how many solutions are in 10(x + 4) – 3 = 14x + 1

The population in order to calculate the mean height will be all the students attending the college.

The population is the entire group of individuals being studied. In this case, the population is all the students who goes to the college.

Every member of a group constitutes a population. It is the inverse of a sample, which is a percentage or proportion of a group. It is sometimes possible to poll every member of a group. The U.S. Census is a quintessential example of a population, as it is required by law that every member of the U.S. population reply. In most circumstances, surveying everyone is unfeasible in statistics.

Consider how long it would take you to phone every dog owner in the United States to find out what brand of dog food they preferred. Furthermore, people may choose not to respond or may forget to respond, resulting in incomplete censuses. By definition, incomplete censuses become samples.

To learn more about population

brainly.com/question/27991860

#SPJ4

Answer:

Its either y = 100 or x = 100

Step-by-step explanation:

I do this kind of math everyday

It takes 1190 minutes for Allie to drive to the store and then to the car wash.

According to the question,

We have the following information:

Time taken by Allie to drive to the store = 456 minutes

Time taken by Allie to drive to the car wash from the store = 734 minutes

Now, we have to find the total time in minutes. So, we will add the total time taken by Allie to drive to the store and then to the car wash.

(Note that the time asked in the question is in minutes. So, we do not need to change the units of given time.)

Now,

The total time taken by Allie to drive to the store and then to the car wash = Time taken by Allie to drive to the store + Time taken by Allie to drive to the car wash from the store

The total time taken by Allie to drive to the store and then to the car wash = (456 + 734) minutes

The total time taken by Allie to drive to the store and then to the car wash = 1190 minutes

Hence, the total time taken by Allie to drive to the store and then to the car wash is 1190 minutes.

To know more about minutes here

https://brainly.com/question/15600126

#SPJ1

Answer:

Arc Length = θ × (π/180) × r, where θ is in degree.

The Arc length of the given partial circle is 4π units or 12.56 units .

Step-by-step explanation:

Answer:

4π

Step-by-step explanation:

Hope this helps!

The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.

To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:

\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:

\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)

        \(= [2(3) - (0)(3)] / (3)^2\)

        = 6/9

        = 2/3

Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,  
y - 0 = (2/3)(x - 1)

y = (2/3)x - 2/3

The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.

Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.

Learn more about point-slope form here:

https://brainly.com/question/20319380

#SPJ11

The complete question is:

Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).

The time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.

What is a unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Let,

Time taken by new computer to send 1 email = x

Time taken by the old computer to send same mail = 2x

Using unitary method

In 1 minute

Work done by new computer = 1/x

Work done by old computer =1/2x

Given the time taken when both computers work together  = 5 minutes

Work done in 1 minute by both = 1/5

So we can write,

1/x + 1/2x = 1/5

3/2x = 1/5

x = 7.5 minutes

Therefore the time taken by the new computer to send an email found using the unitary method, is 7.5 minutes.

To learn more about unitary method, follow the link.

https://brainly.com/question/24587372

#SPJ1

Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.



a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:

Maximize P = 3x + 2y + 4z

Subject to:2x + y + z + s1 = 8

x + 2y + 3z + s2 = 10

x, y, z ≥ 0

b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.

To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.

To learn more about simplex method click here

brainly.com/question/32298193

#SPJ11

The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

To learn more about constraint: https://brainly.com/question/30655935

Answer:

I think its 249.99 to 250.01

Step-by-step explanation:

The range of the variation for the scale will be 249.75 grams to 250.25 grams.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that for a scale to pass inspection, the scale's reading can vary by at most 0.1% from the actual mass of an object on the scale. A test mass has an exact mass of 250.00 grams.

The variation of the mass will be calculated as:-

Variation = 250 x 0.1% = ( 250 x 0.1 ) / 100 = 0.25

Higher variation = 250 + 0.25 = 250.25 grams

Lower variation = 250 - 0.25 = 249.75 grams

Therefore, the range of the variation for the scale will be 249.75 grams to 250.25 grams.

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ5

The marginal benefit from studying one extra hour is 5 percent.

Now,

Given:

To find: Marginal benefit on studying one hour extra.

Finding:

Now, marks scored on studying 4 hours is 80 percent and 5 hours is 85 percent.

Thus, the extra percentage that is scored is because of the 1 hour of extra studying.

The extra percentage = marginal benefit of studying extra = 85 - 80 = 5 percent.

Hence, the marginal benefit from studying one extra hour is 5 percent.

To learn more about marginal benefits, refer to the link: https://brainly.com/question/8136407

#SPJ4

Answer:

15) he would grow 10 1/2 inches in a year

17) 16 and 7/8 buckets of paint

Step-by-step explanation:

Answer:

Step 1: Simplify both sides of the equation.

4/8x−6=−24

1/2 x+−6=−24

1/2 x−6=−24

Step 2: Add 6 to both sides.

