Declining Employment A business had 4000 employees in 2000 . Each year for the next 5 years, the number of employees decreased by 2%.

The graph of the equation x^2/49 + (y + 1)^2/4 = 1 is added as an attachment

The expression that represents the function in words is given as

StartFraction x squared Over 49 EndFraction + StartFraction (y + 1) squared Over 4 EndFraction = 1

Express the equation properly

So, we have

x^2/49 + (y + 1)^2/4 = 1

The above equation is an ellipse

Next, we plot the graph on a coordinate plane using a graphing tool

See attachment for the graph of the equation

Read more about ellipse at

https://brainly.com/question/29187465

#SPJ1

The answer of possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5

The Rational Zero Theorem states that if f(x) is a polynomial with integer coefficients, then any rational zero of f(x) must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

To find the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10, we need to list the factors of the constant term (10) and the factors of the leading coefficient (-5).

Factors of 10: ±1, ±2, ±5, ±10
Factors of -5: ±1, ±5

Now, we can list all possible rational zeros by taking each factor of the constant term and dividing it by each factor of the leading coefficient:

Possible rational zeros: ±1/1, ±2/1, ±5/1, ±10/1, ±1/5, ±2/5, ±5/5, ±10/5

Simplifying the fractions gives us the final list of possible rational zeros:

Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5, ±1, ±2

Removing duplicates, we get:

Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5

Therefore, the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5.

To know more about  Rational Zero Theorem refer here:

https://brainly.com/question/20873708#

#SPJ11

Answer:

Mai is correct. We can use exponential notation to represent the number of coins each day. Let's call the number of coins on the first day "1". Then the number of coins on each subsequent day is twice the number of coins on the previous day. So we have:

Day 1: 1

Day 2: 2 = 2^1

Day 3: 4 = 2^2

Day 4: 8 = 2^3

...

Day n: 2^(n-1)

To find the number of coins Mai has on the 6th day, we substitute n = 6 into the formula for the number of coins:

Day 6: 2^(6-1) = 2^5 = 32

So Mai has 32 coins on the 6th day. Writing out the product of 2's (1.2.2.2.2.2.2) is equivalent to writing 2^6 = 32.

To find out how many coins Mai has after 28 days, we substitute n = 28 into the formula for the number of coins:

Day 28: 2^(28-1) = 2^27 = 134,217,728

So after 28 days, Mai has 134,217,728 coins.

The amount of dry cells that are taken from the full container is 473.

To find the total number of dry cells taken from the full container, we need to add up the number of dry cells placed in the stockroom, on the shelf, and sold to customers. We can use the following equation:

  Total dry cells taken = Dry cells in stockroom + Dry cells on shelf + Dry cells sold to customers

Plugging in the given values, we get:

  Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6

Using the order of operations, we can simplify the equation:

Total dry cells taken = 325 + 45 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 370 + 18 + 25 + 30 + 24 + 6
Total dry cells taken = 388 + 25 + 30 + 24 + 6
Total dry cells taken = 413 + 30 + 24 + 6
Total dry cells taken = 443 + 24 + 6
Total dry cells taken = 467 + 6
Total dry cells taken = 473

Learn more about union in math at https://brainly.com/question/28278437

#SPJ11

If f(x) is the parent function and g(x) is the transformation of f(x), then the required functions are as follows:

5. g(x) = -4ˣ and 6. g(x) = -(1/5)ˣ.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

5.

The given function is as follows:

f(x) = 4ˣ

When the function f(x) = 4ˣ is reflected about the x-axis, then we get the graph of function g(x).

So, g(x) = -4ˣ

6.

The given function is as follows:

f(x) = (1/5)ˣ

When the function f(x) = (1/5)ˣ is reflected about the x-axis, then we get the graph of function g(x).

So, g(x) = -(1/5)ˣ

To learn more about the transformations click here :

https://brainly.com/question/11352944

#SPJ1

1 divided by 2/6 is equal to 3.

Division is a mathematical operation used to divide one number (the dividend) by another number (the divisor) to find out how many times the divisor is contained within the dividend

To divide 1 by 2/6, we need to find out how many times the denominator (2/6) fits into the numerator (1).

