Mrs Ross runs a tutoring business she charges $35 an hour plus a $50 application fee her competitor Mrs brand charges $45 an hour plus $25 application fee right an equation that represent the situation when the cost to be tuned by Mrs Ross and Mr brand is the same

The length of the fabric which Brandon formed a rectangle, is 11 inches.

To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:

\(L^2 + 5^2 = 13^2\)

where L is the length of the fabric.

Solving for L, we get:

\(L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.\)

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Answer:

\(450000 \leqslant 15000 + 4t\)

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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The measure of angle y is 116 ⁰.

First we need to find the value of angle DCO and the value of angle DOC.

∠ DCO = 90 - 58⁰ ( angle subtended by diameter of a circle )

∠ DCO = 32⁰

line OC = OD = radius of the circle

∠ DCO = ∠ DOC = 32⁰

Now, the measure of angle y is calculated as follows;

∠ ODC + ∠ DCO + ∠ DOC = 180 ( sum of angles in a triangle )

y + 32 + 32 = 180

y + 64 = 180

y = 180 - 64

y = 116⁰

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Answer: To find the zeros of the polynomial p(x) = 3x^3 - 10x^2 + 10x - 4, we can use various methods such as factoring, synthetic division, or numerical methods. In this case, let's use a numerical method called the Newton-Raphson method to approximate the zeros.

We start by selecting an initial guess for the root. Let's start with x = 1.

Apply the Newton-Raphson formula to refine the estimate of the root:

x1 = x0 - (p(x0) / p'(x0)),

where x1 is the refined estimate, x0 is the initial guess, p(x0) is the value of the polynomial at x0, and p'(x0) is the derivative of the polynomial at x0.

Repeat step 2 until the estimate converges to the actual root.

Applying these steps, we can find the zeros of p(x) as follows:

Initial guess: x = 1

Using the Newton-Raphson method:

x1 = x0 - (p(x0) / p'(x0))

For p(x) = 3x^3 - 10x^2 + 10x - 4:

p'(x) = 9x^2 - 20x + 10

Using the initial guess x = 1:

x1 = 1 - (3(1)^3 - 10(1)^2 + 10(1) - 4) / (9(1)^2 - 20(1) + 10)

= 1 - (3 - 10 + 10 - 4) / (9 - 20 + 10)

= 1 - (-1) / (-1)

= 1 + 1

= 2

So, the refined estimate of the root is x = 2.

Next, we repeat the Newton-Raphson method with the refined estimate x = 2:

x2 = 2 - (3(2)^3 - 10(2)^2 + 10(2) - 4) / (9(2)^2 - 20(2) + 10)

Calculating x2:

x2 = 2 - (24 - 40 + 20 - 4) / (36 - 40 + 10)

= 2 - (0) / (6)

= 2

The estimate has converged, and we find that x = 2 is a zero of the polynomial p(x).

So, the zero of p(x) = 3x^3 - 10x^2 + 10x - 4 is x = 2, with a multiplicity of 1.

Therefore, the zeros of p(x) are x = 2.

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

The sewing kits bought by Ms, Clark is 17 in number.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,

As given in the question, Ms. Clark spent $89.85 on sewing kits that cost $5 each plus $4.85 tax on the total bill.

Let the number of sewing kits be x,
According to the question,
5x + 4.85 = 89.85
5x = 89.85 - 4.85
5x = 85
x = 17

Thus, the sewing kits bought by Ms, Clark is 17 in number.

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Answer:

Writing expressions | Math (article) | Khan Academy

Step-by-step explanation:

It seems that you're asking about solving a system of differential equations using the elimination method. Unfortunately, the elimination method is used for solving systems of linear equations, not differential equations. The given system consists of second-order nonlinear differential equations.

To use the elimination method to solve the system:

1. Start by multiplying the first equation by y2 and the second equation by -y1.

2. This gives us:

y′′1y2 = 2y1y2t

-y′′2y1 = -y12y2et

3. Now we can add the two equations together:

y′′1y2 - y′′2y1 = 2y1y2t + y12y2et

4. This simplifies to:

(y1y2)'' = 2y1y2t + y12y2et

5. Finally, we can integrate both sides to get the solution:

y1y2 = ∫(2t + e-t) dt

y1y2 = t2 - e-t + C

where C is a constant of integration.

