The count in a bacteria culture was 300 after 10 minutes and 1400 after 40 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?

Let's denote Molly's age as "M" and her father James' age as "J". We know that James is currently 33 years old (J = 33) and his age is three times Molly's age minus three years (J = 3M - 3).We need to find how many years from now (let's call this "Y") will James' age be twice Molly's age. In other words, in Y years, James will be 2 times older than Molly (J + Y = 2(M + Y)).

Now let's solve the problem step by step:

1. We know that J = 33 and J = 3M - 3. So, we can write the equation as: 33 = 3M - 3.
2. Add 3 to both sides: 36 = 3M.
3. Divide both sides by 3: M = 12. So, Molly is currently 12 years old.

Next, we need to find Y:

1. We know that J + Y = 2(M + Y). Substitute J and M with their values: 33 + Y = 2(12 + Y).
2. Simplify the equation: 33 + Y = 24 + 2Y.
3. Subtract Y from both sides: 33 = 24 + Y.
4. Subtract 24 from both sides: Y = 9.

So, in 9 years from now, James will be twice Molly's age.

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Answer:

200g

Step-by-step explanation:

24x2=48

100x2=200

Answer:

0.000 003m express in significant notation

Answer:

6

Step-by-step explanation:

3/4=6/8

1/8x=6/8

x=6

The probability that a randomly selected square foot of merino wool will contain more than one defect is approximately 0.5034.

The average number of defects in a square foot of merino wool is given as 0.7. Since the number of defects follows a Poisson distribution, we can use the Poisson probability formula to calculate the probability of having more than one defect.

The Poisson probability formula is given as:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where x is the number of defects, and λ is the average number of defects in the given unit (in this case, square foot).

To find the probability of having more than one defect, we can sum the probabilities for x = 2, 3, 4, and so on, up to infinity. However, since the Poisson distribution is infinite, we can approximate the probability by subtracting the probability of having at most one defect from 1.

Let's calculate it step by step:

P(0 or 1 defect) = P(0 defects) + P(1 defect)

= (e^(-0.7) * 0.7^0) / 0! + (e^(-0.7) * 0.7^1) / 1!

= e^(-0.7) + 0.7 * e^(-0.7)

≈ 0.4966

P(more than one defect) = 1 - P(0 or 1 defect)

≈ 1 - 0.4966

≈ 0.5034

Therefore, the probability that a randomly selected square foot of merino wool will contain more than one defect is approximately 0.5034.

The probability that a randomly selected square foot of merino wool will contain more than one defect is approximately 0.5034.

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The proportion of the variability in weight that can be explained by it's relationship with height is: 16% (Option C)

It is to be noted that the Coefficient of determination of r is the square of r value.

Hence,

R² = 0.4²

= 0.16 or 16%

The proportion of the variability in weight is option (C) 16%.

Note that the easiest technique to quantify the proportion of variation in an analysis of variance is to divide the sum of squares between groups by the sum of squares total.

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Full Question:

Suppose the correlation between height and weight for adults is r = 0.40. What proportion (or percent) of the variability in weight can be explained by the relationship with height?

A. 40%

B. 36%

C. 16%

D. 60%

E. None of the above.

x= 48

P/s: sorry. I cant explain  

ok done.thank to me :>

Answer:

The formula for solving surface area is LxWxH (LengthxWidthxHeight)

And the formula for solving area is LxW (LenghtxWidth)

Step-by-step explanation:

I hope this helps. I didnt really see any pictures for this.

Answer: 1. 60 square centimeters and the volume was 24 cm3

2. Yes, because if you have length, width and height, that's really all the information you need to find out the area, volume, perimeter, surface area, ect!

Step-by-step explanation: Hope this helps! :)

(I had the same question btw)

Step-by-step explanation:

Hope this is correct

HAVE A GOOD DAY!

Answer:

Graph the line  

y = 2 x − 4

After you have plotted the line, shade in the area to right of the line.

To help you to graph the line, two points are  

( 0 , − 4 )  and  ( 2, 0 )

Remember to make it a dashed line to indicate that it is not included.