One way to approach this is to convert the fraction 2/6 to an equivalent fraction with a denominator of 1. To do this, we can multiply both the numerator and denominator of 2/6 by the same number, in this case 3:

2/6 = (23)/(63) = 6/18

Now, we can divide 1 by 6/18:

1 ÷ 6/18

= 1 x 18/6 (reciprocal of 6/18 is 18/6, which is equivalent to 3)

= 3

Learn more about division here

brainly.com/question/17205173

#SPJ4

Answer:

Below

Step-by-step explanation:

9/5  X   4/1  X  1/6   =  ( 9 x 4 x 1)  / (5 x 1 x 6) = 36/30  = 1 6/30 = 1  1/5

Answer:

1 1/5

Step-by-step explanation:

The cone is composed of a half sphere and a triangular cone, the total volume would be 301.59 cubic centimeters.

This cone is composed of two shapes, these shapes are:

The volume of the cone can be calculated using the following formula:

V=1/3hπr²

V= 1/3 10 π4²

V= 167.55 cm

The volume of the sphere can be calculated using the following formula:

V = 4/3 π r³ /

V = 4/3 π 4³/ 2  

V = 268.08 / 2 = 134.04 cm

Total volume : 134.04 + 167.55 = 301.59 cubic centimeters

Learn more about the volume in https://brainly.com/question/13338592

#SPJ1

The probability that the height of a randomly selected tree is as tall as mine or shorter is 0.1151. The probability that the full height of a randomly selected tree is at least as tall as hers is 0.0362.

To find the probability that the height of a randomly selected tree is as tall as yours or shorter, we need to find the z-score for your tree's height and use the standard normal table to find the corresponding probability. The z-score is calculated as follows:

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

For your tree, the z-score is:

z = (44.7 - 56.6) / 9.9 = -1.198

Using the standard normal table, the probability that the height of a randomly selected tree is as tall as yours or shorter is 0.1151.

For your neighbor's tree, the z-score is:

z = (74.4 - 56.6) / 9.9 = 1.798

Using the standard normal table, the probability that the height of a randomly selected tree is at least as tall as hers is 1 - 0.9638 = 0.0362.

So, the probability that the height of a randomly selected tree is as tall as yours or shorter is 0.1151, and the probability that the height of a randomly selected tree is at least as tall as your neighbor's is 0.0362.

For more such questions on Probability.

https://brainly.com/question/11234923#

#SPJ11

Answer:

An exponential function in the form of y = a(m) x is of the form:

y = a * m^x

where "a" is a constant, "m" is a positive constant (the base of the exponential), and "x" is the independent variable.

To determine the exponential function in this form, you need to have some information about the function, such as its value at a particular point or its rate of growth.

Here are the general steps to determine the exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

Determine the value of "m" by solving for it using the given information.

For example, let's say you are given that the function passes through the point (2, 8) and has a growth rate of 3. To determine the exponential function in the form of y = a(m) x, you would follow these steps:

Plug in the values of x and y into the equation:

8 = a * m^2

Solve for "a" by isolating it on one side of the equation:

a = 8 / m^2

Use the given growth rate of 3 to find the value of "m":

m = 1 + r = 1 + 0.03 = 1.03

Plug in the value of "m" and the value of "a" you found in step 2 into the equation:

y = (8 / 1.03^2) * 1.03^x

Simplifying this equation gives:

y = 7.514 * 1.03^x

So the exponential function in the form of y = a(m) x that passes through the point (2, 8) and has a growth rate of 3 is y = 7.514 * 1.03^x.

Step-by-step explanation:

here is a more detailed explanation of the steps involved in determining an exponential function in the form of y = a(m) x:

Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.

In the equation y = a(m) x, "a" is a constant that represents the value of y when x is equal to 0. So to find the value of "a", we need to know the value of y for a specific value of x, other than 0.

By the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The given function is a polynomial of degree 4. Therefore, by the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

However, we do not know if these roots are all real or if some of them are complex. To determine this, we would need to use techniques such as factoring, synthetic division, or the quadratic formula to solve for the roots of the polynomial.

