Find the surface of the square pyramid shown below

Answer:

[Tex]A(t)=5000(0.7)^t[/tex]

Step-by-step explanation:

The problem presented is one in which the population of the bacteria  depreciates by a decay factor r every year.

Since it is a decay problem, we use the model:

[Tex]A(t)=P(1-r)^t[/tex]

Initial Population, P=5000

Decay Rate,r=30%=0.3

t=time interval

Therefore, the equation that represents this situation is:

[Tex]A(t)=5000(1-0.3)^t[/tex]

[Tex]A(t)=5000(0.7)^t[/tex]

The equation that represents this situation is y = 5000(0.7)ˣ

An exponential decay is given by:

y = abˣ

where a is the initial value of y, b is the rate of decay and y, x are variables.

Since the culture begins with 5000 cells, hence a = 5000. The cells die by 30% each year, hence b = 100% - 30% = 0.7

The equation is: y = 5000(0.7)ˣ

Therefore the equation that represents this situation is y = 5000(0.7)ˣ

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Answer:

it's 90%

Step-by-step explanation:

1. Divide 18 by 20 and you will get a decimal form answer

2. Then you multiple it by 100 and you will get your answer which is 90.00%

18 out of 20 is 90 percent.

To find the percentage of 18 out of 20, you can follow these steps:

1. Divide the given number (18) by the total number (20).

18 ÷ 20 = 0.9

2. Multiply the result by 100 to get the percentage.

0.9 × 100 = 90

Therefore, 18 out of 20 is 90 percent.

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If the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that,

Previous Balance=$568.23

Interest=$2.37

Deposits=$562.32

Withdrawals=$874.36

We have to apply the addition and subtraction operations in order to find the new balance.

New balance = Previous Balance+Interest+Deposits-Withdrawals

New balance = $568.23+$2.37+$562.32-$874.36

New balance =$258.56

Thus, if the previous balance, Interest, deposits withdrawals and are $568,$2.37, and $562.32.His new balance is $258.56.

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Answer:

Step-by-step explanation:

To calculate the interest paid by ethan on the borrowed bike using the formula.

Simple Interest = Principal * rate * time/100

Principal =  $2,190, rate = 2.5%, time = 3years

On substitution

SI = [tex]\frac{2190*3*2.5}{100}[/tex]

[tex]SI = \frac{16,425}{100}\\ SI= $164.25[/tex]

The interest ethan will pay is $164.25

Ethan will pay $164.25 in interest for the loan he took for a new dirt bike, calculated using the formula for simple interest (I = PRT) with P as the principal ($2,190), R as the rate (2.5% or 0.025), and T as the time (3 years).

To calculate simple interest, you can use the following formula: I = PRT, where I is the Interest, P is the principal amount (original amount borrowed), R is the interest rate (in decimal form), and T is the time in years. In this case, the principal amount is $2,190, the interest rate is 2.5% or 0.025 as a decimal, and the time is 3 years.

You would then plug these values into the formula to get:

I = 2190 * 0.025 * 3

After calculating that, we would find that Ethan will pay $164.25 in interest.

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Answer:

its 5760ins

Step-by-step explanation:

80 inches * 36 inches * 2 inches = 5760 inches3

good day, and be safe

∵∴∵∴∵∴∵∴∵      

⊕ΘΞΠΤ⊕      

∵∴∵∴∵∴∵∴∵

Answer:

[tex](x-2)^2[/tex]

Step-by-step explanation:

To find the inverse of this function, you need to replace the location of the x and the y.

You start with [tex]y=\sqrt{x}+2[/tex]. Now, replace the x and the y, and try to isolate the y.

[tex]x=\sqrt{y}+2\\x-2=\sqrt{y}\\y=(x-2)^2[/tex]

Hope this helps!

Answer:

0.72

Step-by-step explanation:

[tex] \cos \: 44 \degree = 0.7193398003 \\ \cos \: 44 \degree =0.72[/tex]

Answer:

3n - 6 = 38

3n -6 + 6 = 38 + 6

3n = 44

3n/3 = 44/3

n = 44/3

Step-by-step explanation:

1. set up the equation (the - affect the 6 not the 3)

2. add 6 to both sides

3. divide both sides by 3 to get n

Answer: [tex]9x^2-x+4[/tex]

Combine Like Terms

[tex]3x^2+-x+7+6x^2+-3\\(3x^2+6x^2)+(-x)+(7+-3)\\9x^2+-x+4[/tex]

Answer:

42 - 24n

Step-by-step explanation:

(7-4n)  6

Distribute

7*6 - 4n*6

42 - 24n

Answer:

42 x - 24 x n - i = 0

Step-by-step explanation:

Expand the following:

6 x (7 - 4 n) = i

6 x (7 - 4 n) = 6 x×7 + 6 x (-4 n):

6×7 x - 4×6 x n = i

6×7 = 42:

42 x - 4×6 x n = i

6 (-4) = -24:

42 x + -24 x n = i

Subtract i from both sides of 42 x - 24 x n = i:

42 x - 24 x n - i = i - i

-i + i = 0:

Answer:  42 x - 24 x n - i = 0

Vertex of the angle is 11.31 cm far from the center of the circle.