Here is a how it should look:

Answer:

To solve this problem, we need to know the value of x, the price per meter of cloth. Let's assume that x is given in naira. Then, the cost of 5 meters of cloth is:

5m * x naira/m = 5x naira

To find the change from 7000 naira after buying the cloth, we need to subtract the cost of the cloth from 7000 naira:

Change = 7000 naira - 5x naira

We can't find a specific answer without knowing the value of x. But, if we assume that x = 1000 naira/m, then the cost of 5 meters of cloth would be:

5m * 1000 naira/m = 5000 naira

Then, the change from 7000 naira would be:

Change = 7000 naira - 5000 naira = 2000 naira

Therefore, if the price per meter of cloth is 1000 naira, then the change from 7000 naira would be 2000 naira. However, if the actual value of x is different, then the answer would be different as well.

Step-by-step explanation:

Answer:

Each piece is 9 inches

Step-by-step explanation:

3 ft = 36 inches

36 inches / 4 equal-length pieces = 9 inches per piece

Answer:

the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.

Step-by-step explanation:

An angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The angle is measured in a counterclockwise direction from the positive x-axis and is considered positive if it lies in the counterclockwise direction and negative if it lies in the clockwise direction.

The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located. An angle in a rectangular coordinate system is in a standard position if its vertex is at the origin of the plane. An angle is said to be in a standard position if its vertex is located at the origin of the coordinate system.

To summarize, an angle in a rectangular coordinate system is in standard position if its vertex is at the origin of the plane, the initial side of the angle is on the positive x-axis, and the terminal side of the angle is in one of the four quadrants. The position of an angle is measured from the reference line called the initial side, which is the positive x-axis, and it ends at the terminal side, which is the side where the angle is located.

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inferential statistics allows for someone to draw conclusions about a population from the information collected in a population sample.

the qestion is incomplete .please read below to find the missing content

Which of the following allows for someone to draw conclusions about a population from the information collected in a population sample?

a. magnitude statistics

b. central tendency

c. inferential statistics

d. effect size

The population is the number of people living together in a place. The population of a city is the number of people living in that city. These people are called residents or residents. The population includes all individuals living in that particular area.

Population refers to the total number of organisms living in a particular area. Population helps us estimate the number of beings and know how to act accordingly. For example, knowing the exact population of a city allows us to estimate the number of resources required. Similarly, animals can do the same.

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Answer:

5.75 ft

Step-by-step explanation:

12 in = 1 ft

⇒ 9 in = 9/12 = 0.75 ft

⇒ 5 ft 9 in = 5 + 0.75 = 5.75 ft

Answer:

(-3,-5)

Step-by-step explanation:

mark me brainliest!!

Answer:

I believe its proposition

Step-by-step explanation:

im almost 100% sure

The area of the shaded sector of the circle is 16π units².

Suppose the circle has radius of 'r' units, then, its area is given as:

\(A = \pi \times r^2\)

sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

\(\pi \times (\dfrac{d}{2})^2\)

sq. units

We are given that;

θ = r radians

r = 4 units

Now,

To convert radians to degrees, we use the formula:

Degrees = Radians × 180°/π

So,

θ = r × 180°/π

Substituting these values in the formula for area of a sector, we get:

Area of a sector = (r × 180°/π / 360°) × π(4)²

Simplifying, we get:

Area of a sector = r² units²

=16π units².

Therefore, by the area of a circle the answer will be 16π units².

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To find all values of x where the tangent lines to y = x and y = x are parallel, we need to find the values of x for which the slopes of the two lines are equal.

The slope of the tangent line to y = x is simply 1,

since the derivative of y = x with respect to x is 1.

Let's differentiate y = x with respect to x using the power rule:

d/dx(x) = 1

Now, let's compute the derivative of dR(³.R²) with respect to R.

We'll use the power rule again:

d/dR(R³.R²) = 3R² * 2R = 6R³

Therefore, the derivative of dR(³.R²) with respect to R is 6R³.

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The equation of the trajectory which can be described using the equations for projectile motion is; y(t) = x·tan(θ) - g·x²/(2·v₀²·cos²(θ)), which is a quadratic equation with a path of a parabola

Projectile motion is the motion of an object that is projected in the air under the influence of gravitational attraction.

