Social distancing guidelines state that we must stay a minimum of 6ft away from each other. How many circles with a 3ft radius could fill a 100 square foot (10ft x 10ft) space without overlap?
*Tip*
Area of a Circle = π r​ ​where r=radius

Answer:

3x^2-10x-8

Step-by-step explanation:

Answer:9

Step-by-step explanation:

12-9=3 12-3=9 3+9=12

So C=9

Hey there!

[tex]\large\boxed{c=9}[/tex]

12 - 9 + c = 12

Combine like terms.

3 + c = 12

Subtract 3 from each side of the equation.

3 - 3 + c = 12 - 3

c = 9

Check:

12 - 9 + c = 12

12 - 9 + 9 = 12

3 + 9 = 12

12 = 12

Hope this helps!

Answer:  The answer is 0.3

Step-by-step explanation:

Lily should expect to buy 1.5 boxes to get all four prizes.

This question belongs to the field of probability in Mathematics. The problem is asking how many boxes Lily should expect to buy in order to get all four prizes. This is a geometric problem because each box has a probability of 1/4 of containing a prize, and each trial is independent with the same probability of success. To solve this problem, we can use the concept of expected value.

The expected value is the average number of boxes Lily needs to buy to get all four prizes. The expected value can be calculated by multiplying the probability of each outcome by the number of boxes it takes to achieve that outcome, and then summing up these products:

Expected value = (1/4) * 1 + (1/4) * 2 + (1/4) * 3 + (1/4) * 4 = 1.5

Therefore, Lily should expect to buy approximately 1.5 boxes to get all four prizes.

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Answer:

1.circle

2.triangle

3.trapezoid

4.parallelogram

Step-by-step explanation:

Answer:

(assuming the height is 13 and the width is 10 or vice versa) 65

Step-by-step explanation:

a = 1/2 base × height

1/2 13 × 10 or 10×13

130 ÷ 2

65

Area of isosceles triangle = [tex]\( \frac{13\sqrt{231}}{4} \)[/tex] square centimeters, approximately 43.03 square centimeters.

To find the area of an isosceles triangle, you can use the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Since it's an isosceles triangle, the height divides the triangle into two right-angled triangles of equal size.

Given:

Base = 13 cm

Height = ?

To find the height, we can use the Pythagorean theorem.

Let's denote the height as  [tex]\( h \),[/tex] and half of the base (since the triangle is isosceles, and the height splits the base into two equal parts) as  [tex]\( \frac{13}{2} \).[/tex]

Then, using the Pythagorean theorem:

[tex]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 10^2 \]\[ (\text{height})^2 + \left(\frac{13}{2}\right)^2 = 100 \]\[ (\text{height})^2 + \frac{13^2}{2^2} = 100 \]\[ (\text{height})^2 + \frac{169}{4} = 100 \]\[ (\text{height})^2 = 100 - \frac{169}{4} \]\[ (\text{height})^2 = \frac{400}{4} - \frac{169}{4} \]\[ (\text{height})^2 = \frac{231}{4} \][/tex]

Now, let's solve for the height:

[tex]\[ \text{height} = \sqrt{\frac{231}{4}} \]\[ \text{height} = \frac{\sqrt{231}}{\sqrt{4}} \]\[ \text{height} = \frac{\sqrt{231}}{2} \][/tex]

Now that we have the height, we can calculate the area using the formula:

[tex]\[ Area = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Substituting the values:

[tex]\[ Area = \frac{1}{2} \times 13 \times \frac{\sqrt{231}}{2} \]\[ Area = \frac{13 \sqrt{231}}{4} \][/tex]

So, the area of the isosceles triangle is  [tex]\( \frac{13 \sqrt{231}}{4} \)[/tex]  square centimeters.

The complete question is here.

Find the area of the isosceles triangle with a base of 13 cm and a height of 10 cm.

Answer:

80 cm³

Step-by-step explanation:

Density = mass/volume

1.19 = 95.2/volume

Volume = 95.2/1.19

= 80

Answer:

80 cm cubed

Step-by-step explanation:

The density of a substance is denoted by d = m/V, where d is the density, m is the mass, and V is the volume.

Here, we know that the mass m = 95.2 grams and the density d = 1.19 g/cm cubed. So, plug these values into the formula:

1.19 = 95.2/V

Divide both sides by 1.19 and multiply both sides by V:

V = 95.2/1.19 = 80 cm cubed

Thus, the volume is 80 cm cubed.

