A plant splits into 3 new plants each week. How many plants will you have after 4 weeks?

Answer:

D

Step-by-step explanation:

B and C aren't correct

Answer:

13

Step-by-step explanation:

AB = 5

AC = 10

BC = ~11

P = 11 + 10 + 5 = 26

26 / 2 = 13

c

because 7+2n

sum is addition

2n is multiplication

In a basket holding 35 pieces of fruit with an apple-to-orange ratio of 2:5, there are 10 apples.

To find the number of apples in the basket, we need to determine the ratio of apples to the total number of fruit pieces.

Given that the ratio of apples to oranges is 2:5, we can calculate the total number of parts in the ratio as 2 + 5 = 7.

To find the number of apples, we divide the total number of fruit pieces (35) by the total number of parts (7) and multiply it by the number of parts representing apples (2):

Apples = (2/7) * 35 = 10.

Therefore, there are 10 apples in the basket of 35 pieces of fruit.

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Answer:

An exponential function is a function of the form

f(x)=bx

where b≠1 is a positive real number. The domain of an exponential function is (−∞,∞) and the range is (0,∞).

Solve the equation: 52x−3=752x−3=7.

Since we can’t easily rewrite both sides as exponentials with the same base, we’ll use logarithms instead. Above we said that logb(x)=ylogb⁡(x)=y means that by=xby=x. That statement means that each exponential equation has an equivalent logarithmic form and vice-versa. We’ll convert to a logarithmic equation and solve from there.

52x−3log

⎛⎝⎜

⎞⎠⎟=7=2x−352x−3=7log5

⁡(7

)=2x−3

From here, we can solve for xx directly.

2xx=log5(7)+3=log5(7)+32

A logarithmic function is a function defined as follows

logb(x)=ymeans thatby=xlogb⁡(x)=ymeans thatby=x

where b≠1b≠1 is a positive real number. The domain of a logarithmic function is (0,∞)(0,∞) and the range is (−∞,∞)(−∞,∞).

Solve the equation:

log3(2x+1)=1−log3(x+2).log3⁡(2x+1)=1−log3⁡(x+2).

With more than one logarithm, we’ll typically try to use the properties of logarithms to combine them into a single term.

log3(2x+1)log3(2x+1)+log3(x+2)log3((2x+1)(x+2))log3(2x2+5x+2)2x2+5x+22x2+5x−1=1−log3(x+2)=1=1=1=3=0log3⁡(2x+1)=1−log3⁡(x+2)log3⁡(2x+1)+log3⁡(x+2)=1log3⁡((2x+1)(x+2))=1log3⁡(2x2+5x+2)=12x2+5x+2=32x2+5x−1=0

Let’s use quadratic formula to solve this.

x=−5±52−4⋅2⋅−1−−−−−−−−−−−√2⋅2=−5±

−−−−−−−−⎷4.x=−5±52−4⋅2⋅−12⋅2=−5±33

4.

What happens if we try to plug x=

Answer:

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

Step-by-step explanation:

Let us represent:

Number of pounds of cashews = x

Number of pounds of Brazil nuts = y

The nut shack sells cashews for $6.00 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 34 pound mixture that sells for $5.44 per pound

Our system of equations is given as:

x + y = 34...... Equation 1

x = 34 - y

6x + 5y = 34 × 5.44

6x + 5y = 184.96.......Equation 2

Ww substitute : 34 - y for x in Equation 2

6(34 - y) + 5y = 184.96

204 - 6y + 5y = 184.96

Collect like terms

- 6y + 5y = 184.96 - 204

-y = -19.04

y = 19.04 pounds

Solving for x

x = 34 - y

x = 34 - 19.04

x = 14.96 pounds

Number of pounds of cashews = x = 14.96 pounds

Number of pounds of Brazil nuts = y = 19.04 pounds

Answer:

21

Step-by-step explanation:

