A school staff meeting had 36 teachers in attendance, 75% of whom were first-year teachers. How many first-year teachers were in the meeting?

Answer:

Please find attached pdf

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

there are 4 colors meaning each one has a 1/4 chance

Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.

Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.

One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.

The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.

Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.

In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.

Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.

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The force F = r^2k(r^) is not conservative because its curl is nonzero. The force is central because it depends only on r and acts along the radial direction. Since it is not conservative, there is no potential energy function V(r) associated with this force

To determine whether the force F = r^2k(r^) is conservative and central, let's analyze its properties.

A force is conservative if it satisfies the condition ∇ × F = 0, where ∇ is the gradient operator. In Cartesian coordinates, the force can be written as F = Fx i + Fy j + Fz k, where Fx, Fy, and Fz are the components of the force in the x, y, and z directions, respectively. The curl of F is given by:

∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

Calculating the components of F = r^2k(r^):

Fx = 0, since there is no force component in the x-direction.

Fy = 0, since there is no force component in the y-direction.

Fz = r^2kr^.

Taking the partial derivatives, we have:

∂Fz/∂x = ∂/∂x (r^2kr^) = 2rkr^2(∂r/∂x) = 2rkr^2(x/r) = 2xkr^3.

∂Fz/∂y = ∂/∂y (r^2kr^) = 2rkr^2(∂r/∂y) = 2rkr^2(y/r) = 2ykr^3.

Substituting these values into the curl equation, we get:

∇ × F = (2ykr^3 - 2xkr^3)k = 2k(r^3y - r^3x).

Since the curl of F is not zero, ∇ × F ≠ 0, we conclude that the force F = r^2k(r^) is not conservative.

Now let's determine if the force is central. A force is central if it depends only on the distance from the origin (r) and acts along the radial direction (r^).

For F = r^2k(r^), the force is indeed central because it depends solely on r (the magnitude of the position vector) and acts along the radial direction r^. Hence, it can be written as F = Fr(r^), where Fr is a function of r.

Since the force is not conservative, it does not possess a potential energy function. In conservative forces, the potential energy function V(r) can be defined, and the force can be expressed as the negative gradient of the potential energy, i.e., F = -∇V. However, since F is not conservative, there is no potential energy function associated with it.

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The only pair of events that are independent among the three given pairs is the one where the probability of A is 0.6, the probability of B is 0.4, and the probability of the intersection of A and B is 0.24.

Pairs of events that are independent have probabilities that are not affected by the occurrence or non-occurrence of the other event. In other words, if A and B are independent events, then the probability of A occurring does not change based on whether or not B occurs, and vice versa.

To determine which pairs of events are independent, we need to calculate the probability of each event occurring and the probability of their intersection. If the probabilities satisfy the formula P(A ∩ B) = P(A)P(B), then the events are independent.

For the given pairs of events, we have:

P(A) = .40, P(B) = .60, P(A ∩ B) = .14. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.14 ≠ .24).

P(A) = .60, P(B) = .40, P(A ∩ B) = .24. These events are independent because P(A ∩ B) = P(A)P(B) (.24 = .24).

P(A) = .70, P(B) = .40, P(A ∩ B) = .28. These events are not independent because P(A ∩ B) ≠ P(A)P(B) (.28 ≠ .28).

Therefore, the pair of events that are independent is P(A) = .60, P(B) = .40, and (A ∩ B) = .24.

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The answer would be A.

Step-by-step explanation:

8 x $2.15= $17.20

If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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Answer:

10.11875

Step-by-step explanation:

just take $10,000 then multiply it by 0.0475 then multiply that py 0.25 then whatever you get just add $10,000

The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

The final value of any quantity growing constantly at a particular rate is given as \(V = V_{0}e^{rt}\) ,

where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.

The current population of squirrels (V₀) = 100.

The growth rate (r) = 5% per month.

The time period (t) = 1 year = 12 months.

Hence, the final population of squirrels (V), is given as:

\(V = V_{0}e^{rt}\) ,

or, \(V = 100e^{(0.05*12)}\) ,

or, \(V = 100e^{0.60}\) ,

or, V = 100*1.822119,

or, V = 182.2119 ≈ 182.

Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

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The differential equation \(y''y'=7\sin2t+5t\cos2t$\) is given by \(y(t)=\pm\int\sqrt{-7\cos2t+\frac{5}{2}t\sin2t+C_1}\,\)\(dt+C_2\)

Given differential equation is \(y''y'=7\sin2t+5t\cos2t\).

To find a differential equation, we need to integrate it twice, i.e., we need to find y' and y separately.

Let us first find y'.

Given the differential equation is,

\(y''y'=7\sin2t+5t\cos2t\)

Multiplying both sides with 2y', we get,

\(2y'y''y'=2(7\sin2t+5t\cos2t)\)

Now, we have to integrate both sides with respect to t.

Integrating LHS, we get,

\(\int 2y'y''\, dt=y'^2\)

Integrating RHS, we get,

\(\int 2(7\sin2t+5t\cos2t)\, dt=-7\cos2t+\frac{5}{2}t\sin2t+C_1\)

where C_1 is the constant of integration.