Hope this helps!

Answer:

rdgvvsssddas

Step-by-step explanation:

42423412

Answer:

Step-by-step explanation:

Looking at the information given, the population mean and population standard deviation are known. We would apply the formula

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = population standard deviation

From the information given,

µ = 70

σ = 10

1) x = 60

The probability that the heart rate if an individual is less than 60 is expressed as

P(x < 60)

z = (60 - 70)/10 = - 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.16

The percentage rates of heart rates less than 60 is 0.16 × 100 = 16%

2) x = 80

The probability that the heart rate if an individual is less than 80 is expressed as

P(x < 80)

z = (80 - 70)/10 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.84

The percentage rates of heart rates less than 80 is 0.84 × 100 = 84%

3) x = 50

The probability that the heart rate if an individual is greater than 50 is expressed as

P(x > 50) = 1 - P(x ≤ 50)

z = (50 - 70)/10 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.23

P(x > 50) = 1 - 0.23 = 0.77

The percentage rates of heart rates greater than 50 is 0.77 × 100 = 77%

Answer:

Sum a + b is irrational

Step-by-step explanation:

Any irrational number plus a rational number is always irrational.

Answer:

2.18

Step-by-step explanation:

tan 70°=x/6

by cross multiplication

xtan70°=6

divide both sides by tan70°

x=6/tan70°

x=6/2.7475

x=2.18

Answer:

88.2 squared

Step-by-step explanation:

The formula to find the area of a circle is a = pi * r ^2

Let's replace the values that we know.

a = 3.14 x 5.3 ^2

First, we should do 5.3 ^2, which is 28.09.

a = 3.14 x 28.09

Now we are able to do 3.14 x 28.09 which is 88.2026

But that isn't it! We need to round to the nearest tenth, which is this digit:

88.2026

Since next to the 2 there is a 0, you take out all the numbers after that 2. Which leaves you with:

88.2

Final answer:

The area of the round mirror with a radius of 5.3 inches, when calculated using the formula A = πr^2 and rounded to the nearest tenth, is 88.2 square inches.

To find the area of the round mirror with a radius of 5.3 inches, we will use the formula for the area of a circle, which is A = πr^2, where A is the area, π is approximately 3.14, and r is the radius of the circle.

Given that the radius of the mirror is 5.3 inches, we can substitute this value into the formula to find the area:

A = π(5.3)^2 ≈ 88.2 square inches.

Let's plug in the radius:

When rounded to the nearest tenth, the area of the mirror is 88.2 square inches.

Calculate the value of z and its probability, since with this we can know how likely it is that this will happen.

We have that the mean (m) is equal to 8.3, the standard deviation (sd) 1.2 and the sample size (n) = 15

They ask us for P (x =7.2)

For this, the first thing is to calculate z, which is given by the following equation:

z = (x - m) / (sd / (n ^ 1/2))

We have all these values, replacing we have:

z = (7.2 - 8.3) / (1.2 / (15 ^ (1/2))

z = -3.55

With the normal distribution table (attached), we have that at that value the approximate probability is:

P (z = -3.55) = 0.0001

The probability is 0.01 %

This affirms that the students do not sleep what the study says because the probability of this happening according to the survey is almost nil.

The limit of the given infinite series is undefined.

The given series is:

∑n=1∞(3n5/6n6+1)

To find the limit, we can simplify the series by dividing the numerator and denominator by the highest power of n:

∑n=1∞(3/n-1/6n-1+n-6)

As n approaches infinity, the terms containing n-1 and n-6 approach 0, so we are left with:

∑n=1∞(3/n)

This is a harmonic series with the form 1+1/2+1/3+1/4+... which is known to diverge. Therefore, the limit of the given infinite series is undefined.

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Answer:

(0,1)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The correct option is Option B: is an A.P., because d = 10

An arithmetic progression, also known as an arithmetic sequence, is a sequence of numbers in which the difference between consecutive terms is constant. This constant difference is called the common difference and is denoted by 'd'.

The given sequence is:

-5, 5, 15, 25, ....

In every Arithmetic Progression (A.P.)

