The amount of time it would take you to go from Chicago to Las Vegas is equal to 1525 miles divided by your average rate of travel. Which equation describes how the time and rate of travel are related?

Answer:

1/2 m

Step-by-step explanation:

It is because 4 = 4/1, 8 = 8/1 and 4/1 divided by 8/1 is also equal to 4/1 times by 1/8 which equals 4/8.

4/8 is simplified to make 1/2m

hope this helps mark brainliest

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

The z-score corresponding to a score that is 12 points above the mean is 2.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

If the sample score is 12 points above the mean, then (x – μ) = 12.

(x – μ) = 12

σ = 6

Substitute the values to the z-score formula.

z-score = (x – μ) / σ

z-score = 12/6

z-score = 2

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The 90% confidence interval for the proportion of district residents in favor of starting the school day 15 minutes later is (0.392, 0.548). The true proportion is estimated to lie within this interval with 90% confidence.

To calculate the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later, we can use the following formula:

CI = p ± z*(√(p*(1-p)/n))

where:

CI: confidence interval

p: proportion of residents in favor of starting the day later

z: z- score based on the confidence level (90% in this case)

n: sample size

First, we need to calculate the sample proportion:

p = 94/200 = 0.47

Next, we need to find the z- score corresponding to the 90% confidence level. Since we want a two-tailed test, we need to find the z- score that cuts off 5% of the area in each tail of the standard normal distribution. Using a z-table, we find that the z- score is 1.645.

Substituting the values into the formula, we get:

CI = 0.47 ± 1.645*(√(0.47*(1-0.47)/200))

Simplifying this expression gives:

CI = 0.47 ± 0.078

Therefore, the 90% confidence interval for the true proportion of district residents who are in favor of starting the school day 15 minutes later is (0.392, 0.548). We can be 90% confident that the true proportion lies within this interval.

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Answer:

Circle the -3 or the -2 in the final product

Step-by-step explanation:

If you multiply it out, the last terms are -2 and -3 which equal 6, not negative 6 so, that would be wrong factoring.

Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
If Daisy calls in sick, then Lisa will be the only stylist at the salon, and all customers will go to her. Let's use x to represent the number of Lisa's customers. Then the income generated by Lisa's customers can be represented by the equation:

18x = projected income

We can solve for x by dividing both sides of the equation by 18:

x = projected income / 18

Substituting the given projected income of $216, we get:

x = 216 / 18 = 12

Therefore, Lisa would need to serve 12 customers to attain the projected income if Daisy calls in sick that day.

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To answer this question, solve the given expression for calculating velocity for a, this way:

The correct answer is B.

Answer:

d. 93 \(m^{2}\)

Step-by-step explanation:

4×3= 12, 12/2 =6, 6×4 = 24

5×3= 15, 15×4= 60

3×3=9,

24+60+9= 93

A real number is in between 14 square root and 15 square root is 3.8.

It should be noted that real numbers include rational and irrational numbers.

✓14 = 3.74

✓15 = 3.87

Therefore, a real number is in between 14 square root and 15 square root is 3.8.

It should be noted that this implies a number that can be sent between the square roots.

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You take \(\frac{2}{7}\) of \(400\).

Which is: \(\frac{800}{7} = 114.8 mL\)

Answer:

(3,-7) I think.

Step-by-step explanation:

Answer:b

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();

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The speed of the stream is 6 \(km/h\)

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h, and the speed of the boat

downstream = (18 + x) km/h.

The time is taken to go upstream = distance/speed

\(24/(18-x)\) hours.

Similarly, the time is taken to go downstream =

\(24/(18+x)\) hours.

According to the question,

\(24/(18-x) - 24/(18+x) = 1\)

\(x^{2} +48x-324=0\)

Using the quadratic formula, we get

\(x=\frac{-48+\sqrt{48^{2}+1296 } }{2}\)

x = 6 or -54

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54.

Hence the speed of the stream is 6 km/h.

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The equation of the line through the points (−9,3) and (−6,−3) is y = -2x - 15.

To find the equation of the line through the points (−9,3) and (−6,−3), we use the point-slope formula given as

`y - y1 = m(x - x1)` where `m` is the slope of the line and `(x1, y1)` is the coordinates of a point on the line. The slope of the line can be found using the formula:

m = (y2 - y1) / (x2 - x1)Here, (x1, y1) = (−9,3) and (x2, y2) = (−6,−3)

Substitute the values in the formula, m = (-3 - 3) / (-6 + 9) = -6/3 = -2.Therefore, the slope of the line is -2.Now, we need to use one of the given points, say (−9,3), and the slope, m = -2, in the point-slope formula to find the equation of the line.y - y1 = m(x - x1)Here, (x1, y1) = (−9,3).

Substitute the values in the formula,y - 3 = -2(x - (-9))y - 3 = -2(x + 9)y - 3 = -2x - 18y = -2x - 18 + 3y = -2x - 15

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Answer:

120 square meters

Step-by-step explanation:

\(h = \sqrt{ {17}^{2} - {8}^{2} } = \sqrt{289 - 64} = \sqrt{225} = 15\)

So the area is (1/2)(16)(15) = 120 square meters

In statistics, the "central tendency" refers to a single value which represents middle or center of a set of data. The 3 common measures of central tendency are named as mean, median, and mode.

When scores have a central tendency, it means that most of the scores in a set of data are clustered around a particular value.

For Example, if we have a data set of test scores, and most of the scores are around 70, then 70 would be the central tendency of the data set.

The central tendency is an important concept in statistics because it provides a way to summarize a large set of data with a single value.