Based on the terms you provided, I can help you identify the true statement(s):

1. As the sample size n increases, the distribution of the sum of the observations approaches a normal distribution.
2. The sample mean varies from sample to sample.
3. If the underlying population is not normal, the Central Limit Theorem (CLT) states that the distribution of the sample mean X approaches a normal distribution as the sample size n increases.
These statements are true. Note that the statement "As the sample size n increases, the variance of the sample mean X also increases" is incorrect, as the variance of the sample mean actually decreases when the sample size increases. Additionally, the statement "The distribution of the mean X is never exactly normal" is not universally true, as the distribution of the mean can be exactly normal under specific circumstances.

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Answer:

Gene is incorrect.

Step-by-step explanation:

Let x represent the number.

We have been given that Gene stated that finding 25% of a number is the same as dividing the number by 1/4. We are asked to determine whether Gene is correct or not.

We know that percent means a quantity out of 100. We can represent 25% of x as:

We can further simply it as:

We can see that finding 25% of a number is equal to finding one-fourth of a number.

When we divide a number by 1/4, we will get:

Dividing a number by 1/4 will be 4 times the number, therefore, Gene is not correct.

Answer:

C. 1/4 lb of chicken per person

Step-by-step explanation:

Find the rate of change for the situation.

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

A. 9/17lb per person

B. 4 lb per person

C. 1/4 lb per person

D. 36 people

Solution

9 lbs of chicken for 36 people

Chicken per person = Total lbs of chicken / Total number of people

= 9 lbs / 36 people

Chicken per person = 1/4 lb of chicken per person

17 lbs of chicken for 68 people

Chicken per person = Total lbs of chicken / Total number of people

= 17 lbs / 68 people

= 1/4 lb of chicken

Chicken per person = 1/4 lb of chicken per person

Therefore, the rate of change of the situation = 1/4 lb of chicken per person

Answer:

  ECHA

Step-by-step explanation:

You want the slopes of four representations of linear functions.

The line rises 1 unit for each 2 to the right. Its slope is ...

  m = rise/run = 1/2 . . . letter E

The formula for the slope between two (x, y) pairs is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-8 -(-12))/(1 -(-1)) = 4/2 = 2 . . . letter C

  m = (-3 -(-6))/(-4 -2) = 3/-6 = -1/2 . . . letter H

The line rises -2 units for each 1 to the right. Its slope is ...

  m = -2/1 = -2 . . . letter A

The puzzle #4 solution is ECHA.

<95141404393>

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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The description of the solutions for the given equation is that it has either one solution or two identical solutions.

The given equation is:

32x - 4 = 4x² + 60

To find the description of the solutions, we can first rewrite the equation in standard form, which is a quadratic equation in the form of:

ax² + bx + c = 0

Let's rearrange the given equation to match the standard form:

4x² - 32x + 64 = 0

Now we can compare the coefficients of the standard form equation:

a = 4

b = -32

c = 64

To determine the description of the solutions, we can look at the discriminant (b² - 4ac) of the quadratic equation.

Discriminant = (-32)² - 4 × 4 × 64

= 1024 - 1024

= 0

Since the discriminant is equal to zero, this indicates that the quadratic equation has equal and real solutions.

In other words, the equation has one solution or two identical solutions.

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The rate of change of the function that has a graph that passes

through the points (-1, 3) and (-2,-4) is slope and is equal to 7.

We have given two points  (-1, 3) and (-2,-4) .

Rate of change of graph is given by slope

Using slope formula , we get

      m = -4 - 3 / -2 - (-1)

      m = -7 / -2 + 1

      m = -7 / -1

       m = 7

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The location at t=3 of the particle whose path satisfies r(t) = ⟨14−9t^2,2−4t⟩ and r(0) = ⟨10,5⟩ is ⟨-17, -7⟩.