     Given in the question,

In ΔOPV and ΔOQV,

OP ≅ OQ (Radii of the circle)

PV ≅ QV (Tangents from a point outside the circle)

OV ≅ OV (Reflexive property)

ΔOPV ≅ ΔOQV (SSS property of congruence)

Therefore, m∠PVO = m∠QVO = 45°

By triangle sum theorem,

m∠POV + m∠PVO + m∠OPV = 180°

m∠POV + 45° + 90° = 180°

m∠POV = 45°

Hence, ΔOPV is an isosceles triangle.

OP = PV = 8 cm

By applying Pythagoras theorem in ΔOPV.

OV² = OP² + PV²

OV² = 8² + 8²

OV = √128

OV = 11.31 cm

   Therefore, vertex V is 11.31 cm from the center of the circle.

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The distance from the vertex of the angle to the center of the circle is 0 centimeters.

In this problem, we have two tangents to a circle, and we are given that the angle between them is 90 degrees. We need to find the distance from the vertex of the angle to the center of the circle.

Since the angle between the tangents is 90 degrees, the tangents are perpendicular to each other. This means that the vertex of the angle is located on the circumference of the circle, and it forms a right triangle with the center of the circle and one of the points where the tangents intersect the circle.

Using the Pythagorean theorem, we can find the distance from the vertex to the center of the circle. Let's call this distance x. We know that the radius of the circle is 8 centimeters, so one leg of the right triangle is 8 centimeters. The other leg is x centimeters, and the hypotenuse is the radius of the circle plus x centimeters.

Applying the Pythagorean theorem, we have:

x^2 + 8^2 = (8 + x)^2

Simplifying the equation, we get:

x^2 + 64 = 64 + 16x + x^2

Cancelling out x^2 terms, we have:

64 = 64 + 16x

Subtracting 64 from both sides, we get:

0 = 16x

Dividing both sides by 16, we get:

x = 0

Since we cannot have a distance of 0, the equation does not have a solution. This means that the vertex of the angle is located at the center of the circle, and the distance is 0 centimeters.

Answer:

This question says:

"the lenghts of the sides and the diagonal of a rectangle are 3 odd consecutive numbers".

This means that if x is an odd number, then the meassures are:

x, x + 2, x + 4.

We add 2 in each case, because the next consecutive number of, for example, 3 is 3 + 2 = 5, and so on.

Now, from the Pitagoras theorem we know that, for a triangle rectangle, we have

A^2 + B^2 = H^2

where A and B are the cathetus, and H is the hypotenuse.

In our case the smaller odd numbers will be the cathetus and the larger one will be the hypotenuse.

x^2 + (x + 2)^2 = (x + 4)^2

x^2 + x^2 + 4x + 4 = x^2 + 8x + 16

x^2 - 4x -12 = 0

now we need to solve this for x

we know that for a quadratic equation of the form:

ax^2 + bx + c = 0

the solutions are:

[tex]x = \frac{-b +- \sqrt{b^2 -4ac} }{2a}[/tex]

in our case we have:

[tex]x = \frac{4 +- \sqrt{16 +48} }{2} = \frac{4+-8}{2}[/tex]

The only positive value is x = 12/2 = 6

but 6 is not odd, so we can never have that the sides and the diagonal are odd consecutive numbers.

Answer:

170 degrees

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary, meaning that they add up to 180 degrees. This means that x+10=180, or that x=170 degrees. Hope this helps!

Answer:

cannibalism

Step-by-step explanation:

The inverse of the function f(x) = 1/5x is found by switching the roles of y and x, then solving for y. This results in the inverse function f^-1(x) = 5x, which undoes the effect of the original function.

The inverse of a function, in this case f(x) = 1/5x, is the function that will reverse the effect of the original function. In this case, to find the inverse function of f(x), you swap the roles of y and x in the original function and solve for y.

So, f(x) = 1/5x becomes x = 1/5y. Multiply both sides by 5 to get rid of the denominator on the y-side, which results in 5x = y. Thus, the inverse function is f^-1(x) = 5x.

It's indeed an inverse function as it reverses the effect of the initial function f(x).

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Answer:

1/12

Step-by-step explanation:

If the Captain hits the pirate ship, it won't affect whether she's also hit by the pirate's cannons (and vice-versa), because they both fired at the same time. So, these events are independent.

Since they are independent, in order to get the probability that both the pirate and the Captain hit each other's ships, we just need to multiply together the probability that the captain hits and the probability that the pirate hits.

The probability that the Captain hits is 1/2

The probability that the pirate hits is 1/6

So, the probability that both the pirate and the Captain hit each other's ships is 1/2 * 1/6 = 1/12

Final answer:

The probability that Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%, calculated by multiplying the individual probabilities of each hitting the other's ship (0.5 for Captain Jessica and approximately 0.167 for the pirate).