To learn more about Functions from the given link

https://brainly.com/question/22340031

#SPJ1

Answer:

Select the math statement that is true.

Step-by-step explanation:

You're welcome.

The vector AC can be expressed in terms of vector AB and vector BC as follows:

In Euclidean geometry, a parallelogram is described as a simple quadrilateral with two pairs of parallel sides.

We have that  ABCD is a parallelogram, vector AC is equivalent to vector BD, which can be expressed in terms of vector AB and vector BC as follows:

Vector BD = Vector AB + Vector BC

We can substitute BD for AC in the above equation because  vector AC is equivalent to vector BD, we obtain the following:

Vector AC = Vector AB + Vector BC

In conclusion, vector AC can be expressed in terms of vector AB and vector BC as the sum of vector AB and vector BC.

Learn more about parallelograms at: https://brainly.com/question/970600

#SPJ1

The linear system shown is "inconsistent" in nature.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

The given figure is represented linear system represents two parallel lines.

Now, the solution set of the two system of equations could be find by finding their points of intersection.

And when the lines do not intersect then it is said the linear system of the two lines do not have any solution.

Now, we have been given two parallel lines and parallel lines never intersect each other. thus the solution set of both the system of equations represented by these parallel lines is an empty set.

And when the system of linear equation has no solution , then the system is said to be inconsistent.

Hence, The linear system shown is "inconsistent" in nature.

Learn more about linear equations;

https://brainly.com/question/10413253

#SPJ9

The complete question is;

The linear system shown is _____.

independent

equivalent

inconsistent

Answer:

103,92,81,70,59,48,37,36,15,4

Step-by-step explanation:

every number has difference of 11

Answer: (6x²+5) (6x²- 5)

Please give me brainliest :)

Step-by-step explanation:

To find the function values, we need to substitute the given values of x into the function:

a) f(2) = 95(0.84)^2 ≈ 66.96

This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

b) f(6) = 95(0.84)^6 ≈ 35.33

This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.

To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).

Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.

After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function

To find:

Interpret the given function values and determine an appropriate domain for the function.

Solution:

The general form of an exponential function is

Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.

We have,

Here, 110 is the initial value and 0.83 is the decay factor.

It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.

We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.

We know that  for any value of x. So,  for all values of x.

Therefore, domain of the function is  and the range is .

Hope this helps!!!

GTPex-

The simplified trigonometric expression is sin(a).

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here the given trigonometric expression is,

=> [tex]\frac{sec(a)}{cot(a)+tan(a)}[/tex]

We know that [tex]cot(a)=\frac{cos(a)}{sin(a)}[/tex] and [tex]tan(a)=\frac{sin(a)}{cos(a)}[/tex] and [tex]sec(a)=\frac{1}{cos(a)}[/tex]

Then,

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos(a)}{sin(a)}+\frac{sin(a)}{cos(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{cos^2a+sin^2a}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{\frac{1}{cos(a)} }{\frac{1}{cos(a)sin(a)} }[/tex]

=> [tex]\frac{1}{cos(a)}\times\frac{sin(a)cos(a)}{1}[/tex]

=> sin a

Hence the simplified trigonometric expression is sin(a).

To learn more about trigonometric function refer the below link

https://brainly.com/question/25618616

#SPJ1

The graph of the quadratic equation has a minimum value, The extreme value is at the point (7,-3), and The graph of the quadratic equation has a maximum value are all true about the equation.

A quadratic equation is a mathematical expression made up of four terms which are arranged in the form of a polynomial. It is usually used to solve for the unknown values of two or more variables. It is also defined as a mathematical equation containing a second-order polynomial that can be written in the form of ax2 + bx + c = 0.

The graph of the quadratic equation has a minimum value, The extreme value is at the point (7,-3), and The graph of the quadratic equation has a maximum value are all true about the equation. The solutions for the equation are 3 and 7, which can be found by using the Quadratic Formula. The extreme value is at the point (7,-3) since this is the lowest value of the graph.