Therefore, the solution to the system using the elimination method is:

y1y2 = t2 - e-t + C

For such problems, you may want to consider using numerical methods like Euler's method or Runge-Kutta methods to obtain approximate solutions, or consult with a specialist in differential equations to explore other possible techniques for solving the given system.

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Main Answer:To solve this equation, we need an initial condition or boundary condition to determine the specific solution. Once we have the solution for z, we can substitute it back into the first equation (y′′ = 2yzt) to find the solution for y.

Supporting Question and Answer:

How do we solve a system of differential equations using the elimination method?

To solve a system of differential equations using the elimination method, we differentiate the equations and manipulate them to eliminate one variable at a time. This allows us to express one variable in terms of the other variables, reducing the system to a simpler set of equations.

Body of the Solution: To solve the system of differential equations using the elimination method, we will eliminate one variable at a time by differentiating the equations. Let's denote y₁ as y and y₂ as z for simplicity.

Given system:

y′′ = 2yzt z′′ = 2yz - e^t

Step 1: Differentiate the first equation with respect to t. y′′′ = 2(z′t + z) + 2yzt

Step 2: Substitute the value of y′′′ into the second equation. 2(z′t + z) + 2yzt = 2yz - e^t

Simplifying the equation:

2z′t + 2z + 2yzt = 2yz - e^t

Step 3: Rearrange the terms to isolate z′.

2z′t + 2z - 2yz + e^t = 0

Step 4: Divide the equation by 2t to isolate z′.

z′ + z/t - y + e^t/2t = 0

This equation represents a first-order linear differential equation in terms of z.

Final Answer:The single required equation is: z′ + z/t - y + e^t/2t = 0

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The height of the arch at a distance of 1.5 meters from the center is approximately D. 1.73 meters

The shape of a semi-elliptical arch can be described by the equation:

y = c * sqrt(1 - (x/a)^2)

where "a" is half the span of the arch, "c" is the central height of the arch, and (x,y) are the coordinates of a point on the arch, measured relative to the center of the arch.

In this case, we have a span of 6 meters, so a = 3 meters. The central height of the arch is 2 meters, so c = 2 meters. We want to find the height of the arch at a distance of 1.5 meters from the center, so x = 1.5 meters.

Substituting these values into the equation, we get:

y = 2 * sqrt(1 - (1.5/3)^2)

y = 2 * sqrt(1 - 0.25)

y = 2 * sqrt(0.75)

y = 2 * 0.866

y = 1.732

Therefore, the height of the arch at a distance of 1.5 meters from the center is approximately 1.73 meters. Answer D

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Your question is incomplete, but probably the complete question is :

A semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. Find the height of the arch at a distance of 1.5 m from the center of the arch.

A.   1.41 m C.   1.56 m

B.   1.63 m D.   1.73 m

Bond A: Price = $614.46, New Price = $595.50, Percentage change = -3.08%, New Price (market interest rate 8.05%) = $637.13, Percentage change (market interest rate 8.05%) = 3.69%.

Bond B: Price = $791.59, New Price = $762.05, Percentage change = -3.73%, New Price (market interest rate 8.05%) = $819.15, Percentage change (market interest rate 8.05%) = 3.48%.

Bond C: Price = $1019.55, New Price = $970.53, Percentage change = -4.81%, New Price (market interest rate 8.05%) = $1053.72, Percentage change (market interest rate 8.05%) = 3.35%. Relationship: Bond C > bond B > bond A.

