What is the apothem of a equilateral triangle with radius 9cm

Answer:

Step-by-step explanation:

9-5=4

8*4*10=320

5*10*3=150

320+150=470

470 cm³

Answer:

4.16% is the hourly growth rate

Step-by-step explanation:

What we can do here is to first set up an exponential relationship that relates the present number of bacteria, the initial number of bacteria, the growth rate of the bacteria and the number of hours.

What we want to establish here has a resemblance with the compound interest formula in finance.

Let’s see the initial number of bacteria as the amount deposited, the present number of bacteria as the amount after some months, the growth rate as the monthly percentage while the number of hours works like the number of months.

Mathematically, what we have will be;

P = I(1 + r)^h

where P is the present bacteria number, I is the initial, r is the growth rate while h is the number of hours.

Thus, we have the following values from the question;

P = 1530

I = 1,300

r = ?

h = 4

Substituting these values, we have;

1530 = 1300(1 + r)^4

divide both sides by 1,300

1.177 = (1+r)^4

Find the fourth root of both sides

(1.177)^(1/4) = 1+ r

1.0416 = 1 + r

r = 1.0416-1

r = 0.0416

This in percentage is 4.16%

Answer:

"The probabilities are equal."

Step-by-step explanation:

Since the amount of times the paper cup landed on its open, and closed end is equal, then the answer is "The probabilities are equal."

Answer: the probability’s are equal

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

An easy way to do this is to simply take 360(the sum) and divide it by 5(the number of numbers) to get 72.  Thus, 72 is the middle number and the numbers are:

72

72,72,73

70,71,72,73,74

The smallest of these numbers is 70

Hope it helps <3

Hello!

Answer:

70 is the smallest number.

Step-by-step explanation:

If the sum of 5 consecutive numbers is 360, we can solve for the smallest number algebraically:

Let 'x' represent the smallest number:

and (x + 1), (x + 2), (x + 3), and (x+4) represent the other consecutive numbers:

x + (x + 1) + (x + 2) + (x + 3) + (x+ 4) = 360

Combine like terms:

5x + 10 = 360

Subtract 10 from both sides:

5x = 350

Divide both sides by 5:

x = 70. This is the smallest of the consecutive numbers.

We can check our work:

70 + 71 + 72 + 73 + 74 = 360.

Hope this helped!

Answer:

option D 25 is the right answer

Answer:  D) 25

Step-by-step explanation:

I graphed the coordinates and partitioned it into four triangles and one rectangle. Then I found the area for each partition.

The sum of the partitions is 25.

Answer:

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Step-by-step explanation:

[tex]\alpha \text{ and } \beta \text{ in Quadrant I}[/tex]

[tex]$\tan(\alpha)=\frac{1}{7} \text{ and } \sin(\beta)=\frac{1}{\sqrt{10}}=\frac{\sqrt{10} }{10} $[/tex]

Using Pythagorean Identities:

[tex]\boxed{\sin^2(\theta)+\cos^2(\theta)=1} \text{ and } \boxed{1+\tan^2(\theta)=\sec^2(\theta)}[/tex]

[tex]$\left(\frac{\sqrt{10} }{10} \right)^2+\cos^2(\beta)=1 \Longrightarrow \cos(\beta)=\sqrt{1-\frac{10}{100}} =\sqrt{\frac{90}{100}}=\frac{3\sqrt{10}}{10}$[/tex]

[tex]\text{Note: } \cos(\beta) \text{ is positive because the angle is in the first qudrant}[/tex]

[tex]$1+\left(\frac{1 }{7} \right)^2=\frac{1}{\cos^2(\alpha)} \Longrightarrow 1+\frac{1}{49}=\frac{1}{\cos^2(\alpha)} \Longrightarrow \frac{50}{49} =\frac{1}{\cos^2(\alpha)} $[/tex]

[tex]$\Longrightarrow \frac{49}{50}=\cos^2(\alpha) \Longrightarrow \cos(\alpha)=\sqrt{\frac{49}{50} } =\frac{7\sqrt{2}}{10}$[/tex]

[tex]\text{Now let's find }\sin(\alpha)[/tex]

[tex]$\sin^2(\alpha)+\left(\frac{7\sqrt{2} }{10}\right)^2=1 \Longrightarrow \sin^2(\alpha) +\frac{49}{50}=1 \Longrightarrow \sin(\alpha)=\sqrt{1-\frac{49}{50}} = \frac{\sqrt{2}}{10}$[/tex]

The sum Identity is:

[tex]\sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\sin(\beta)\cos(\alpha)[/tex]

I will just follow what the question asks.