For more questions related to polynomial,

https://brainly.com/question/20121808

#SPJ1

The perimeter of a rectangle is the sum of the lengths of all four sides, which can be expressed as:

P = 2x + 2y

where x is the length of the rectangle in centimeters and y is the width of the rectangle in centimeters.

If the perimeter of the rectangle is z, then we can write the formula as:

z = 2x + 2y

Simplifying this equation, we get:

p = z

Therefore, the formula for p, the perimeter of the rectangle, is:

p = 2x + 2y

where x is the length of the rectangle in centimeters and y is the width of the rectangle in centimeters.

For more such questions on Rectangle, visit:

brainly.com/question/29123947

#SPJ11

Purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.

To calculate the break-even point on their mortgage, we need to determine how much Lenny and Lisa paid for the points and how much they save on their interest rate over the life of the loan.

First, we need to determine how much Lenny and Lisa paid for the points. One point is equal to 1% of the total loan amount, so 3 points is equal to 3% of 675,250:

3 points = 3% x 675,250 = 20,257.50

Next, we need to calculate how much Lenny and Lisa save on their interest rate by purchasing the points. Their original interest rate was 7.25%, but they were able to reduce it to 6.875% by purchasing 3 points. This means they save 0.375% on their interest rate.

To calculate how much they save over the life of the loan, we need to use an amortization schedule. An amortization schedule shows how much of each payment goes towards interest and how much goes towards principal, and it also shows the remaining balance on the loan after each payment.

Using an online mortgage calculator, we can generate an amortization schedule for Lenny and Lisa's loan. Based on this schedule, they will pay a total of 931,231.40 in interest over the life of the loan if they keep their original interest rate of 7.25%. If they reduce their interest rate to 6.875%, they will pay a total of 846,689.56 in interest over the life of the loan.

This means that by purchasing 3 points and reducing their interest rate, Lenny and Lisa will save 84,541.84 in interest over the life of the loan.

To determine the break-even point on their mortgage, we divide the cost of the points by the amount they save on their interest rate per year.

for such more question on interest rate

https://brainly.com/question/25720319

#SPJ4

Step-by-step explanation:

when 2 shapes are similar, then that means (among few other things) that both have the same angles at their vertexes.

by looking at the relative sizes of the sides, we can map which vertex of one correlates to which vertex (and angle) in the other.

D -> X

C -> Y

G -> U

F -> V

E -> W

so, the angle W = angle E = 136°.

Answer:

(-2 . x) + (-2 . 5) = 4

-2x + -10 = 4

-2x = 4 + 10

-2x / -2 = 14/- 2

x = -7

All the best to you!

Answer:

To solve the inequality:

-10 - 66h ≥ -3

We can begin by isolating the variable h on one side of the inequality. First, we can add 10 to both sides:

-10 + 10 - 66h ≥ -3 + 10

Simplifying, we get:

-66h ≥ 7

Next, we can divide both sides by -66, remembering to reverse the inequality since we are dividing by a negative number:

h ≤ -7/66

Therefore, the solution to the inequality is h ≤ -7/66.

Step-by-step explanation:

The minimum value of f(x) over the interval [3,5] is -512 and the maximum value is 225.

To find the minimum and maximum values of the function f(x) = x^(4) - 32 x^(2) over the interval [3,5], we can use the following steps:

1. Find the first derivative of the function: f'(x) = 4x^(3) - 64x
2. Set the first derivative equal to zero to find the critical points: 4x^(3) - 64x = 0
3. Solve for x to find the critical points: x = 0, x = 4√2, x = -4√2
4. Check the value of the function at the critical points and at the endpoints of the interval to find the minimum and maximum values.
5. The minimum value occurs at x = 4√2, where f(4√2) = (4√2)^(4) - 32(4√2)^(2) = -512
6. The maximum value occurs at x = 5, where f(5) = 5^(4) - 32(5)^(2) = 225
7. Therefore, the minimum value is -512 and the maximum value is 225.

The least value of f(x) over the interval [3,5] is -512 and the largest value is 225.