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Answer:

\( \displaystyle B)x = {5}^{9} \)

Step-by-step explanation:

we are given a logarithmic equation

\( \displaystyle \log_{5}(x) - \log_{5}(25) = 7\)

simplify the log:

\( \displaystyle \log_{5}(x) -2 = 7\)

add 2 to both sides:

\( \displaystyle \log_{5}(x) = 9\)

remember that,

\( \displaystyle \log_{a}(b) = c \iff {a}^{c} = b\)

so we obtain:

\( \displaystyle x = {5}^{9} \)

hence,

our answer is B)

5.25 or 5 1/4

I worked it out I hope this helps :)

Thethe inverse of f(x) and its domain can be written as  f-¹(x) =  1/(x+1 )- 5 where x \(\neq\)-1

Given : f (x) = 1/(x+5 )-1

we can make f(x) as y which implies that  f(x) = y

Then we will have  y= 1/(x+5) -1

if we flip x as well as y the we weill have ,

x= 1/y+5 -1

we can rearrange as ( x+1)=  1/(y+5 )

making y+5 the subject of the formular, we have

( y+5)=  1/(x+1 )

y=  1/(x+1 )- 5

f-¹(x) =  1/(x+1 )- 5

x+1 \(\neq\) 0

x \(\neq\) -1

Therefore, option C is correct which is f-¹(x) =  1/(x+1 )- 5 where x \(\neq\)-1

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properly written question:

15 points f (x) = 1/x+5 -1. Find the inverse of (x) and its domain.

The probability that a student who attends the football game also attends the dance is 23/43, or approximately 53.5% rounded to the tenths place.

Now we can use the information given in the question to fill in the Venn diagram. We know that 43% of students attend the football game, so the size of circle F will be 43% of the total number of students.

Similarly, we know that 48% of students attend the dance, so the size of circle D will be 48% of the total number of students. Finally, we know that 23% of students attend both the game and the dance, so the size of the overlapping area FD will be 23% of the total number of students.

Using these values, we can calculate the probability that a student who attends the football game also attends the dance. This is given by the formula:

P(D|F) = P(D and F) / P(F)

where P(D|F) represents the probability of attending the dance given that the student attends the football game, P(D and F) represents the probability of attending both events, and P(F) represents the probability of attending the football game.

Substituting the values we know, we get:

P(D|F) = 0.23 / 0.43

P(D|F) = 0.5348 = 53.48%

To express this as a simplified fraction, we can divide both the numerator and denominator by 100:

P(D|F) = 23/43

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Answer:

k=70

Step-by-step explanation:

to get k by itself you need to multiply k/7 by 7, and you multiply on both sides. 10 times 7 =70

Answer:

Step-by-step explanation:

k/7 = 10

or, k = 7*10

Therefore, k=70.

The distinction between real variables and nominal variables is based on the type of measurement used to represent the variable.

A variable is a characteristic that can take different values or levels. Real variables are measured on a numerical scale and can take any value within a certain range.

On the other hand, nominal variables are categorical variables that represent non-numerical attributes. They are used to classify data into different groups or categories based on their characteristics. Examples of nominal variables include gender, race, nationality, and occupation. These variables cannot be measured using a numerical scale, but they can be represented using labels or codes.

The distinction between real variables and nominal variables is important because they require different methods of analysis. Real variables can be analyzed using statistical methods such as mean, standard deviation, and correlation, while nominal variables require different methods such as frequency tables and chi-square tests.

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Answer:

C

Step-by-step explanation:

Using the Sine rule in Δ ABC

Calculate the measure of ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31° , then

\(\frac{sin31}{9.3}\) = \(\frac{sin85}{b}\) → C

Given

You have to calculate f(g(x))

You have to calculate the composite of the functions, this means, replace g(x) into f(x)

Once you replaced g(x) into f(x) you can solve the polynomial

The first step is to solve the terms in parentheses, to make it easier I'll solve them separatelly and then put the results together.

