Zoe has plantains and apples in a ratio of 25:6. How many plantains does she have if she has 300 apples?

Answer:

23,24,26,27 sorry if you get it wrong

Answer: 20

Step-by-step explanation:

x+y=5

x-y=4

---------

x+y=5

x=4+y

--------

(4+y)+y=5

4+y+y=5

 4+2y=5

      2y=1

        y=0.5

        x=4.5

---------

x²-y²=(4.5)²-(0.5)²=20.25-0.25=20

The value of the average life (t_average) of unstable nuclei in terms of the decay constant (λ) is given by ln(2)^2 / λ.

To derive the value of the average life (t_average) of unstable nuclei in terms of the decay constant (λ), we can start by defining the average life.

The average life (t_average) of unstable nuclei represents the average time it takes for half of the original sample of nuclei to decay. It is closely related to the concept of the half-life of a radioactive substance.

Let's denote N(t) as the number of nuclei remaining at time t, and N₀ as the initial number of nuclei at time t = 0.

The decay of unstable nuclei can be described by the differential equation:

dN(t)/dt = -λN(t)

This equation states that the rate of change of the number of nuclei with respect to time is proportional to the number of nuclei present, with a proportionality constant of -λ (the negative sign indicates decay).

Solving this differential equation gives us the solution:

N(t) = N₀ * e^(-λt)

Now, let's find the time t_half at which half of the original nuclei have decayed. At t = t_half, N(t_half) = N₀/2:

N₀/2 = N₀ * e^(-λt_half)

Dividing both sides by N₀ and taking the natural logarithm:

1/2 = e^(-λt_half)

Taking the natural logarithm of both sides:

ln(1/2) = -λt_half

Using the property of logarithms, ln(1/2) = -ln(2):

ln(2) = λt_half

Now, we can solve for t_half:

t_half = ln(2) / λ

The average life (t_average) is defined as the average time it takes for half of the nuclei to decay. Since we are considering an exponential decay process, the average life is related to the half-life by a factor of ln(2):

t_average = t_half * ln(2)

Substituting the expression for t_half, we have:

t_average = (ln(2) / λ) * ln(2)

Simplifying further:

t_average = ln(2)^2 / λ

Therefore, the value of the average life (t_average) of unstable nuclei in terms of the decay constant (λ) is given by ln(2)^2 / λ.

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The equation "ax2 = y," which has one solution unless a = 4, and none unless a = 4, has a solution. x = √(-4ay) / (2a) restricted by the condition that y be negative.

We may use the quadratic formula to determine the solutions to an equation for various values of an to construct a solution to the equation "ax² = y," which has no solution when a = 4 & just one solution in all other cases.

According to the quadratic formula, the answers to the problem "ax2 + bx + c = 0" are provided by

x = (-b +/- √(b² - 4ac)) / (2a)

In this formula, if we add "ax² = y," we obtain

x = (-0 +/- √(0² - 4ay)) / (2a)

which simplifies to

x = √(-4ay) / (2a)

If a = 4, the equation becomes

x = √(-16y) / 8

The equation has no solutions if y is positive because the value of (-16y) is fictitious. The value of (-16y) is real if y is negative, but the equation is still unsolvable since x cannot have a negative value. As a result, when a = 4, the problem has no solutions.

The equation has a single solution provided by any other value of a.

x = √(-4ay) / (2a)

For example, if a = 3, the equation becomes

x = √(-12y) / 6

Since √(-12y) is imaginary if y is positive, the problem has no solutions. If y is negative, √(-12y) has a real value, and there is only one solution to the problem.

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The midpoint of the segment PQ where P¨= (-4, -1) and Q = (3, 3) is the point  (-1/2, 1)

If we have a segment whose endpoints are (a, b) and (c, d), then the midpoint of that segment will be:

( (a + c)/2, (b + d)/2).

In this case, we can see that the endpoints of the segment are:

(-4, -1) and (3, 3), replacing that in the midpoint formula that I wrote above we will get:

Midpoint: (  (-4 + 3)/2 , (-1 + 3)/2) = (-1/2, 1)

In this way, we conclude that the midpoint of the segment PQ where P¨= (-4, -1) and Q = (3, 3) is the point  (-1/2, 1).

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Answer:

SAS, because vertical angles are congruent.

Answer:

The correct answer would be 3x/5y

Step-by-step explanation:

You are substracting, and the denominator is the same for both 5x/5y and 2x/5y, so it will remain the same (5y). This only leaves you needing to substract 5x-2x, which equals 3.

