anja simplified the expression startfraction 10 x superscript negative 5 baseline over negative 5 x superscript 10 baseline endfraction to startfraction 15 over x superscript 15 baseline endfraction. what mistake did anja make?

The center of the dilation, point C, is located at the same point as it was before the dilation. This is because the center of dilation is the point from which the dilation occurs, and it does not change during the dilation process.

To find the coordinates of point C, we can use the properties of dilations. The coordinates of the vertices of the dilated triangle are found by multiplying the coordinates of the original triangle by the scale factor.

So, if the coordinates of point X are (x1, y1), the coordinates of point X' will be (0.5x1, 0.5y1). Similarly, the coordinates of point Y' will be (0.5x2, 0.5y2) and the coordinates of point Z' will be (0.5x3, 0.5y3), where (x2, y2) and (x3, y3) are the coordinates of points Y and Z, respectively.

Since point C is the center of dilation, the coordinates of point C will be the same as the coordinates of the midpoint of the line segment connecting points X and X', points Y and Y', and points Z and Z'. The midpoint of a line segment is found by averaging the coordinates of the endpoints. So, the coordinates of point C will be:

C = ((x1 + 0.5x1)/2, (y1 + 0.5y1)/2) = (0.75x1, 0.75y1)

Therefore, the center of the dilation, point C, is located at (0.75x1, 0.75y1).

https://brainly.com/question/29229399

#SPJ1

The use and interpretation of an R or s chart are critical when examining an X-bar chart because they provide additional information about the variation within the subgroups. This allows for a more comprehensive analysis of the process and helps identify any issues or sources of variability.

When using an X-bar chart, the focus is on monitoring the process mean or average. However, the X-bar chart alone does not provide information about the variation within the subgroups. This is where the R or s chart comes into play. The R chart measures the range of values within each subgroup, while the s chart measures the standard deviation.
By using an R or s chart alongside the X-bar chart, we can assess the variability within the subgroups and determine if it is stable over time. If the variation within the subgroups is high and unpredictable, it may indicate that the process is out of control or that there are sources of variation that need to be addressed. The R or s chart provides additional insights into the process performance and helps in identifying the presence of special causes of variation.
In summary, the use and interpretation of an R or s chart in conjunction with an X-bar chart allow for a more comprehensive analysis of process variation. This helps in understanding the stability and capability of the process and enables appropriate actions to be taken to improve quality and performance.

learn more about X-bar chart here

https://brainly.com/question/31861365



#SPJ11

A function \(P(t) = 170.(1.30)^t\)  that gives the deer population P(t) on the reservation t years from now

We were told there were 170 stags on reservation. The number of deer is increasing at a rate of 30% per year.

We could see the deer population grow exponentially since each year there will be 30% more than last year.

Since we know that an exponential growth function is in form:

\(f(x) = a*(1+r)^x\)

where a= initial value, r= growth rate in decimal form.

It is given that a= 170 and r= 30%.    

Let us convert our given growth rate in decimal form.

\(30 percent = \frac{30}{100} = 0.30\)

Upon substituting our given values in exponential function form we will get,

    \(P(t) = 170.(1+0.30)^t\)

⇒ \(P(t)= 170.(1.30)^t\)

Therefore, the function \(P(t) = 170.(1.30)^t\) will give the deer population P(t) on the reservation t years from now.

Complete Question:

There are 170 deer on a reservation. The deer population is increasing at a rate of 30% per year. Write a function that gives the deer population P(t) on the reservation t years from now.

Learn more about Function:

https://brainly.com/question/12431044

#SPJ4

Answer:

(2,-4)

Step-by-step explanation:

We subtract 5 to the y-coordinate, so we have (2,-4)

Answer:

Step-by-step explanation:

Both B and C would be using e

Option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations or systems of equations:

3x-2y = 7 Equation 1

3x+4y= 17 Equation 2

As we know, in the elimination method:

We try to eliminate the variables at a time by making a similar coefficient of the x or y.

In option (B) Subtract the left side of equation 2 from the left side of equation 1.

It is not allowed to perform because first, we have to make the coefficient of y similar.

Thus, option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ5

Answer:

x = 6

Step-by-step explanation:

"Six times the quantity, x-2, is 24" can be rewritten symbolically as

6(x - 2) = 24.  We are to solve this for x.

To do that, divide both sides of the above equation by 6, to isolate x - 2:

x - 2 = 4

Adding 2 to both sides isolates x:  x = 6

In this problem, we are given the conditional probability density function (pdf) of X given Y=y, denoted as fX|Y(x|y), and we need to find the conditional expectation E(X | Y=y) and derive the unconditional pdf of X.