[tex]\text{Find the value of }\alpha+2\beta[/tex]

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]\text{I will first calculate }\cos(2\beta)[/tex]

[tex]$\cos(2\beta)=\frac{1-\tan^2(\beta)}{1+\tan^2(\beta)} =\frac{1-(\frac{1}{7})^2 }{1+(\frac{1}{7})^2}=\frac{24}{25}$[/tex]

[tex]\text{Now }\sin(2\beta)[/tex]

[tex]$\sin(2\beta)=2\sin(\beta)\cos(\beta)=2 \cdot \frac{\sqrt{10} }{10}\cdot \frac{3\sqrt{10} }{10} = \frac{3}{5} $[/tex]

Now we can perform the sum identity:

[tex]\sin(\alpha + 2\beta)=\sin(\alpha)\cos(2\beta)+\sin(2\beta)\cos(\alpha)[/tex]

[tex]$\sin(\alpha + 2\beta)=\frac{\sqrt{2}}{10}\cdot \frac{24}{25} +\frac{3}{5} \cdot \frac{7\sqrt{2} }{10} = \frac{129\sqrt{2}}{250}$[/tex]

But we are not done yet! You want

[tex]\alpha + 2\beta[/tex] and not [tex]\sin(\alpha + 2\beta)[/tex]

You actually want the

[tex]$\arcsin\left(\frac{129\sqrt{2}}{250}\right)\approx 0.8179$[/tex]

Answer:

ok bye guy................

Answer:

Total number of fruits remaining =  25

Step-by-step explanation:

Let the number of

apples = 4x

bananas = 5x

Therefore

4x-2 / 5x = 2 / 3

Solve for x, cross multiply

3(4x-2) = 2(5x)

12x - 6 = 10 x

2x = 6

x = 3

Apples = 4*3 = 12

Bananas = 5*3 = 15

Apples remaining = 12-2 = 10

Total number of fruits remaining = 10+15 = 25

Answer:

[tex]\boxed{25 \ fruits}[/tex]

Step-by-step explanation:

Let apples be 4x and Bananas be 5x

So, the given condition is:

[tex]\frac{4x-2}{5x} = \frac{2}{3}[/tex]

Cross Multiplying

5x*2 = 3(4x-2)

10x = 12x - 6

Adding 6 to both sides

10x+6 = 12x

12x - 10x = 6

2x = 6

x = 3

Now, Fruits remaining in the bowl are:

=> 4x-2 + 5x

=> 12 - 2 + 15

=> 10+15

=> 25

Answer:

We reject the students claim because the P-value is less than the significance level.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = 25,235

Alternative hypothesis;Ha; μ > 25,235

Now, let's find the test statistic. Formula is;

t = (x' - μ)/(σ/√n)

We are given;

x' = 27,524

μ = 25,235

σ = 6000

n = 100

Thus;

t = (27524 - 25235)/(6000/√100)

t = 2289/600

t = 3.815

So from online p-value calculator as attached, using t=3.815, DF = 100-1 = 99 and significance level of 0.05, the P-value is gotten as p = 0.000237.

The p-value is less than the significance level of 0.05. Thus,we reject the students claim.

Answer: 2 minutes

Step-by-step explanation:

Given the following :

Plane A's descent :

y = -2,500x + 14,000

Plane B's Ascent :

y = 4,000x + 1,000

where y = altitude x = minute

Time to be at the same altitude :

Being at the same altitude means ;

Plane A's descent = Plane B's Ascent

-2,500x + 14,000 = 4,000x + 1,000

-2500x - 4000x = 1000 - 14000

-6500x = - 13000

x = 13000 / 6500

x = 2

x = 2minutes.

Do you know the adjustments for the graph to show the intersecting lines.