5x/5y-2x/5y= 3x/5y

Step-by-step explanation:

\(\frac{5x}{5y}-\frac{2x}{5y}\\ \frac{5x -2x}{5y}\\ \frac{(5-2)x}{5y} \\ \frac{3x}{5y}\)

\(\frac{3x}{5y} \\\)

The perimeter of shed is, (6x+ 4)

The area of the shed is, (2x² + 5x + 3)

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

Shirley is building a shed. The length is 2x + 3 feet long and the width is

x + 1 feet long.

Now, We know that;

The perimeter of rectangle = 2 (Length + Width)

Substitute all the values, we get;

⇒ Perimeter = 2 (2x + 1 + x + 1)

⇒ Perimeter = 2 (3x + 2)

⇒ Perimeter = (6x + 4)

And, Area of rectangle = Length × Width

Substitute all the values , we get;

⇒ Area = (2x + 3) × (x + 1)

⇒ Area = (2x² + 2x + 3x + 3)

⇒ Area = (2x² + 5x + 3)

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The null hypothesis to test for instruments' relevance is option D) H0:π2=0 or π3=0 or π4=0.In order to test the relevance of the instrument, the first stage equation's null hypothesis should be stated as: H0: π2 = 0 or π3 = 0 or π4 = 0.The relevance requirement will be fulfilled if we can refute the null hypothesis.

The null hypothesis will not be rejected if the F-statistic is less than 10.0. However, if the F-statistic is greater than 10.0, the null hypothesis will be rejected, indicating that the variables are relevant and that the instrument satisfies the relevance requirement.In summary, to test for instruments' relevance in TSLS, the null hypothesis of the first stage equation is stated as H0: π2 = 0 or π3 = 0 or π4 = 0.

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(a) ( x_{t+1}=\frac{1}{2} x_{t}+3 ), the solution to this difference equation is x_t = 2^t + 3, The difference equations in this problem are both linear difference equations with constant coefficients.

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 3

1 | 7

2 | 15

3 | 31

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

(b) ( x_{t+1}=-3 x_{t}+4 )

The solution to this difference equation is

x_t = 4 \cdot \left( \frac{1}{3} \right)^t + 4

This can be found by solving the equation recursively. For example, the first few terms of the solution are

t | x_t

--- | ---

0 | 4

1 | 5

2 | 2

3 | 1

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

The difference equations in this problem are both linear difference equations with constant coefficients. This means that they can be solved using a technique called back substitution.

Back substitution involves solving the equation recursively, starting with the last term and working backwards to the first term.

In the first problem, the equation can be solved recursively as follows:

x_{t+1} = \frac{1}{2} x_t + 3

x_t = \frac{1}{2} x_{t-1} + 3

x_{t-1} = \frac{1}{2} x_{t-2} + 3

...

x_0 = \frac{1}{2} x_{-1} + 3

The general term of the solution can be found by noting that

x_{t+1} = \frac{1}{2} x_t + 3 = \frac{1}{2} (2^t + 3) + 3 = 2^t + 3

The second problem can be solved recursively as follows:

x_{t+1} = -3 x_t + 4

x_t = -3 x_{t-1} + 4

x_{t-1} = -3 x_{t-2} + 4

...

x_0 = -3 x_{-1} + 4

The general term of the solution can be found by noting that

x_{t+1} = -3 x_t + 4 = -3 \left( 4 \cdot \left( \frac{1}{3} \right)^t + 4 \right) + 4 = 4 \cdot \left( \frac{1}{3} \right)^t + 4

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Answer: 4

Step-by-step explanation:

1. We want to have x by itself, so we can isolate it by moving -9 to the other side of the equation.

2. This leaves us with 2x=-1+9

3. This equals 2x=8

4. Now we want to completely leave x by itself, so since we know that it is being multiplied by 2, we have to move it to the other side.

5. This leaves us with x=8/2

6. Finally, 8/2=4.

7. x=4.

Answer:

x = 4

Step-by-step explanation:

So, the basic way that we solve a one variable equation is isolating the x variable on one side. We can see that we have a -9 on the left side, and a -1 on the right. Let's simplify this to isolate the x variable:

First, add 9 to both sides:

\(2x-9=-1\\+9.........+9\)

2x=8

Now, we can divide both sides by 2:

x = 4

Remember when doing these solving for x problems:

Whatever you do to one side, you have to do to the other

The Diwali occurred on 0.408 or 40.8% of the year in 2017.

To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.

Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.

There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.

So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408

So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.

Therefore, Diwali occurred on 0.408 or 40.8%

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The precentile for a student in the class who studies 8 hours a week is 5.74%.