(a) The conditional expectation E(X | Y=y) can be found by integrating x multiplied by the conditional pdf fX|Y(x|y) with respect to x over its support. In this case, the support of X is x>0. So we have:

E(X | Y=y) = ∫(x * fX|Y(x|y)) dx, for x>0

To find the integral, we need to substitute the given values of fX|Y(x|y). However, the equation and values are not provided in the question, so the calculation of E(X | Y=y) cannot be performed without that information.

(b) To derive the unconditional pdf of X, we need to use the law of total probability. The unconditional pdf fX(x) can be obtained by integrating the conditional pdf fX|Y(x|y) multiplied by the marginal pdf of Y, fy(y), over the entire range of y. In this case, the marginal pdf of Y is given as fy(y) = Be^(hy) for y>0.

The unconditional pdf of X is given by:

fX(x) = ∫(fX|Y(x|y) * fy(y)) dy, for y>0

Again, we need the specific equation and values for fX|Y(x|y) to perform the integration and derive the unconditional pdf of X. Without that information, we cannot proceed with the calculation.

In conclusion, the solution to this problem requires the specific equation and values for the conditional pdf fX|Y(x|y) and the marginal pdf fy(y), which are not provided in the question. Therefore, we cannot determine the values of E(X | Y=y) or derive the unconditional pdf of X without that information.

Learn more about integrating here:

https://brainly.com/question/31744185

#SPJ11

(1) The family has bought 6 tickets.

(2) The teacher has bought 28 tickets.

What is an expression?

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

(1) To solve this problem, we need to set up the equation: cost = price * number of tickets. We are given the cost ($62.50) and the price ($10), and we want to solve for the number of tickets. Substituting these values into the equation and solving for the number of tickets gives:

number of tickets = cost / price

number of tickets = $62.50 / $10

number of tickets = 6.25

Since the number of tickets must be a whole number, the family bought 6 tickets.

(2) To solve this problem, we can use the same equation as before: cost = price * number of tickets. We are given the cost ($278.50) and the price ($10), and we want to solve for the number of tickets. Substituting these values into the equation and solving for the number of tickets gives:

number of tickets = cost / price

number of tickets = $278.50 / $10

number of tickets = 27.85

Since the number of tickets must be a whole number, the teacher bought 28 tickets.

Hence,

(1) The family has bought 6 tickets.

(2) The teacher has bought 28 tickets.

To learn more about the expression, visit:

https://brainly.com/question/1859113

#SPJ4

Answer:that hard

Step-by-step explanation:

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

Learn more about differential equations click;

https://brainly.com/question/32645495

#SPJ4

Answer:

Step-by-step explanation:

The simple formula for slope is: \(\frac{rise}{run}\) or "rise over run".

The rise is 3 and run is 2.

Hope it helped :)

Answer:

9/5

Step-by-step explanation:

(-1/4)(-4/5 / 2/3)6 =

= (-1/4)(-4/5)(3/2)6

= (-1/4)(-4/5)(3/2)6

= 1/5(3)(3)

= 9/5

Answer:

Step-by-step explanation:

The probability the class average is less than 79 is 0.1587.

What is Normal Distribution ?

Given that,

Normally distributed with a mean μ = 80

sample standard deviation σ = 6

In a class, number of students n = 30   (This may be 36 in ques but we take 30 as mentioned in question )

Let, x = be the individual score

∑x = be the class average

It's given, class average is less than 79.

Now, the probability that the class average is less than 79.

P(∑x < 79) = P( (∑x - μ) / (σ/√n)  < (79 - 80) / (6 /√30) )

                = P( (∑x - μ) / (σ/√n)  < (-1) / 1.09 )

                = P( (∑x - μ) / (σ/√n)  < -1 )     [Round off the Denominator it gives 1]

we know, Standard normal distribution Z = (∑x - μ) / (σ/√n)

so,

P(∑x < 79) = P( Z < -1 )

By Standard normal distribution table,

P( Z < -1 ) = 0.1587

Hence, the probability the class average is less than 79 is 0.1587.

To read more about Normal Distribution

https://brainly.com/question/23418254

#SPJ4

Answer:

x+345-398

Step-by-step explanation:

x+345-398

=x-53

where x is the amount of money he previously had on his account

Answer:

x = \(\frac{m-n}{e+1}\)

Step-by-step explanation:

m + n + ex = 2m - x ( add x to both sides )

m + n + ex + x = 2m ( subtract m + n from both sides )

ex + x = 2m - m - n = m - n ( factor out x from each term on the left side )

x(e + 1) = m - n ← divide both sides by (e + 1)

x = \(\frac{m-n}{e+1}\)

Answer:

y decreases by 4 as x increases by 2

or

there is a -2 change between the relationship of x and y

I hope I understood the question correctly

Answer:

[11000, 11600]

Step-by-step explanation:

Give me Brainliest if that helped! :)

1) angle UWV

2) angle VWU

f(x) = p(x) when x = 24, which means that both groomers will cost the same amount per year if Cheryl takes her puppy for grooming services 24 times in one year.