Answer:

           [tex]\bold{a=5\,,\quad b=-4\frac27}[/tex]

Step-by-step explanation:

[tex]5+\frac{2\sqrt3}7+4\sqrt3=5+\frac27\sqrt3+4\sqrt3=5+4\frac27\sqrt3=5-(-4\frac27)\sqrt3[/tex]

Answer:

x=60 degrees

Step-by-step explanation:

Formula for angle at x=1/2(240-120)

x=60

Answer:

x = 1

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] : [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{4}[/tex] : x

Multiply all parts by 12 to clear the fractions

6 : 8 = 9 : 12x , simplifying

3 : 4 = 3 : 4x

Thus

4x = 4 ( divide both sides by 4 )

x = 1

Answer:

True

Step-by-step explanation:

Real Numbers are just numbers like:

1 12.38 −0.8625  34  π (pi) 198

In fact:

Nearly any number you can think of is a Real Number

Real Numbers include:

yes   Whole Numbers (like 0, 1, 2, 3, 4, etc)

yes   Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc )

yes   Irrational Numbers (like π, √2, etc )

Real Numbers can also be positive, negative or zero.

So ... what is NOT a Real Number?

not   Imaginary Numbers like √−1 (the square root of minus 1)

are not Real Numbers

not   Infinity is not a Real Number

Mathematicians also play with some special numbers that aren't Real Numbers.

Real numbers can be represented on a number line.

Answer:

son

Step-by-step explanation:

son-sin

Answer: The depth is 12m

Step-by-step explanation:

The area is 350m^2

And the depth in each point of the base is at the same depth D.

Then we have a cuboid.

Now, the volume of a cuboid is equal to:

V= L*W*D

L = lenght, W = width and D = depth.

Such that L*W = area = 350m^2

then we have:

V = D*350m^2

Now we want V = 4200m^3

4200m^3 = D*350m^2

D = (4200/350) m = 12m

The depth is 12m

Answer:

D. RO

Step-by-step explanation:

Answer:

The center is ( 1,-3) and the radius is 3

Step-by-step explanation:

The equation of a circle can be written in the form

( x-h)^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius

(x-1)^2 + (y+3)^2= 9

(x-1)^2 + (- -3)^2= 3^2

The center is ( 1,-3) and the radius is 3

Answer:

3x + 2y = 12.

Step-by-step explanation:

Two conspicuous points on the graph are at (0, 6), and (4, 0).

That means the slope of the line is (6 - 0) / (0 - 4) = 6 / -4 = -3 / 2.

The intercept of the line is at (0, 6).

This means that the equation of the line is y = -3/2x + 6.

y = -3/2x + 6

Add 3/2x to both sides

3/2x + y = 6

Multiply all terms by 2

3x + 2y = 12

Hope this helps!

Answer:

324π in²

Step-by-step explanation:

The surface area of a sphere = 4πr² ( r is the radius )

Calculate r using the volume (V) formula

V = [tex]\frac{4}{3}[/tex]πr³

Here V = 972π , thus

[tex]\frac{4}{3}[/tex]πr³ = 972π ( divide both sides by π )

[tex]\frac{4}{3}[/tex]r³ = 972 ( multiply both sides by 3 to clear the fraction )

4r³ = 2916 ( divide both sides by 4 )

r³ = 729 ( take the cube root of both sides )

r = [tex]\sqrt[3]{729}[/tex] = 9

Thus

surface area = 4π × 9² = 4π × 81 = 324π in²

Answer:

$24

Step-by-step explanation:

Inversely proportional means that the two variables (price and weight in this case) will always have the same product. Therefore, we can write the following equation:

25 * x = 20 * 30 (where x is the price of a 25 oz. racquet)

25x = 600

x = $24

Answer:

C

Step-by-step explanation:

In a function, each domain has one range. But a range can have many domains.

Think about it like this:

Patty is eating dinner

Patty is swimming

Both can't happen at the same time.

But:

Patty is eating dinner

Leo is eating dinner

C has two domains of -3, each having different ranges.

Hope that helps, tell me if you need further info. =)

Answer:

C. C{(6,-9),(-3,6),(-3,-7),(-9, -2)}

Step-by-step explanation:

If you see the same x-coordinate used more than once, it is not a function.

Here, you only see this in choice C, where x = -3 for two points. That makes this relation not a function.

Answer: (–9, 9)

Step-by-step explanation:

if the original point (x,y) gets dilated by a scale factor 'k' with a center of dilation at the origin, then

The coordinates of the image point are (kx, ky).

Given: The coordinates of  line segment A B are A(-6,8) and B(-3,3).

then , the coordinates of B after dilation by scale factor of 3 with a center of dilation at the origin,

[tex](-3,3)\to(3(-3),3(3))\\\\\Rightarrow\ (-3,3)\to(-9,9)[/tex]

Hence, the coordinates of the image of point B, after the segment has been dilated by a scale factor of 3 with a center of dilation at the origin = (–9, 9).