1) To solve the binomial square, you have to apply the distributive property of multiplications

2) To solve the multiplication of the parentheses term by multiplying each term by 5

Now put the results together and order the like terms together

The result of the combination is

Answer:

The answer is: 13 minutes

Step-by-step explanation:

First Let us form equations with the statements in the two scenario

\(time=\frac{distance}{speed}\)

Let the time in which the bell rings be 'x'

1. If Andrew walks (50 meters/minute), he arrives 3 minutes after the bell rings. Therefore the time of arrival at this speed = (3 + x) minutes

\(3 + x =\frac{distance}{50}\\distance = 50(3+x) - - - - - (1)\)

2. If Andrew runs (80 meters/minute), he arrives 3 minutes before the bell rings. Therefore the time taken to travel the distance = (x - 3) minutes

\(x - 3 = \frac{distance}{80} \\distance = 80(x-3) - - - - - (2)\)

In both cases, the same distance is travelled, therefore, equation (1) = equation (2)

\(50(3+x)=80(x-3)\)

\(150 +50x=80x-240\\\)

Next, collecting like terms:

\(150 + 240 = 80x - 50x\\390 = 30x\\30x = 390\\\)

dividing both sides by 3:

x =  390÷30 = 13

∴ x = 13 minutes

As per the unitary method, the number of care is 9 and the number of additional method is 2.

The term unitary in set theory is defined as the way to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Here we have given that the total number of units is 56.

And here we also know that the number of units in each care is 6.

Now, we have to find the total number of care, that can be obtained by dividing the total care by the units in each care,

then it can be written as,

=> 56/6

When we divide the term then we get the quotient as 9 and the remainder as 2.

Therefore, while looking into these we have identified that there are 9 cares and 2 additional units are in the group.

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Answer:

49

Step-by-step explanation:

First you must do x times 6, x is really just 1. After you do that, you times it by 7.

Answer:

7x + 42.

Step-by-step explanation:

Just distribute (multiply) both x and 6 by 7.

7 x X is 7x.

7 x 6 is 42.

Thus, your answer is 7x + 42.

Hope this helps!

Answer:

Rate when price rises 20% = $36

Rate when price downs 20% = $24

Step-by-step explanation:

Given:

Current rate to mow = $30 per lawn

Find:

Rate when price rises 20%

Rate when price downs 20%

Computation:

Rate when price rises 20%

Rate when price rises 20% = Current rate to mow + 20%[Current rate to mow]

Rate when price rises 20% = 30 + 20%[30]

Rate when price rises 20% = 30 + 6

Rate when price rises 20% = $36

Rate when price downs 20% = Current rate to mow - 20%[Current rate to mow]

Rate when price downs 20% = 30 - 20%[30]

Rate when price downs 20% = 30 - 6

Rate when price downs 20% = $24

The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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Answer:

the answer is 4

Step-by-step explanation:

Answer:

root of 50 + root of 10

answer 5root 2 plus root 10

Answer:

\(b = \$7\)

Step-by-step explanation:

Given that:

Cost of book that Tyler wants to buy for his school = $13

He wants to buy books for his sisters as well.

Total amount of money present with Tyler = $27

Money to be spent on books for his sisters is same and is represented as \(b\).

To find:

The value of \(b\).

Solution:

As per question statement, the sum of all the books bought must be equal to $27.

The sum of money spent on all the books = Cost of Tyler's book + Cost of books for his sisters

\(\Rightarrow \$13 + b + b = \$27\\\Rightarrow \$13 + 2b = \$27\\\Rightarrow 2b =\$14\\\Rightarrow b =\$7\)

Therefore, Tyler must spend $7 on each of her sister's books.

The correct answer is D. All of the above. When the spread of scores around the arithmetic mean gets smaller, it means that the data points are closer to the mean.

This has several implications:
A. The coefficient of variation (CV) gets smaller: The coefficient of variation is the ratio of the standard deviation to the mean. When the standard deviation decreases (due to smaller spread of scores), the CV also decreases.
B. The interquartile range (IQR) gets smaller: The IQR represents the range between the first quartile and the third quartile. When the spread of scores decreases, the values at the first and third quartiles are closer together, resulting in a smaller IQR.
C. The standard deviation gets smaller: The standard deviation measures the average distance of data points from the mean. As the spread of scores decreases, the data points are closer to the mean, resulting in a smaller standard deviation.
In summary, when the spread of scores around the arithmetic mean gets smaller, the coefficient of variation, interquartile range, and standard deviation all decrease.

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