Learn more about function at https://brainly.com/question/29129022

#SPJ11

a) The exponential growth equation is y = ( 1.2 )ˣ

b) The exponential decay equation is y = ( 0.71 )ˣ

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

y = ( 1.2 )ˣ

where the growth rate is r = 20 %

Let the exponential decay equation be represented as B

Now , the value of B is

y = ( 0.71 )ˣ

where the decay rate is r = 29 %

The graph A represents an exponential decay graph and the graph B represents an exponential growth graph

Hence , the exponential equations are solved

To learn more about exponential growth factor click :

https://brainly.com/question/13674608

#SPJ1

The sign of each of the functions in the given interval is positive.

Suppose \( \theta \) is in the interval \( \left(90^{\circ}, 180^{\circ}\right) \), we can find the sign of each of the following functions by using the unit circle and the reference angles.

77. \( \cos \frac{\theta}{2} \)
Since \( \theta \) is in the second quadrant, \( \frac{\theta}{2} \) will be in the first quadrant. Therefore, the sign of \( \cos \frac{\theta}{2} \) will be positive.

78. \( \sin \frac{\theta}{2} \)
Similarly, since \( \theta \) is in the second quadrant, \( \frac{\theta}{2} \) will be in the first quadrant. Therefore, the sign of \( \sin \frac{\theta}{2} \) will be positive.

79. \( \sec \frac{\theta}{2} \)
The secant function is the reciprocal of the cosine function, so the sign of \( \sec \frac{\theta}{2} \) will be the same as the sign of \( \cos \frac{\theta}{2} \), which is positive.

In conclusion, the sign of each of the functions in the given interval is positive.

Learn more about reference angles

brainly.com/question/1603873

#SPJ11

Answer:

Assuming that the expression is meant to be written as:

(a^5 ⋅ 2^3)^3

We can simplify it using the rules of exponents. First, we can simplify the expression inside the parentheses:

a^5 ⋅ 2^3 = a^5 ⋅ 8 = 8a^5

Now we can substitute this simplified expression into the original expression:

(8a^5)^3

To simplify this, we use the power rule of exponents, which states that when we raise a power to another power, we multiply the exponents:

(8a^5)^3 = 8^3 ⋅ (a^5)^3 = 512a^15

Therefore, the simplified expression is 512a^15.

If the ground already has an elevation of  15 degree. The degree that the ladder need to be set is 65.4 degrees.

Angle at which the ladder is set from the horizontal =  x.

Angle between the ladder and the ground =  (75 - 15 + x) degrees

Using trigonometry, we can write the equation:

tan(75 - 15 + x) = 10 / L

where:

L=  length of the ladder.

Simplifying the left-hand side using the trigonometric identity for the tangent of the difference of two angles, we get:

tan(60 + x) = 10 / L

Multiplying both sides by L, we get:

L * tan(60 + x) = 10

Dividing both sides by tan(60 + x), we get:

L = 10 / tan(60 + x)

Using a calculator, we can evaluate the right-hand side to be:

L = 10 / tan(60 + x) ≈ 5.768 / tan(x)

So, the equation we need to solve for x is:

5.768 / tan(x) = L

Substituting the value of L obtained from the previous problem, we get:

5.768 / tan(x) = 2.68

Multiplying both sides by tan(x), we get:

5.768 = 2.68 tan(x)

Dividing both sides by 2.68, we get:

tan(x) ≈ 2.153

Using a calculator, we can find the value of x that satisfies this equation by taking the inverse tangent (tan^-1) of both sides:

x ≈ 65.4 degrees

Therefore, the ladder needs to be set at an angle of approximately 65.4 degrees from the horizontal in order to reach a height of 10 feet when the ground already has an elevation of 15 degrees and the ladder is placed at a 75-degree angle with the ground.

Learn more about angle here:https://brainly.com/question/25716982

#SPJ1

The complete question is:

Write and solve an equation for the following situation in order for a ladder to reach a height of 10 feet it needs to be placed at a 75 degree  to the ground . The ground already has an elevation of  15 degree. What degree does the ladder need to be set?