Putting both values in the original differential equation, we get, \(y'^2=-7\cos2t+\frac{5}{2}t\sin2t+C_1\)

Taking the square root of both sides, we get \(y'=\pm\sqrt{-7\cos2t+\frac{5}{2}t\sin2t+C_1}\)

Again, we have to integrate it, we get,

\(\int\frac{dy}{\sqrt{-7\cos2t+\frac{5}{2}t\sin2t+C_1}}=\int dt\)

On integrating both sides, we get the general solution of the given differential equation, i.e.,

\(y(t)=\pm\int\sqrt{-7\cos2t+\frac{5}{2}t\sin2t+C_1}\, dt+C_2\)

where C_2 is another constant of integration.

Therefore, the differential equation

\(y''y'=7\sin2t+5t\cos2t\) is given by \(y(t)=\pm\int\sqrt{-7\cos2t+\frac{5}{2}t\sin2t+C_1}\, dt+C_2\).

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She can arrange the 9 paintings in 362,880 different ways, and she can select 126 different combinations of 4.

And so on for the rest of the positions.

The total number of different combinations is equal to the product between the numbers of options:

C = 9*8*7*6*5*4*3*2*1 = 9! = 362,880

b) This will be given by the combinations of 4 out of 9, or:

C(9, 4), where:

\(C(9, 4) = \frac{9!}{(9 - 4)!*4!} = \frac{9*8*7*6}{4*3*2*1} = 126\)

She can select 126 different combinations of 4 paintings.

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Answer:

Mean: 63. Median: 69. Mode: 41. Range: 51.

Step-by-step explanation:

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list. The "range" of a list a numbers is just the difference between the largest and smallest values.

Answer:

5

Step-by-step explanation:

Add 6 to both sides. The answer is 5.

Answer:

5

Step-by-step explanation

since we are looking for the value of x,we have to make it the subject of the formula(stand alone).

Therefore,-6 would cross over the equality sign and it would become =6.

NOTE:when a negative number crosses the equality sign,it becomes a positive number.

This implies that x= -1+6

NOTE:when you come across - + +(minus plus plus),u would have to minus.

and to know the sign that would be at the front of the answer,just take a look at the sign the bigger number holds.At this point it is plus.

Therefore,x= -1 +6

x=5(u could have stated it was +5 but it isnt necessary since there is an invisible plus sign at the front of a number as long as minus is not there

Answer:

2x - 1

Step-by-step explanation:

Simplify. Note that you cannot combine a term with a variable with a constant term. Divide 5 from both terms in the parenthesis:

1/5(10x - 5) = (10x - 5)/5

Divide 5 from both terms in the parenthesis:

10x/5 = 2x

-5/5 = -1

2x - 1 is your answer.

~

Answer:

1/5 (10x - 5)

\(taking common \: 5 \: from (10x - 5) \\ 1 \div 5 \times 5(2x - 1)\)

2x-1 is your answer

To order a calzone with 6 distinct topping from available list of 8 vegetarian toppings, number of choices of calzone available is 28.

Therefore, the answer is 28.

Total number of available toppings equals 8 and the number of toppings selecting is 6.

The number of ways calzone can be chosen with 6 distinct topping from 8 vegetarian toppings can be obtained by combination formula.

nCm = n!/ (m! × (n - m)!)

Therefore, the number of ways = nCm

= 8C6

= 8!/ (6! × (8 - 6)!)

= 8!/ (6! × 2!)

= (8 × 7)/ 2

= 28

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Answer: if this is supposed to be in slope-intercept form

the equation would be: y = -2/5x + 7

Step-by-step explanation:

so the slope is: -2/5 and the point is (10,3) considering that x = 10 and y = 3

so we would plug this information into this equation: y = mx + b (slope-intercept form)

3 = -2/5(10) + b

3 = -4 + b

b = 7

and if we plug this in:

y = -2/5x + 7

Answer:

50 km per hour

Step-by-step explanation:

distance = 100km

time= 2hrs

average speed 100/2

50 km per hour

Answer:

Step-by-step explanation:

Best advice: make a sketch (which I can't do here).

When you reflect in the x axis, only the y value changes...so (3, -4) reflects to (3,4).

Translating down (i.e. in the negative direction) again means the x value (the abscissa) doesn't change, only the y value (the ordinate)...so the final value of the point is (3,1).

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer:

The octagon is regular, all of its sides and angles are congruent. Thus, the measure of each angle is equal to the sum of its angles divided by 8. Therefore, each angle in the polygon has a measure of 1080/8 =135 degrees.

The name of the polygon is, ''Octagon.''

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Formula for sum S of n interior angles of n sided polygon is,

S = (n - 2) × 180°

Since, polygon is regular all its interior angles is same, sum of them is 135 degree times n

So, we have S = 135°n

As per formula,

S = (n - 2) × 180°

135n = (n - 2) × 180°

180n - 360 = 135n

180n = 135n + 360

180n - 135n = 360

45n = 360

n = 8

Hence, The name of the polygon is, ''Octagon.''