The functions f(x) and p(x) represent the annual cost of using Fluffy Puppy and Pristine Paws for grooming services, respectively.

In particular, f(2) represents the cost of using Fluffy Puppy for 2 standard visits in one year. This is equal to the annual membership fee of $120 plus the cost of 2 standard visits at $10.50 per visit, or:

f(2) = $120 + (2 x $10.50)

f(2) = $120 + $21

f(2) = $141

Similarly, p(x) represents the cost of using Pristine Paws for x standard visits in one year. The cost consists of a monthly membership fee of $5 multiplied by 12 months in a year, plus the cost of x standard visits at $13 per visit, or:

p(x) = ($5 x 12) + ($13 x x)

p(x) = $60 + $13x

Therefore, the equation f(x) = p(x) represents the situation where the annual cost of using Fluffy Puppy and Pristine Paws for grooming services is the same, or when the number of standard visits x satisfies the equation:

$120 + ($10.50 x) = $60 + ($13 x)

Solving this equation gives:

$10.50 x - $13 x = $60 - $120

-$2.50 x = -$60

x = 24

So, f(x) = p(x) when x = 24, which means that both groomers will cost the same amount per year if Cheryl takes her puppy for grooming services 24 times in one year.

Learn more about   cost from

https://brainly.com/question/25109150

#SPJ11

Answer:

To write 16.20 as a fraction you have to write 16.20 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number. 16.20 = 16.20/1 = 162/10 And finally we have:

Step-by-step explanation:

hope it work for you.

Answer: 119 minutes

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the solution is the point of intersection, which we can see is at point (-2,0)

Answer:

c. probability of success changes from trial to trial.

Step-by-step explanation:

Answer:

Outlier, clusters, and gap in your value.

Step-by-step explanation:

An OUTLIER is a data point that falls away from the rest of the points in a scatter plot. It doesn't seem to fit with the rest of the points. DATA CLUSTERS are groups of points that are all graphed close together. A GAP IN VALUE occurs when there are points clustered at two different spots on a scatter plot.

Answer:

1/2

Step-by-step explanation:

Using exponent rules, 2^3 * 2^-4 = 2^(3-4) = 2^-1 = 1/2

Answer:

was there more

Step-by-step explanation:

(i will edit answer)

The amount distributed per person and number of person can be found out by using the concept of square numbers

A "square" is the product of an integer or number (not a fraction) multiplied by itself.

The amount collected by charity Rs 15700

It is to be distributed such a way that number of people and amount distributed per person is same.

Let this number be 'a'

The number of person× amount distributed per person=total money collected

a×a=15700

Taking square root on both sides

\(a^{2} =15700\\\)

\(a=\sqrt{15000}\)

\(a=\pm125.299\)

-125.299 is neglected as number of people cannot be negative

Hence, a=125.299

The number of people and amount per person is 125 since number of people cannot in decimal.

So the possible amount for distribution in total

=125*125

=15625

The amount left undistributed

= total amount collected for the event-possible amount for distribution

=15700-15625

=75

The amount left = Rs 75

To know more about square numbers visit:

https://brainly.com/question/28610159

#SPJ4

The solution(s) of the equation are x = 0 and the solutions of the cubic equation x^(3)+3x^(2)+25x+75 = 0.

The solution(s) of the equation can be found by rearranging the terms and then factoring. Here are the steps:

Step 1: Rearrange the terms to have all the x terms on one side of the equation:
-4x^(4)+25x^(2)+75x+5x^(4)+3x^(3) = 0

Step 2: Combine like terms:
x^(4)+3x^(3)+25x^(2)+75x = 0

Step 3: Factor out the common factor of x:
x(x^(3)+3x^(2)+25x+75) = 0

Step 4: Use the zero product property to find the solutions:
x = 0 or x^(3)+3x^(2)+25x+75 = 0

The first solution is x = 0. The other solutions can be found by solving the cubic equation x^(3)+3x^(2)+25x+75 = 0. This equation does not have any rational solutions, so the solutions will be irrational or complex.

To know more about cubic equation click on below link:

https://brainly.com/question/1727936#

#SPJ11