The common difference d

d= 2nd term - 1st term = 3rd term - 2nd term

d = 5-(-5) = 15 - 5

d = 10

Hence the common difference is 10,

Therefore  the sequence is an A.P., because d = 10

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The correct question

The sequence: -5, 5, 15, 25, ...

A. is not an A.  P.

B. is an A.P., because d = 10

C. is an A.P because d = 5

D is an A. P., because d = -10

a) The function that represent this situation is y = 90 + 8x.

b)  His weight be after 8 weeks is 154 lbs.

Step-by-step explanation:

It is given that,

a) Write a function to represent this situation. Use x and y as your variables.

Hence the equation can be framed as,

Total weight = starting weight + weight gained in x weeks.

We know that, each week he gains 8 lbs. Therefore, for 8 weeks he gained 8x lbs of weight.

⇒ y = 90 + 8x.

∴ The function that represent this situation is y = 90 + 8x.

b) What would his weight be after 8 weeks?

To find his week after 8 weeks, substitute x=8 in the function y = 90 + 8x.

⇒ 90 + 8(8)

⇒ 90 + 64

⇒ 154 lbs.

∴ His weight be after 8 weeks is 154 lbs.

Answer:

C'(1, 2 )

Step-by-step explanation:

The translation (x + 3, y - 2 ) means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, thus

C(- 2, 4 ) → C'(- 2 + 3, 4 - 2 ) → C'(1, 2 )

Answer:

C = ( 1 , 2 )

Step-by-step explanation:

original : C =  ( -2 , 4 )

formula : ( x+3 , y-2 )

( -2 + 3 ) , ( 4 - 2 )

C = ( 1 , 2 )

ill answer the other 3 as well :)  

original : A = ( -6 , 2 )

formula : ( x+3 , y-2 )

( -6 + 3 ) , ( 2 - 2 )

A = ( -3 , 0 )

___________________

original : B = ( -5 , 4 )

formula : ( x+3 , y-2 )

( -5 + 3 ) , ( 4 - 2 )

B = ( -2 , 2 )

___________________

original : D = ( 1 , 2 )

formula : ( x+3 , y-2 )

( 1 + 3 ) , ( 2 - 2 )

D = ( 4 , 0 )

yw :)

Answer:

20cm

Step-by-step explanation:

7.2 + 7.2 + 2.8 + 2.8 = 20

Each side of the rectangle is equal to the side opposite from it. That means you have 2 sides of 7.2 cm and 2 sides of 2.8 cm.

To find perimeter, you add all the sides. So that's 7.2 + 7.2 + 2.8 + 2.8, which is 20 cm altogether.

Answer: The functions are v1(t)=10000*(1.04)^5  and v2(t)=8000(1.06)^5

v1(5)=12166$

v2(5)=10705 $

Step-by-step explanation:

Given:

Investment cost for 1st=10,000$  ,at 4%rate.

Investment cost for 2nd=8000$ ,at 6% rate.

To Find:

Exponential growth functions ,

that could be used to find v1(t) and v2(t),

the value of each investment after 5 years

And difference between their values.

Solution:

Consider for 1st investment function be v1(t) and for 2nd be v2(t)

and t be time period

Exponential growth is given by, as time function,

v(t)=initial cost*(1+rate)^time period.

for 1st investment its cost is 10000$  at 4 % rate.

[tex]v1(t)=10000(1+0.04)^t[/tex]

[tex]v1(t)=10000(1.04)^t[/tex]

for 2nd investment its cost is 8000$  at 6% rate.

[tex]v2(t)=8000(1+0.06)^t[/tex]

[tex]v2(t)=8000(1.06)^t[/tex]

For t=5 calculating for both investment,

[tex]v1(5)=10000(1.04)^5[/tex]

[tex]=10000*1.2166[/tex]

v1(5)=12166 $

For 2nd investment,

[tex]v2(5)=8000(1.06)^5[/tex]

[tex]=8000*1.3382[/tex]

v2(t)=10705.8 $

Now after 5 years the difference is =v1(t)-v2(t)

Which is about 1460 $ only.

This because of the both functions depends upon time,initial investment and rate of interest .

Here time period being same.But the rate of interest are different and initial values are different.