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Answer: 90%

Step-by-step explanation:

Answer:

15 percent

Step-by-step explanation:

Answer:

About 13%

Step-by-step explanation:

92 minus 80

12/92 equals to ./100

Simplify 18/92

3/23= ?/100

Multiply 3 by 100

Then divide it by 23

1. When t = 0, the position (displacement) of the object can be found by substituting t = 0 into the given equation of motion:d = 3sin(8π(0)) - 2 = 0 - 2 = -2 meters.2. The maximum displacement of the object from its t=0 position can be found by taking the amplitude of the displacement function. Since the function is of the form d = Asin(ωt) - B, where A is the amplitude, ω is the angular frequency and B is the vertical shift, it can be seen that the amplitude in this case is A = 3 meters. So, the maximum displacement is 3 meters.3. The time taken for one oscillation can be found by dividing the period, T, of the oscillation by the number of oscillations in that period. The period of the oscillation is the time taken for one complete cycle of the sine wave, which is 1/8 seconds. Thus, the time taken for one oscillation is:1 oscillation = T/1/8 s = 8T s4. The frequency of the oscillation is the reciprocal of the period, which is f = 1/T. Thus, the frequency is:f = 1/T = 1/(1/8) Hz = 8 Hz.

A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

A system of linear equations is a group of equations with multiple variables. The number of solutions to the system of equations depends on how many equations and how many variables are in the system. A system of 3 linear equations can have 0, 1, or an infinite number of solutions.

If the number of equations is greater than the number of variables, the system is said to be overdetermined and has no solutions.

If the number of equations is equal to the number of variables, the system is said to be determined and has either one or an infinite number of solutions, depending on if the equations are dependent or independent.

If the number of equations is less than the number of variables, the system is said to be underdetermined and has an infinite number of solutions.

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The value of x is 29 cm.

To find the value of x, we can use the formula for the volume of a prism, which is V = A * h, where V is the volume, A is the area of the cross-section, and h is the height. In this case, we are given that the volume is 2465 cm^3 and the area of the cross-section is 85 cm^2. We need to solve for the height, h.

Using the formula, we have 2465 = 85 * h. To solve for h, we divide both sides of the equation by 85, giving us h = 2465 / 85 = 29 cm.

Therefore, the value of x is 29 cm.

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Answer:

Y=7+3x, x=-3, y=-2

Step-by-step explanation:

3x-5y=1. Equation 1

3x-y=-7. Equation 2

-y=-7-3x isolate for y in equation 2

y=7+3x multiplied by -1 to get positive y

3x-5(7+3x)=1 substitute y value of equation 2 (7+3x) into equation 1

3x-35-15x=1

-12x=36

x=-3

solve for y.

3x-5y=1

3(-3)-5y=1

-9-5y=1

-5y=10

y=-2

The answer is A. The normal distribution in its standardized form has a mean of 0 and a standard deviation of 1. This means that the distribution is centered around 0, and the spread of the data is determined by the standard deviation of 1. This is useful in statistical analysis because it allows us to compare data from different distributions on a standardized scale.

The normal distribution is a continuous probability distribution that is often used in statistical analysis. It is characterized by a bell-shaped curve and is symmetrical around its mean. In its standardized form, the normal distribution has been transformed to have a mean of 0 and a standard deviation of 1. This transformation is achieved by subtracting the mean of the distribution from each data point and dividing by the standard deviation. This standardization allows us to compare data from different normal distributions on a standardized scale.

The normal distribution has many properties that make it useful in statistical analysis. It is often used as a model for many real-world phenomena, such as the distribution of human height, IQ scores, and many others. The normal distribution is also useful because it is well understood and has many mathematical properties that make it easy to work with.

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The formula is recursive and \(a_1=1,a_2=-1,a_3=5 , a_4=-7 , a_5=17\) .

What is sequence?

The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, but a sequence is an ordered group of elements in which repetitions of any kind are permitted. One of the typical examples of a series or a sequence is a mathematical progression.

We know that recursive formula is defines using previous terms . Then

the given equation formula \(a_n=-2a_{n-1}+3\) is recursive formula.

Now \(a_1=2\) . Here put n=2 then,

=> \(a_2=-2a_{2-1}+3 = -2a_1+3 = -2\times2+3 = -4+3 = -1\)

Put n=3 then,

=> \(a_3=-2a_{3-1}+3 = -2a_2+3 = -2\times-1+3 = 2+3 =5\)

Put n=4 then,

=> \(a_4=-2a_{4-1}+3=-2a_3+3 = -2\times5+3=-10+3=-7\)

Put n=5 then,

=> \(a_5=-2a_{5-1}+3=-2a_4+3=-2\times-7+3=14+3=17\)

Hence The formula is recursive and \(a_1=1,a_2=-1,a_3=5 , a_4=-7 , a_5=17\) .

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