It can help you understand the overall pattern of the data and make comparisons between different data sets.

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Answer:

3^14

Step-by-step explanation:

Multiplication of two values with same base and different exponent:

When we are multiplicating two values with the same base and different exponents, we keep the base and add the exponents. For example:

In this question:

a) There is no solution for m in this case, b) The value of m that satisfies the equation is -18.

a) To find the value of m in the function g(x−3)=x−1, we need to substitute x with 6−m3​ in the given function and solve for m.

## Step 1: Substitute x with 6−m3​ in the function g(x−3)=x−1:

g((6−m3​)−3) = (6−m3​)−1

## Step 2: Simplify the expression on the left-hand side:

g(3−m3​) = (6−m3​)−1

## Step 3: Since g(3−m3​) is equal to (6−m3​)−1, we can set them equal to each other:

3−m3​ = 6−m3​−1

## Step 4: Solve the equation for m:

3−m3 ​= 5−m3​

## Step 5: Simplify the equation:

-m3​+m3​=5−3

=> 0≠2

Since 0 does not equal 2, there is no value of m that satisfies the equation. Therefore, there is no solution for m in this case.

b) To find the value of m in the function f(2x+1)=x−43x+1​, we need to substitute x with 3m+54​ in the given function and solve for m.

## Step 1: Substitute x with 3m+54​ in the function f(2x+1)=x−43x+1​:

f(2(3m+54​)+1)=(3m+54​)−43(3m+54​)+1​

##Step 2: Simplify the expression on the left-hand side:

f(6m+109​)=(3m+54​)−43(3m+54​)+1​

## Step 3: Since f(6m+109​) is equal to (3m+54​)−43(3m+54​)+1​, we can set them equal to each other:

6m+109​=(3m+54​)−43(3m+54​)+1​

## Step 4: Solve the equation for m:

6m+109​=−9m−162​+1​

##Step 5: Simplify the equation:

6m+109​=−9m−161​

## Step 6: Combine like terms:

6m+9m=−161−109

=> 15m=−270

## Step 7: Divide both sides of the equation by 15:

m=−270/15

##Step 8: Simplify the fraction:

m=−18

Therefore, the value of m that satisfies the equation is -18.

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Answer:

\(l(\overline {AB})\approx9.22\: units\)

Step-by-step explanation:

Answer:

answer is 15 and second one i dont know yet sorry am doing scoo

Step-by-step explanation:

Answer:

83/10 ; 9.01 ; 97/10 ; 9.87

Step-by-step explanation:

Simplify the fractions, and then you can easily see the answer.

Answer: 83/10, 9.01, 97/10, 9.87

Step-by-step explanation:

We can choose to either write all the numbers indecimals or fractions. Let's choose decimals.

83/10=8.30

97/10=9.70

9.87

9.01

Now that we know the decimals, we can put them in order.

8.30, 9.01, 9.70, 9.87

Though this is correct, it is not the answer we are looking for. When we were given the problem, we had fractions. We must change the decimals back into fractions.

83/10, 9.01, 97/10, 9.87

This is our correct answer.

The volume of each of the 3 samples is given as follows:

The density is given by the division of the mass by the volume, hence:

Density = Mass/Volume

The equation can be solved for the volume as follows:

Volume = Mass/Density.

The density of ice is given as follows:

0.9 g/ cm³.

Hence the volume of each sample is given as follows:

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Answer:

-0.5x² + 20x + 100

Step-by-step explanation:

Given:

R = 25x - 0.5x²

C = 100 + 5x

P = R - C

Where,

P = profits

R = Revenue

C = Cost

which expression represents her profit in dollars?

P = R - C

R = 25x - 0.5x²

C = 100 + 5x

= 25x - 0.5x² -(-100 + 5x )

= 25x - 0.5x² + 100 - 5x

= -0.5x² + 20x + 100

The expression which represents her profit in dollars is -0.5x² + 20x + 100

Answer: 10^10

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer: 6 weeks

Step-by-step explanation: $7x6=42

therefore marilyn has to do chores for 6 weeks to get $38

The value of the x in the given angle measures is 28.

What is the right angle triangle?

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.

We have given,

In triangle ABC,

∠ABD = 90

∠ABC = 2x + 1,

∠CBD = 33

In triangle ABC, given that ∠ABD is divided into two angles,

So, ∠ABD = ∠ABC + ∠CBD,

90 = 2x + 1 + 33,

90 = 2x + 34,

2x = 90 - 34

2x = 56

x = 28

Therefore, the value of the x in the given angle measures is 28.

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Step-by-step explanation:

You will do 7+4+3 Bob's money is 7/14×268/1

Fred's money is 4/14×268/1

Geo's money is 3/14×268/1

When you get your answer in all add them all up

Answer:

3 2/3 is the answer

Step-by-step explanation:

Conversion a mixed number 2 3/

4

to a improper fraction: 2 3/4 = 2 3/

4

= 2 · 4 + 3/

4

= 8 + 3/

4

= 11/

4

To find new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/

4

= 8/

4

b) Add the answer from previous step 8 to the numerator 3. New numerator is 8 + 3 = 11

c) Write a previous answer (new numerator 11) over the denominator 4.

Two and three quarters is eleven quarters

Divide: 11/

4

: 3/

4

= 11/

4

· 4/

3

= 11 · 4/

4 · 3

= 44/

12

= 4 · 11 /

4 · 3

= 11/

3

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/

4

is 4/

3

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step , cancel by a common factor of 4 gives 11/

3

.

so you simplify to get 3 2/3