To find the location at t=3 of a particle whose path satisfies r(t) = ⟨14−9t^2,2−4t⟩ and r(0) = ⟨10,5⟩, we can follow these steps:

Find the velocity vector v(t) by taking the derivative of r(t) with respect to t:

v(t) = dr/dt = ⟨-18t, -4⟩

Find the initial velocity vector v(0) by substituting t=0 into v(t):

v(0) = ⟨0, -4⟩

Find the acceleration vector a(t) by taking the derivative of v(t) with respect to t:

a(t) = d^2r/dt^2 = ⟨-18, 0⟩

Find the displacement vector from t=0 to t=3 by integrating the velocity vector from t=0 to t=3:

∫v(t) dt = ⟨-27, -12⟩

Find the position vector at t=3 by adding the displacement vector to the initial position vector:

r(3) = r(0) + ∫v(t) dt = ⟨10, 5⟩ + ⟨-27, -12⟩ = ⟨-17, -7⟩

Therefore, the location at t=3 of the particle whose path satisfies r(t) = ⟨14−9t^2,2−4t⟩ and r(0) = ⟨10,5⟩ is ⟨-17, -7⟩.

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(a) The probability of zero arrivals during the next minute is approximately 0.2231. (b) The probability of z service times less than or equal to a given value can be calculated using the exponential distribution formula.

(a) The probability of zero arrivals during the next minute can be calculated using the Poisson distribution with a rate of 1.5 per minute. Plugging in the rate λ = 1.5 and the number of arrivals k = 0 into the Poisson probability formula, we get P(X = 0) = e^(-λ) * (λ^k) / k! = e^(-1.5) * (1.5^0) / 0! = e^(-1.5) ≈ 0.2231.

(b) In the second part of the problem, the employee serves each customer in 1 minute on average, and the service times follow an exponential distribution. The probability of z service times less than or equal to a given value can be calculated using the exponential distribution. We can use the formula P(X ≤ z) = 1 - e^(-λz), where λ is the rate parameter of the exponential distribution. In this case, since the average service time is 1 minute, λ = 1. Plugging in z into the formula, we can calculate the desired probability.

Note: Since the specific value of z is not provided in the problem, we cannot provide an exact probability without knowing the value of z.

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Answer:

the area should be in in2

Answer:

16 and 56

Step-by-step explanation:

gcf of 24 and 48 is 24

gcf of 14 and 32 is 2

gcf of 16 and 28 is 4

Let's find one by one

#1

24 and 48

No

#2

14 and 32

No

#3

GCF is 4

No

#4

16 and 56

Yes

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

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Answer:

x > - 7

Step-by-step explanation:

Given

- 3x < 21

Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity.

x > - 7

The solution of inequality - 3x < 21 is,

⇒ x > - 7

We have to given that,

The inequality is,

⇒ - 3x < 21

We can simplify the inequality as,

⇒ - 3x < 21

Divide 3 both side,

⇒ - 3x /3 < 21 / 3

⇒ - x < 7

Take - 1 as common,

⇒ - x < 7

⇒ x > - 7

Therefore, The solution of inequality - 3x < 21 is,

⇒ x > - 7

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Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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Given data:

The total numbers of tickets purchased is a+b=20.

The total cost of the tickets is 15a+10b=225.

The first equation can be written as,

Substitute the above expression in the second equation.

The value of a is,

Thus, the numbers of tickes purchased by children are 15, and the numbers of tickets purchased by adults are 5.

The 50 students are an example of a sample population

A sample is a subset of a population that is used to represent the entire population. In this case, the 50 students who received the questionnaire are a sample of the population of students on the university campus. The results of the questionnaire would be used to make inferences about the satisfaction of the entire student population with the financial aid office on campus. The importance of the sample lies in the fact that it allows researchers to make inferences about a larger population based on a smaller, more manageable group of individuals. This is done by selecting a sample that is representative of the population of interest.