Answer:

n = 3

Step-by-step explanation:

Ratio from Triangle A to Triangle B is 2:1.

n+2 = 5

n = 3

Answer:  

1: -2.33 or -7/3

2: - 2.16 or -13/6

3: 3.49 x 10^4

4: 4.28*10-7

5: 0.81 or 9/11

6. 3

7: 8

8: 9 or up

9: 5 or up

10: 0-36

I hope any of this helps.... :D

Answer:

224 card combinations

Step-by-step explanation:

The total number of card designs can be found by multiplying the number of options available for each design element.

Total number of cards= 2x4x7x4=?

224 cards altogether

Answer: 14

Step-by-step explanation:

the question is just asking you to replace the x and y with the corresponding numbers.

x = 4

y = -3

Since x is 4 squared it would be 16.

-4 times -3 equals positive 12.

That would make the equation

(16 + 12) divided by 2

16 + 12 = 28 divide that by 2 and you’ll get 14.

Answer: 14

Step-by-step explanation:

First plug 4 in for x.

4^2 is equal to 16 because 4 x 4 is 16.

Next, plug in -3 for y.

-4 x -3

4 times 3 is 12 and they are both negative, therefore it turns out as a positive 12.

Then add the numbers on the top of your equation.

16+12=28.

Finally divide the sum by 2.

28 divided by 2= 14

Your answer is 14.

Hope this helps!

Answer:

A = (1/2)(3)(7 + 3) = 5(3) = 15

15 goes into the box.

Answer:

(x, -y)

Step-by-step explanation:

Look at the coordinates of the point C before the transformation (-2, 2)

look at the coordinates of the point C after the transformation, (-2,-2)

What is the difference between these two points?

Well the x is the same, the y is just the negative version of itself!

Answer:i need a better pic

Step-by-step explanation:

Answer:

The measurements of all the right angles and the lengths of the two sides and the measurement of the included angle.

Step-by-step explanation:

the measurements of two angles

the measurements of two angles and the length of the included side

the lengths of two sides and the measurement of the included angle

Answer:

Base=36

Height=18

Step-by-step explanation:

To work this out you would first multiply 12 by 3, which gives you 36. Then you would multiply 6 by 3, which gives you 18.

1) Multiply 12 by 3.

[tex]12*3=36[/tex]

2) Multiply 6 by 3.

[tex]6*3=18[/tex]

3) Base=36

Height=18

[tex]\large\bf{\underline{\underline{\mathfrak{Question}:}}}[/tex]

The base and height of a triangle with base 12 in and the height 6 in are both tripled.

[tex]\large\bf{\underline{\underline{\mathfrak{Solution}:}}}[/tex]

It is given that,

[tex]:{\Longrightarrow{\small{\rm{The\:base\:of\:a\:triangle\:=\:12}}}}[/tex]

[tex]:{\Longrightarrow{\small{\rm{The\:height\:of\:a\:triangle\:=\:6}}}}[/tex]

And if both base and height get tripled then the base and height would be:

[tex]:{\Longrightarrow{\small{\rm{The\:base\:of\:a\:triangle\:=\:3×12}}}}[/tex]

[tex]{\therefore{\small{\rm{The\:new\:base\:of\:a\:triangle\:=\:36}}}}[/tex]

And,

[tex]:{\Longrightarrow{\small{\rm{The\:height\:of\:a\:triangle\:=\:3×6}}}}[/tex]

[tex]{\therefore{\small{\rm{The\:new\:height\:of\:a\:triangle\:=\:18}}}}[/tex]

Answer:

The distance in miles between  the towns is 67.5.

Step-by-step explanation:

Given:

On a map the scale is shown as 0.5 inches equaling 15 miles.

If the distance are 2.25 inches apart on the map between the towns .

Now, to find the distance in miles between  the towns.

The distance on the map between the towns = 2.25 inches.

Let the actual distance between the two towns be [tex]x.[/tex]

The scale of the map is 0.5 inches equaling 15 miles.

If, 0.5 is equivalent to 15 miles.

Thus, 2.25 is equivalent to [tex]x.[/tex]

Now, to solve using by cross multiplication method:

[tex]\frac{0.5}{15} =\frac{2.25}{x}[/tex]

By cross multiplying we get:

[tex]0.5x=33.75[/tex]

Dividing both sides by 0.5 we get:

[tex]x=67.5\ miles.[/tex]

The actual distance between the two towns = 67.5 miles.

Therefore, the distance in miles between  the towns is 67.5.