1/2 x−6+6=−24+6

1/2x=−18

Step 3: Multiply both sides by 2.

2*( 1/2

x)=(2)*(−18)

x=−36

Answer:

x=−36

Answer:

B, C, & D

Step-by-step explanation:

The maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

To maximize the profit function P(t) = 60t^2 + 420t - 440, we need to find the value of t that will give us the maximum profit.

One way to do this is to use calculus. We can take the derivative of P(t) with respect to t and set it equal to zero to find the critical points:

P'(t) = 120t + 420

Set P'(t) = 0 and solve for t:

120t + 420 = 0

t = -3.5

This gives us one critical point at t = -3.5. However, this value of t doesn't make sense in the context of the problem - we can't sell tickets at a negative price!

So we need to check the endpoints of the domain of the function, which is given by the constraint that t is greater than or equal to zero (we can't charge a negative price for tickets either).

When t = 0, P(0) = -440.

When t is very large, say t = 100, P(100) = 600000 - 44000 - 440 = 555120.

Therefore, the maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

More on maximum functions can be found here: https://brainly.com/question/13581879

#SPJ1

The probability that the first successful alignment requires at most four trials is 0.0064 and can be obtained using geometric probability.

Given:

p=0.8

Using the formula of geometric probability:

\(P(X=k)=q^{k-1}p=(1-p)^{k-1}p\)

a. Evaluate the definition at k=4:

\(P(X=4) = (1-0.8)^{4-1} \times 0.8\\ P(X=4) = 0.2^3 \times 0.8\\ P(X=4) =0.0064\)

To learn more about geometric probability with the given link

https://brainly.com/question/17514579

#SPJ4

Answer:

-4 degrees Farenheit

Step-by-step explanation:

8-12=-4

The new vertices of the trapezoid after translation:

A'( - 7, 8 ), B'( 7, 2 ), C'( - 1, 0 ), and D'( - 3, 4 ).

Consider the trapezoid ABCD with vertices as:

A( - 3, 6 ), B( 0, 7 ), C( 1, 4 ), and D( - 5, 2 )

When a figure is relocated from one place to another without changing its size, shape, or orientation, a transition known as translation takes place.

For example: ( x, y ) → ( x + 4, y - 1 )

Consider the point ( - 3, 6 ),

Point A when translated 4 units horizontally to the left and 2 units upward will be:

A( - 3, 6 ) → A'( - 3 - 4, 6 + 2 ) = A'( - 7, 8 )

Point B when translated to the right by 7 units and downwards by 5 units will be:

B( 0, 7 ) → B'( 0 + 7, 7 - 5 ) = B'( 7, 2 )

Point C when translated to the left by 2 units and downwards by 4 units will be:

C( 1, 4 ) → C'( 1 - 2, 4 - 4 ) = C'( - 1, 0 )

Point D when translated to the right by 2 units and upwards by 2 units will be:

D( - 5, 2 ) → D'( - 5 + 2, 2 + 2 ) = D'( - 3, 4 )

Learn more about translation here:

brainly.com/question/12861087

#SPJ1

Answer:

5n - 2

Step-by-step explanation:

8 subract 3 is 5

5 minus 3 is 2

5n - 2

When examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

What is statistical validity?

Statistical validity is defined as a procedure or an extent of drawing conclusions to which research works or studies can be considered precise and accurate which are derived from the already existing or reliable statistical tests.

It can also be the statistics which are derived from the research works or studies.

What is frequency in statistics?

Frequency in statistics can be defined as the number of times an observation or a record or a value occurred in the duration of the research work. The frequencies of different records are represented in a tabular form.

For a given set of data the frequency can either be 0 or more than that.

Frequency of a given record or an observation cannot be negative as the least number of times the instance of an object can appear is zero.

What is margin of error estimate?

The margin of error estimate is a percentage figure which can be some percentage more or less than the actual or ideal value.

The margin of error is the range of values greater or lesser than the sample outcome statistic in the accuracy or confidence region or the  interval.

Hence, when examining the statistical validity of a frequency claim, one should look for the margin of error estimate.

Know more about "statistical validity" here: https://brainly.com/question/12489703

#SPJ4

Given data:

The number of hour Stacy studied maths is 2/6 hour.

The number of hour Stacy studied science is 3/6 hour.

The total number of hours Stacy studied in 5 days is,

Thus, the total number of hours Stacy studied in 5 days is 25/6 hours, so option (D) is correct.