By studying a sample, researchers can make predictions about the characteristics of the larger population, such as the percentage of students who are satisfied with the financial aid office on campus. This can be done with a high degree of accuracy if the sample is chosen and analyzed properly. Additionally, studying a sample can also be much more cost-effective and time-efficient than studying the entire population. However, it's important to keep in mind that the sample may not be perfectly representative of the population and it may introduce some errors, called sampling errors, in the inferences made about the population.

So, 50 students as an example of a population sample to fill out the questionnaire.

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The Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).

We can split the function into two parts:

f(t) = e^(2t) - 8h(t-4)

Taking the Laplace transform of each part separately, we get:

L{e^(2t)} = ∫_0^∞ e^(-st) e^(2t) dt = ∫_0^∞ e^(t(2-s)) dt = 1/(s-2) (by using the Laplace transform formula for e^(at))

L{8h(t-4)} = 8 e^(-4s) (by using the formula for the Laplace transform of the unit step function h(t-a))

Thus, the Laplace transform of f(t) is:

f(s) = L{f(t)} = L{e^(2t)} - L{8h(t-4)} = 1/(s-2) - 8 e^(-4s)

Therefore, the Laplace transform of f(t) is f(s) = (1/(s-2)) - 8 e^(-4s).

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The circumference of circle M is 2cm, the correct option is (D) 2 cm.

If circle M is dilated by a scale factor of 3 to obtain circle N, we can determine the circumference of circle M by dividing the circumference of circle N by the scale factor.

The scale factor of 3 means that every linear dimension (such as radius or diameter) in circle N is three times larger than the corresponding dimension in circle M. Since the circumference is directly proportional to the radius or diameter of a circle, we can conclude that the circumference of circle N is three times the circumference of circle M.

Given that the circumference of circle N is 6 cm, we can divide this value by 3 to find the circumference of circle M:

Circumference of circle M = Circumference of circle N / Scale factor

Circumference of circle M = 6 cm / 3

Circumference of circle M = 2 cm

Therefore, the correct answer is:

D. 2 cm

The circumference of circle M is 2 cm.

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The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:

286 + 6s ≥ 316

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The measure of angle ABC is 64°.

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.

Given that, BM bisects ∠ABC and ∠MBC=32°.

Here, ∠ABC=∠MBC+∠MBA

Since, BM bisects ∠ABC, ∠MBC=∠MBA

∠ABC=∠MBC+∠MBC

∠ABC=2∠MBC

∠ABC=2×32°

∠ABC=64°

Therefore, the measure of angle ABC is 64°.

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Answer:

x=2

Step-by-step explanation:

5x+3=x+11

5(2)+3=2+11

10+3 = 2+11

13=13

Therefore, x=2

(basically you just plug in random numbers and see if it gets you the same answer on both sides)

Hope this helps!!

the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²). To find the derivative of y = sec⁻¹(1/x), we will use the chain rule of differentiation. Let's start by using the definition of the inverse secant function:

sec⁻¹(θ) = cos⁻¹(1/θ)

Then we can rewrite the given function as:

y = cos⁻¹(x)

Using the chain rule, the derivative of y with respect to x is:

dy/dx = d/dx [cos⁻¹(x)]

= -1/√(1 - x²) * d/dx [x]

= -1/√(1 - x²)

Therefore, the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

We can check this result by taking the derivative of y using the definition of the inverse secant function:

y = sec⁻¹(1/x)

sec(y) = 1/x

cos(y) = x

-sin(y) dy/dx = 1

dy/dx = -1/sin(y)

Using the Pythagorean identity sin²(y) + cos²(y) = 1, we can solve for sin(y) as:

sin(y) = √(1 - cos²(y)) = √(1 - x²)

Substituting this expression into the derivative, we get:

dy/dx = -1/√(1 - x²)

which is the same result we obtained using the chain rule. Therefore, we have confirmed that the derivative of y = sec⁻¹(1/x) with respect to x is -1/√(1 - x²).

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