Explanation:

To calculate the probability that both Captain Jessica and the pirate Michael hit each other's ships when they fire their cannons at the same time, we must consider each event independently and then multiply the probabilities of the two events since they are independent. Le'ts calculate the combined probability step-by-step.

First, we know that Captain Jessica has a probability of hitting the pirate ship which is ½ or 0.5.

Second, the dread pirate Michael has a probability of hitting the Captain's ship which is ⅙ or approximately 0.167 (1 divided by 6).

Since these are independent events, we multiply the two probabilities to find the combined probability of both events occurring together: 0.5 * 0.167 = 0.0835.

Therefore, the probability that both Captain Jessica and the pirate Michael hit each other's ships simultaneously is 0.0835 or 8.35%.

Answer: 10 + 1/2 spoons of vanilla.

Step-by-step explanation:

This question says:

For 1kg of cake, we need 1/3 kg of flour and 3 spoons of vanilla.

How much vanilla do we need if we want to make a cake of 3 + 1/2 kg?

Ok, if for 1kg we need 3 spoons, then for (3 + 1/2)kg we need (3 + 1/2) times 3 spoons, this is:

(3 + 1/2)*3 spoons

=3*3 + 3/2 = 9 + 3/2 = 9 + 2/2 + 1/2 = 10 + 1/2

We need 10 + 1/2 spoons of vanilla.

Answer:

V = 24 mi^3

Step-by-step explanation:

The volume is given by

V = l*w*h

V = 4*3*2

V = 24 mi^3

Answer: 0%

Step-by-step explanation:

if you toss a coin 4 times you cant get 5 results.

Answer:

i am very sorry but i am trying to solve it so wait a few minutes please

Step-by-step explanation:

Answer: D

x+3/x-3

Step-by-step explanation:

Answer:

[tex]13.65^0.[/tex]

Step-by-step explanation:

Given,

Height of tee, H = 43 yard

Direct distance of the hole is, D = 177 yards

Now, Angle of depression of tee

[tex]\tan \theta = \dfrac{H}{D}[/tex]

[tex]\tan \theta = \dfrac{43}{177}[/tex]

[tex]\tan \theta =0.2429[/tex]

[tex]\theta = 13.65^\circ[/tex]

Hence, angle of depression from tee to the green is [tex]13.65^0.[/tex]

Answer:

3x would equal 18 is x was 6

Step-by-step explanation:

x=6

3*6=18

3x would equal 18

Answer: the answer is 12

Answer:

the area of the circle is [tex]2.25\pi\ cm^2[/tex].

Step-by-step explanation:

We have,

Circumference of a circle is 3π cm

Formula of circumference of a circle is given by :

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

r is radius of circle

[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{3\pi }{2\pi}\\\\r=1.5\ cm[/tex]

Area of a circle is given by :

[tex]A=\pi r^2\\\\A=\pi (1.5)^2\\\\A=2.25\pi\ cm^2[/tex]

So, the area of the circle is [tex]2.25\pi\ cm^2[/tex].

Tara starts with $20, in which she buys 2 items for d amount. Subtract 2d from the total for your answer.

1) 20 - 2d

To find the average distance, add all the numbers together, and divide by the amount of numbers there are:

3) (t + w)/2

~

Answer:

Ladder reaches 9.76 high.

Step-by-step explanation:

From the figure attached,

Ac is the ladder which reaches at the point A when leans against the side of a house.

Length of the ladder = 10 feet

Distance of the ladder form the base of a house = 2.2 ft

By Pythagoras theorem,

AC² = AB² + BC²

(10)² = h² + (2.2)²

h² = 100 - 4.84

h = √95.16

h = 9.755 feet

  ≈ 9.76 feet

Therefore, the ladder reaches the 9.76 high.

The answer is 9.7 feet

Answer:

If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex]   times the corresponding area of the  original drawing.

Step-by-step explanation:

If the scale factor is represented by , then the area of the scale drawing is [tex]k^{2}[/tex]   times the corresponding area of the  original drawing.

For example:

Given a scale factor of 25%, would the quotient of the area of the scale drawing to the area of the original  drawing be?

Answer:

The quotient of the areas would be equal to the square of the scale factor. Therefore, the quotient  of the scale drawing to the original in this example would be equal to [tex](\frac{1}{4}) ^{2}[/tex]

Hope it will find you well.

Answer:

34

8

Step-by-step explanation:

1/2bc - 6ac + 2ab

(1/2)(-1)(-3) - (6)(2)(-3) + (2)(2)(-1)

(1/2)(4) - (-36) + (-4)

2 + 36 - 4

34

1/4(ac)² + 1/6ac

(1/4)[(2)(-3)]² + (1/6)(2)(-3)

(1/4)(-6)² + (1/6)(-6)

(1/4)(36) + (-1)

9 - 1

8