Answer:option A.

Step-by-step explanation: because the point B is dialated and that’s where you will find you answer and edge cumulitive exam 2020.

Answer:

126 cm³

Step-by-step explanation:

The volume (V) of the prism is calculated as

V = Al ( A is the cross sectional area and l the length ), thus

V = 21 × 6

   = 126 cm³

Answer:

OPtion B)

Step-by-step explanation:

Answer: Choice C)

y < (-1/5)x + 1

The boundary line is y = (-1/5)x+1 as it goes through the points shown. The boundary line is dashed or dotted, meaning that points on this boundary line are not in the solution set. So we will not have an "or equal to" as part of the inequality sign. More specifically, the inequality sign is "less than" because we shade below the boundary line. So that's how we end up with y < (-1/5)x+1.

Answer:

(x+2.4)^2+(y+4.8)^2=2025

If you'd like additional help with math or another subject, check out growthinyouth.org!

Step-by-step explanation:

Answer: y = 2x+1

Step-by-step explanation:

It is the only line with (1,3) as a solution.  A slower algebraic way to solve this would be to plug in 1 for x and 3 for y, then, out of the equations in which it works, plug in -2 for x and -3 for y.  The equation that remains true for both points is the answer.

Hope it helps <3

Answer:

[tex]\boxed{y = 2x + 1}[/tex]

Step-by-step explanation:

The line passes through (1, 3).

The solution of the line is the points it crosses.

x = 1

y = 3

Plug x as 1 and y as 3 in the equation.

y = -2x + 1

3 = -2(1) + 1

3 = -2 + 1

3 = -1 False

Plug x as 1 and y as 3 in the equation.

y = 2x + 1

3 = 2(1) + 1

3 = 2 + 1

3 = 3 True

Plug x as 1 and y as 3 in the equation.

y = x - 1

3 = 1 - 1

3 = 0 False

Plug x as 1 and y as 3 in the equation.

y = -x + 1

3 = -(1) + 1

3 = -1 + 1

3 = 0 False

Answer:

Based on the function, the growth rate is 4.5%

Step-by-step explanation:

In this question, we are given the exponential equation and we are told to deduce the growth rate.

Mathematically, we can rewrite the exponential equation as follows;

S(t) = 152(1.045)^t = 152(1 + 0.045)^t

What we see here is that we have successfully split the 1.045 to 1 + 0.045

Now, that value of 0.045 represents the growth rate.

This growth rate can be properly expressed if we make the fraction given as a percentage.

Thus the issue here is converting 0.045 to percentage

Mathematically, that would be;

0.045 = 4.5/100

This makes is 4.5%

So the growth rate we are looking for is 4.5%

Answer:

after 2 seconds

Step-by-step explanation:

Given

h(x) = - x² + 4x + 12

The ball will reach its maximum at the vertex of the parabola

Find the zeros by letting h(x) = 0, that is

- x² + 4x + 12 = 0 ← multiply through by - 1

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

The x- coordinate of the vertex is at the midpoint of the zeros, thus

[tex]x_{vertex}[/tex] = [tex]\frac{-2+6}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Substitute x = 2 into h(x)

h(2) = - 2² + 4(2) + 12 = - 4 + 8 + 12 = 16

The cannonball reaches its maximum height of 16 ft after 2 seconds

Answer:

2 seconds

Step-by-step explanation:

I just did it just trust me. This isn't reated to the answer but I had spagehtti for lunch

Answer:

Rs. 924000.

Step-by-step explanation:

Cost of  house = 765000

Additional money spent on it = 115000

Total cost incurred by Ravi = 765000 + 115000 = 880000

Gain  = 5% of total cost

gain in Rs = 5/100 * 880000 = Rs. 44000

Total selling price of house = total cost incurred + profit = 880000+ 44000

Total selling price of house = Rs. 924000

Thus, Ravi got  Rs. 924000.

Answer:

Sister is 70

Step-by-step explanation:

John is 39.

8 less than twice his age is

39*2-8 = 70

Answer:

70 years old.

Step-by-step explanation:

Since John's sister is 8 years younger than TWICE his age, we just need to multiply 39*2 which equals 78. Now we just need to subtract 8 which equals 70.

Hope this helps!! <3