To find the percentile for a student who studies 8 hours a week, we need to first standardize the student's study time by subtracting the mean study time and dividing it by the standard deviation of study time. This will give us the student's z-score. We can then look up the student's z-score in a standard normal table to find the percentile.

The student's z-score is (8 - 9.92) / 4.54 = -1.67.

Looking up -1.67 in a standard normal table, we find that the percentile is about 5.74%. This means that about 5.74% of the students in the class studied for less than 8 hours per week.

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As per the given standard deviation, the percentile for a student in the class who studies 8 hours a week is 50.80%

The term standard deviation in math is known as a measure which shows how much variation from the mean exists.

Here we have given that in one statistics course students reported studying an average of 9.92 hours a week with a standard deviation of 4.54.

Through this details, we have identified that the value of the following are given that,

=> weekly study time = 10 hours

=> average study time = 9.92 hours

=> standard deviation = 4.54 hours

Then the formula to calculate the Test statistic is written as

=> z = (weekly study time - average study time)/standard deviation

Apply the values on it, then we get

=> z = (10 - 9.92)/4.54

=> z = 0.08/4.54 = 0.02

While we take the value of z table, then we get the Cumulative area of the test statistic is 0.5080.

And the percentile is calculated by multiply the value by 100 as,

=> 0.5080 × 100 = 50.80

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To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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Angles Formulas at the center of a circle can be expressed as:

Central angle, θ = (Arc length × 360º)/(2πr) degrees

Sum of Interior angles=180°(n-2)

The angles formulas are used to find the measures of the angles. An angle is formed by two intersecting rays, called the arms of the angle, sharing a common endpoint.

The corner point of the angle is known as the vertex of the angle. The angle is defined as the measure of the turn between the two lines.

There are various types of formulas for finding an angle; some of them are the central angle formula, double-angle formula, etc...

We use the central angle formula to determine the angle of a segment made in a circle.

We use the sum of the interior angles formula to determine the missing angle in a polygon.

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Yes, a follow-up study is required to provide 80% confidence that the point estimate is correct to within 0.02 of the population proportion.

To determine if a follow-up study is needed, we consider the sample size and the desired level of confidence. In this case, the sample size is 326, and the proportion of individuals who answered "no" to the question about disrupted business presentations is 23/326 ≈ 0.0706. To estimate the population proportion with a margin of error of 0.02 and 80% confidence, we need to calculate the required sample size. Using appropriate formulas or statistical software, the necessary sample size is determined to be 1692. Therefore, a follow-up study is necessary to achieve the desired level of confidence and precision in estimating the population proportion.

To calculate the required sample size for a follow-up study, statistical methods such as the formula for sample size calculation for proportions can be used. These methods take into account the desired level of confidence, the margin of error, and the estimated proportion from the initial sample. By conducting a follow-up study with an adequate sample size, we can achieve more reliable and accurate results, increasing the confidence in the estimated population proportion.

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Answer:

  {-3, 0, 6}

Step-by-step explanation:

There are points of inflection where the second derivative of f(x) is 0. That derivative is a cubic expression, so its zeros are most easily found using a graphing calculator. The attached shows its zeros to be at x = {-3, 0, 6}.

The x-values of the points of inflection are {-3, 0, 6}.

_____

The first derivative is ...

  f'(x) = x^4 -4x^3 -36x^2

The second derivative is ...

  f''(x) = 4x^3 -12x^2 -72x = 4x(x^2 -3x -18) = (4x)(x -6)(x +3)

It has zeros at x = -3, 0, +6.

On solving the provided question, we can say that equation is  z = x-u/p => z = 300-348/80 = 0.65, The z score for a per - day expense of $400 is 0.65

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

The z score for a $400 per day charge is 0.65, but around 84.13% of hotels cost more than $268.

The z score is used to calculate how many standard deviations above or below the mean the raw score is. Giving the z score are:

equation is

z = x-u/p

u = mean, x = raw score, p standard deviation

z = 300-348/80 = 0.65

The z score for a per - day expense of $400 is 0.65

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Answer:

c).    14 < x < 15

d).    7 < x < 8

Step-by-step explanation:

c).   (x/3)^3 = 124

Take the cube root of both sides

x/3 = 4.986630952238646

multiply both sides by 3

x = 14.959892856715938

14 < x < 15

-----------------------------

d). (x/2 - 1)^3 = 25

Take the cube root of both sides

x/2 - 1 = 2.924017738212866

Add 1 to both sides

x/2 = 3.924017738212866

multiply both sides by 2

x = 7.848035476425732

7 < x < 8

Using the Gini coefficient with BIOLOG substrate utilization data provides a quantitative measure to compare bacterial soil communities based on their metabolic diversity and resource utilization patterns.