Answer:

\(\frac{1}{256}\)

Step-by-step explanation:

So generally a geometric sequence can be defined as: \(a_n=a_1(r)^{n-1}\) which is the explicit form. The r, is what each previous term is being multiplied by to get the next value which is evident in the recursive form: \(a_n = r(a_{n-1})\\\). Knowing this we can take two values which are "next" to each other to find what r is. In this case I'll just is 1 and 1/4, given these two values we know that: \(\frac{1}{4} = 1 * r\), 1*r is just r... so what each term is being multiplied by is 1/4. So let's plug the values into the explicit formula: \(a_n=(\frac{1}{4})^{n-1}\) (I didn't put an a_1 value in front, since it's just 1... so it's a bit redundant). Anyways using this formula we simply plug in 5 as n into the equation to find the 5th term: \(a_5 = (\frac{1}{4})^{5-1} = (\frac{1}{4})^4 = \frac{1^4}{4^4} = \frac{1}{256}\)

When six integers are chosen from the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, there must be at least one pair of integers that adds up to 11. This can be proven using a proof by contradiction.

To solve this problem, we can use a proof by contradiction. We assume that there are six integers chosen from A such that no two integers add up to 11.

If there is no pair of integers in the six chosen that sum up to 11, then we can consider the pairs of integers (1,10), (2,9), (3,8), (4,7), and (5,6). These are the only possible pairs of integers in A that add up to 11.

However, since there are five pairs and we can choose at most one integer from each pair, we can choose at most five integers in total. This is a contradiction since we were asked to choose six integers from A. Therefore, our assumption that there are no pairs of integers that add up to 11 is false.

Hence, we conclude that there must be at least one pair of integers among the six chosen that adds up to 11.

To know more about integer here

https://brainly.com/question/4196546

#SPJ4

Answer:

15

Step-by-step explanation:

Answer:

7 7/8 cups of flour

Step-by-step explanation:

2.25 times 3.5 equals 7.875

The points of the vertices of the triangle after reflection on the line y = -x is given by A'(3,-3) , B'(-3,-6) and B'(-3,-6)  .

We know that when a point is reflected around a line on the coordinate axes then the coordinates reflect following some rules.

Now when the point (a,b) is reflected around the line y = -x then ,the coordinates of the image becomes (-b,-a)

Therefore :

A(3,-3)→A'(3,-3 , does not change as the point lies on the line y=-x)

B(6,3)→B'(-3,-6)

C(3,3)→B'(-3,-6)

In a transition known as reflection over a line k, each point of the original figure (pre-image) must have an image that is the same distance from the line of reflection as the first comment but is on the other side of the line. Remember that a flip is a reflection. The size of the figure does not alter when it is reflected.

A figure created by a line reflection that is consistent with the original figure is called an isometry (a transformation that preserves length). Because naming the figure in a reflection implies changing the order of the letters, a reflection is more accurately referred to as a non-direct or opposing isometry .

To learn more about reflection visit:

https://brainly.com/question/24215981

#SPJ9

Answer: 3 -3 -3

-3 -6 -3

Step-by-step explanation:

When Myriam was flying in the plane at a cruising altitude of 10 km, she felt no different sitting in her seat than she had felt on the ground. This is because both the plane and its occupants, including Myriam, are moving at the same speed and direction relative to each other. In other words, there is no relative motion between Myriam and the plane's interior.

From the perspective of the passengers inside the plane, they are essentially moving together as a single unit. The air inside the cabin is also moving with the same velocity as the plane. Therefore, there is no noticeable change in sensation or feeling of motion. This is similar to how we don't feel the motion of being inside a moving car if we are not looking outside or feeling any external forces.

The sensation of motion primarily arises when there is a change in velocity or when there are external forces acting on our bodies. In the case of an airplane flying smoothly at a constant speed and altitude, there are no significant forces or changes in velocity experienced by the passengers, so they feel no different than if they were on the ground.

The magician's trick of pulling a tablecloth out from under a set of dishes on a table is explained by the principle of inertia, which is a fundamental concept of Newton's First Law of Motion. According to Newton's First Law, an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and direction, unless acted upon by an external force.

When the magician pulls the tablecloth rapidly, the key is to apply a quick and forceful pull in a horizontal direction. By doing so, the frictional force between the tablecloth and the dishes is overcome, and the tablecloth slides out from underneath the dishes. Due to the inertia of the dishes, they tend to resist changes in their state of motion, so they remain relatively stationary even as the tablecloth is rapidly removed.

The magician's trick is more successful when the tablecloth is pulled rapidly rather than slowly. Pulling the tablecloth slowly would increase the time over which the frictional force acts, causing a greater chance for the dishes to be affected by the force and potentially get disturbed or toppled. A rapid pull reduces the duration of the force acting on the dishes, allowing them to maintain their state of motion (or rest) due to inertia and minimizing the likelihood of disruption.

To learn more about Newton's First Law of Motion, visit:

https://brainly.com/question/974124

#SPJ11

Answer:

3.7

Step-by-step explanation:

The lenght of an arc with a radius of 3m and substended angle of 70 degrees is 3.7meters

The length of an arc is expressed as:

L = r theta

Given the following parameters

r = 3m

theta = 70 degrees = 70π/180

L = 3(70π/180)

L = 3.7 metres

Hence the lenght of an arc is 3.7meters

Learn more on length of an arc here: https://brainly.com/question/2005046