = \frac{32}{42} \times \frac{16}{12}[/tex]

[tex]\frac{4200}{x} = \frac{512}{504}[/tex]

Applying cross multiplication:

512x = 504 x 4200

x = 504 x 4200/512

x = 4134.

The amount of men that can leave is:

4200 - 4134 = 66.

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The correct answer is "all real numbers greater than or equal to 2".

Answer:

D. y =  √(x - 12)

Step-by-step explanation:

x  = y² + 12

y² = x - 12

y = √(x - 12)

The graph that aligns with the information is graph D.

We know that vector addition is scalar addition.

Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>

2v = < -2.5, 4.5>

2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >

2v-u = < 1 , 6 >

This vector is basically i + 6j which is drawn in option D

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The unknown value in the table using the constant of proportionality is; 96

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.

We are given the coordinates;

(12, 42), (18, 63), (40, y)

where x-values represents time in seconds and y-values represents number of pencils that were produced.

To find the constant of proportionality is as good as finding the slope between two consecutive points as;

m = (63 - 18)/(42 - 12)

m = (45/30)

m = 1.5

Thus to find the unknown value y, we will use the formula;

(y - y1)/x - x1) = m

So we will use the coordinates; (18, 63), (40, y)

Plugging them into the formula above will result in;

(y - 63)/(40 - 18) = 1.5

y - 63 = 1.5 * 22

y - 63 = 33

y = 33 + 63

y = 96

Thus, we can conclude that using the constant of proportionality, the number of pencils that were produced after a time of 40 seconds is 96 pencils.

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You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point.

The "slope formula" for a straight line connecting any two locations is another name for the rise over run formula. The rise is the difference between the y-coordinates of the two locations. The run is the difference between the x-coordinates of two locations. Divide the rise by the run to find the slope.

The rise over run formula is also known as the slope formula because the fraction consists of a rise, whether the line is moving up or down, divided by the run, which can be either left or right. The slope of the line dictates the direction of the line as well as its steepness.

Thus, "You can find the run by subtracting the _x_ coordinate of the lead point from that of the right point".

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The corporation's margin of safety is 0.73.

Margin of safety is the amount of sales a company makes in excess of the breakeven point.

Margin of safety = (forecasted sales -  break-even sales) / forecasted sales

Break even sales = fixed cost / (price per unit - variable cost)

12,147,000 / (3500 - 1680) = 6,674.18

Margin of safety = (24,600 - 6,674.18) / 24,600 = 0.73

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The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

The equation is given as:

f(x) = 2(0.35)^x

The reflection of a function over the y-axis is :

f'(x) = f(-x)

So, we have:

f(-x) = 2(0.35)^(-x)

From the list of options, we have

h(x) = 2(0.35)^(-x)

Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

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Answer:

5 hours 20 minutes.

Step-by-step explanation:

8 * 2/3

= 16/3

= 5 1/3

= 5 hours 20 minutes.

The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.

a. Based on the information given, the probability that the person will be able to keep a pack of fuzzy peaches will be:

= 10/(10 + 7 + 3) × 10/(10 + 7 + 3)

= 10/20 × 10/20

= 1/4

= 0.25

The probability that the person will be able to keep a pack of fuzzy peaches will be 0.25.

b. The probability to be able to keep any of the candy will be:

= (10/20 × 10/20) + (7/20 × 7/20) + (3/20 × 3/20)

= 100/400 + 49/400 + 9/400

= 158/400

= 0.395

The probability to be able to keep any of the candy will be 0.395.

c. The probability that you will not be able to keep any of the candy will be:

= (10/20 × 10/20) + (7/20 × 13/20) + (3/20 × 17/20)

= 100/400 + 91/400 + 51/400

= 242/400

= 0.605

The probability that you will not be able to keep any of the candy will be 0.605.

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Answer:

x = 1.4

Step-by-step explanation:

Visualize the figure as a rectangle with width 4 and height 1 combined with a triangle with base 1 and height 1.

Next, use the Pythagorean Theorem, a^2 + b^2 = c^2. Variables a and b represent the lengths of the legs, in this case 1 and 1, and variable c represents the length of the hypotenuse, in this case x.

1^2 + 1^2 = x^2

2 = x^2

x = 1.41421356237

Step-by-step explanation:

imagine that this shape is the combination of 2 shapes :

1. a rectangle 4×1

it goes from the top down the side of 4 until the tilted line x begins.

2. a right-angled triangle

x being the Hypotenuse (the baseline opposite of the 90° angle). and the legs are the invisible line of 1 (going from the top right of x in parallel to the 1 line all the way to the 5 line) and the part of the 5 line below the 4 line : 5-4 = 1.

so, x can be solved by using Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b are the legs.

x² = 1² + 1² = 2

x = sqrt(2) = 1.414213562... ≈ 1.4