The Gini coefficient, commonly used to measure income inequality in economics, can also be applied to ecological studies to assess the diversity and evenness of resource utilization within a community.

When combined with BIOLOG substrate utilization data, which provides information on the metabolic capabilities of bacterial communities, the Gini coefficient offers a valuable alternative quantitative measure for comparing these communities.

The Gini coefficient calculates the inequality of resource utilization by evaluating the distribution of substrate utilization among the different bacterial species present in the soil community. It considers both the number and relative abundance of bacterial taxa utilizing different substrates.

A higher Gini coefficient indicates a more uneven distribution of substrate utilization, suggesting a higher specialization within the community, whereas a lower Gini coefficient suggests a more even distribution, indicating a more generalized resource utilization pattern.

By applying the Gini coefficient to BIOLOG substrate utilization data, researchers can quantify the metabolic diversity and functional redundancy within bacterial soil communities. This approach provides insights into the ecological dynamics of these communities and can help assess the impact of environmental changes or disturbances on their functioning.

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1. The equation is; N/20 = (1/2)^t/16

2. The values that fill the table are;  10 mg, 5 mg,  2.5 mg,  0.3125 mg, 0.0391 mg

The half-life is a crucial parameter since it tells us how stable, quickly something degrades, and how long something lasts. It is employed for a number of things, such as judging the safety and handling of radioactive materials.

We know that;

N/No = (1/2)^t/t1/2

The equation is now;

N/20 = (1/2)^t/16

To fill the table;

1;

N =  (1/2)^16/16 * 20

N = 10 mg

2;

N =  (1/2)^32/16 * 20

N = 5 mg

3;

N = (1/2)^48/16 * 20

= 2.5 mg

4;

N =  (1/2)^96/16 * 20

N = 0.3125 mg

5;

N = (1/2)^144/16 * 20

= 0.0391 mg

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i cant understand your question define briefly

The given vectors are:
Vector A = (-11, b, 2)
Vector B = (b, b^2, b)

The values of b for which the given vectors are orthogonal are 0, -3, and 3.

To find the values of b for which the given vectors are orthogonal, we need to use the dot product of the vectors.

To determine if two vectors are orthogonal, their dot product should be equal to zero.

The dot product is calculated as follows:

Dot Product (A, B) = A1 * B1 + A2 * B2 + A3 * B3

Substituting the components of Vector A and Vector B:

(-11 * b) + (b * b^2) + (2 * b) = 0

Now, simplify the equation:

-11b + b^3 + 2b = 0
b^3 - 9b = 0

Factor the equation:

b(b^2 - 9) = 0

Now, we can find the values of b:

b = 0
b^2 - 9 = 0
b^2 = 9
b = ±3

So, the values of b for which the given vectors are orthogonal are 0, -3, and 3.

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Answer:

\(\displaystyle m\angle RTU=73^\circ\)

Step-by-step explanation:

Interior Angle of a Circle

An interior angle of a circle is formed at the intersection of two lines that intersect inside a circle.

Lines AC and BD of the figure attached below intersect forming arcs p and q. The measure of the interior angle x  is:

\(\displaystyle x=\frac{p+q}{2}\)

The question includes the drawing of a circle with lines US and RV intersecting at point T. The measure of the interior angle RTU is:

\(\displaystyle m\angle RTU=\frac{68^\circ+78^\circ}{2}\)

\(\displaystyle m\angle RTU=\frac{146^\circ}{2}\)

\(\boxed{\displaystyle m\angle RTU=73^\circ}\)

Answer:

however it works for you along as you get the right answer

Step-by-step explanation:

Answer:

Yeah you will most likely get the same answer

Step-by-step explanation:

as long as you don't mix up (for this example of course) the service call fee (which is the constant) and the fee for each hour of labor (the coefficient of the variable), you are good

Answer: y=0.05x-23540

Step-by-step explanation: We turn 5% into a decimal which is 0.05 and we add x to it so we can pick how many years. Then we subtract 23540 because he has used that money to buy the car.

Answer:

a rotation of 180° about point (0.5, -0.5) followed by a dilation of 0.5

Step-by-step explanation:

Answer:

11.5

Step-by-step explanation:

We solve using :

Pythagoras Theorem

LM² = MN² + NL²

NL² = LM² - MN²

NL = √LM² - MN²

NL = √14² - 8²

NL =  √(132)

NL = 11.489125293

NL = 11.5

Therefore, the length of NL = 11.5