Let θ represent the angle at which the path of the object makes with the horizontal, and let v₀ represent the velocity of the object. The path of the object can be described using the equations of the motion of a projectile, as follows;

Horizontal component of the velocity, v₀ₓ = v₀ × cos(θ)

Vertical component of the velocity, \(v_{0y}\) = v₀ × sin(θ)

The horizontal motion of the object is therefore;

x(t) = v₀ₓ × t = v₀ × cos(θ) × t

The vertical motion which is under the influence of gravity is; y(t) = \(v_{0y}\)  × t - (1/2) × g × t²

v₀ × sin(θ) × t - (1/2) × g × t²

The horizontal component indicates that we get;

t = x/(v₀ × cos(θ))

Plugging in the above expression for t into the equation for y(t), we get;

y(t) = \(v_{0y}\)  × t - (1/2) × g × t² = \(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

\(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = (v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

(v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = x·tan(θ) - g·x²/(2·v₀×cos(θ))²

The equation, y = x·tan(θ) - g·x²/(2·v₀×cos(θ))², is a quadratic equation, which is an equation of a parabola, therefore, the trajectory of an object thrown at an angle to the horizontal is a parabola.

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The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , \(\frac{h}{s}\).

=> \(\frac{3.8}{1.3} = \frac{h}{4.5}\)

=> h = \(\frac{3.8*4.5}{1.3}\)

=> 13.2 m.

Hence the height of the tree is 13.2 m.

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Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer: First option and Third option.

Step-by-step explanation:

Where "r" is the radius of the circle.

As you look in the formula, the area of the circle depends on the square of the radius.

Now you have to observe the picture that is attached.

If you look you can identify that the radius of the circle is the following:

Knowing the radius, you need to substitute it into the formula given above:Finally, you must evaluate in order to calculate the area of that circle. You get that this is:

The First and Third answer

Hope this helpe :)

The resulting formulas after the first three iterations are: Iteration 1: p ∧ (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r), Iteration 2: (True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r), Iteration 3: (True ∨ True) ∧ (True ∨ r) ∧ (q ∨ ¬r)

Applying unit propagation on the given formula with an empty set of literals, the resulting formulas after the first three iterations are:

Iteration 1: p ∧ (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

Since there are no assigned literals yet, no unit clauses are present. No changes occur in this iteration.

Iteration 2: (¬p ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

In this iteration, the literal 'p' is assigned the value true to satisfy the unit clause 'p'.

The formula becomes:

(True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

Iteration 3: (True ∨ ¬q) ∧ (¬q ∨ r) ∧ (q ∨ ¬r)

In this iteration, the literal '¬q' is assigned the value true to satisfy the unit clause '¬q'.

The formula becomes:

(True ∨ True) ∧ (True ∨ r) ∧ (q ∨ ¬r)

Unit propagation is a process in propositional logic where unit clauses, which are clauses containing only one unassigned literal, are identified and assigned a truth value to satisfy them.

The process continues iteratively until no more unit clauses remain.

In the given formula, the first iteration does not result in any changes since there are no unit clauses present.

In the second iteration, the unit clause 'p' is identified, and we assign it the value true. This assignment satisfies the unit clause, and the formula is modified accordingly.

In the third iteration, the unit clause '¬q' is identified, and we assign it the value true. This assignment satisfies the unit clause, and the formula is modified again.

It is important to note that the given formula is not yet in its simplified or final form, as there may be further iterations of unit propagation or other simplification rules to apply.

The process of unit propagation continues until no more unit clauses can be satisfied.

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Answer:

Richel could earn $ 85 if she works 10 hours

Step-by-step explanation:

As given

Richel earns in 4 hours = $34

By unitary method

Richel earns in 1 hour =  34/4

Richel earns in 10 hours=   34/4 x 10 =340/4 = 85$

Hence, Richel could earn $ 85

Answer:

Given below!!!

I hope im righ!!!

To show that w = u × v and v = w × u, we need to demonstrate that the cross product of vectors u and v yields the same result as the cross product of vectors w and u.

Given that u = v × w, let's calculate the cross product of w and u:

w × u = (u × v) × u

Since the cross product is not associative, we need to use the vector triple product identity:

w × u = u × (v × u) - (u · u) v

Since u is orthogonal to v, the dot product (u · v) is zero. Therefore, we can simplify the equation:

w × u = u × (v × u)

Next, let's calculate the cross product of v and u:

v × u = (u × v) × v

Using the vector triple product identity:

v × u = v × (u × v) + (v · v) u

Again, since u is orthogonal to v, the dot product (v · v) is zero:

v × u = v × (u × v)

Thus, we have shown that w = u × v and v = w × u, indicating that the cross products are equivalent in both directions.

In summary, when u, v, and w are orthogonal unit vectors, the cross product of u and v yields the same result as the cross product of w and u, as well as the cross product of v and w.

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