Tom, Susie, Marilyn, Joe, Erica, Tori, Meredith and Derek are taking water skiing lessons. In how many ways could they line up if:
a.) there are no special conditions (i.e., anyone can be anywhere in the line)?
b.) Tom, Joe, and Derek line up first, but in any order?
c.) Erica wants to go right before Derek?
d.) Joe and Marilyn want to be beside each other but don't care which order?
e.) Tori does not want to go first and Joe does not want to go last?
f.) Tom and Susie do NOT want to be beside each other?
g.) the whole group is standing in a circle rather than a line?
h.) in the line, Erica, Tori and Meredith want to all be beside each other, in any order?

Answer:

B and D

Step-by-step explanation:

It is an Acute triangle because all the angles are acute, meaning all the angles are less than 90°.

It is an Equilateral triangle because all the sides are equal. Shown in the picture, the lines going through all the sides mean that they are all the same length.

Answer:

B and D.

Step-by-step explanation:

the angles are less than 90, making it acute. The triangle has all sides equal, making it an equilateral.

Hope this helps!

Answer:

Sure, here are the answers to your questions:

a. The maximum value of f(x,y) is 674.

b. The point(s) where the function attains its maximum are (-6,3) and (6,3).

c. The minimum value of f(x,y) is -5.

d. The point(s) where the function attains its minimum are (0,0) and (-3,-1).

Here are the steps on how I got the answers:

First, we need to find the critical points of the function. This can be done by finding the points where the gradient is equal to zero.

The gradient of f(x,y) is given by the following vector:

∇f(x,y) = (4x - 4, 6y)

Setting this vector equal to zero, we get the following system of equations:

4x - 4 = 0

6y = 0

Solving this system of equations, we get the following critical points:

(-6,3)

(6,3)

Next, we need to evaluate the function at each critical point and at the boundary points of the domain.

The boundary points of the domain are given by the following points:

(-13,0)

(13,0)

(0,-13)

(0,13)

Evaluating the function at each of these points, we get the following values:

f(-13,0) = -674

f(13,0) = -674

f(0,-13) = -674

f(0,13) = -674

f(-6,3) = 674

f(6,3) = 674

f(0,0) = -5

f(-3,-1) = -5

Finally, we need to compare the values of the function at the critical points and at the boundary points to find the maximum and minimum values.

The maximum value of the function is 674, which is attained at the points (-6,3) and (6,3).

The minimum value of the function is -5, which is attained at the points (0,0) and (-3,-1)

Step-by-step explanation:

Answer:

14.42 units

Step-by-step explanation:

Assuming that this is a right triangle (i.e ∠ACB = 90°), we can use the Pythagorean formula to solve this:

AB² = AC² + BC²

AB² = 12² + 8²

AB = √(12² + 8²)

AB = 14.42 units

Answer:

l9-7l is the answer

Step-by-step explanation:

Answer:

I and j I believe

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Upon examining the graph, you can realize that angle 3x is the same as the angle directly to the left of 9x. Since that makes a straight line, we can realize that that sums up to 180. We call this a linear pair.

so you have:

3x+9x = 12x = 180

x = 15

A important concept to know here is vertical angles. Vertical angles occur when two lines intersect each other. The opposite angles formed at an intersection are congruent, which is why 1 is congruent to 3x.

Therefore, angle 1 is 45 degrees.

Answer:

1250

Step-by-step explanation:

The maximum error in the area is 33.933 sq cm. The relative error is 0.0148. The percent error will be 1.48%.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

1)  A = pi(r²)

dA = 2(pi)r(dr)

= 2(3.14)(27)(0.2) sq cm

= 33.93 sq. cm

2)  Relative error is the above divided by actual area

actual area=3.14*27*27

=2289.06 sq cm

Relative error=0.0148

3) % error -- convert the above to a % by appropriate shifting of decimal point

% error=0.0148*100

=1.48%

The area's largest inaccuracy is 33.933 sq cm. 0.0148 is the relative inaccuracy. There will be a 1.48% error percentage.

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Answer:

The answer is B

Step-by-step explanation:

On the chart it takes it 18,0 to reach the amount of feet above ground.

Answer:

20,000

Step-by-step explanation:

The correct answer is (d) 454, as none of the given options correctly indicates the smallest value of 'n' that satisfies the given condition.

To find the smallest value of n that ensures the error estimate from the Trapezoidal Rule approximation of the definite integral is less than 0.00001, we can use the error formula for the Trapezoidal Rule:

Error ≤ (b - a)^3 * M / (12 * n^2),

where 'a' and 'b' are the limits of integration, 'M' is the maximum value of the second derivative of the integrand function on the interval [a, b], and 'n' is the number of subintervals.

In this case, the limits of integration are from 0 to 8, and the integrand is x + 3. To find the maximum value of the second derivative, we can calculate the second derivative of the integrand function:

f''(x) = 0,

since the second derivative of a linear function is always zero.

Now, we can substitute the known values into the error formula:

0.00001 ≤ (8 - 0)^3 * 0 / (12 * n^2).

Simplifying further, we have:

0.00001 ≤ 0,

which is not possible.

Since the error estimate depends on the maximum value of the second derivative, and in this case, it is zero, the error estimate will always be zero. Therefore, no matter how many subintervals 'n' we choose, the error estimate will not be less than 0.00001.

Therefore, the correct answer is (d) 454, as none of the given options correctly indicates the smallest value of 'n' that satisfies the given condition.

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A(n) IQ test evaluates a child's performance in relation to other kids in terms of how well they can perform specific activities at a specific time.

Each individual IQ exam is made up of a number of smaller questions, and no reading nor writing are required. Some verbal subtests consist of spoken questions with no set time restriction. Other subtests are frequently timed and typically have a visual or spatial focus. It takes one to two hours to give the exam.

115 to 129: Superior or intelligent. 130 through 144: Fairly talented. From 145 through 159: Very talented. Exceptionally talented from 160 to 179.

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The percent error in this measurement would be 16%.

1. Calculate the difference between the measured speed and the actual speed: 5 mph - 4.2 mph = 0.8 mph

2. Calculate the percent error: (0.8 mph / 4.2 mph) x 100 = 19.05%

3. Round to the nearest whole number: 19.05% = 19%

The percent error in this measurement is 19%, which means that the measured speed was 19% higher than the actual speed.

This can be caused by a variety of factors, including the radar gun being set to an incorrect sensitivity, the speed of the ball being too high for the radar gun to accurately measure, or the radar gun not being able to accurately detect the speed of the ball due to environmental factors such as wind or lighting.

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The percentage of the total sales that was donated to charity would be = 5%

Percentage of a value is defined as the representation of a part of the who value per 100 with the use of the symbol %.

The total sales that was realised from the pet store = $7,380.

The total amount that was donated by the store to charity = $369

The percentage of $7,380 that was donated;

= 369/7380× 100/1

= 36900/7380

= 5%

Therefore the percentage of $7,380 that was donated would be = 5%.

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Answer:

59.69 ft (nearest hundredth)

Step-by-step explanation:

The edge of a circular pool is the circumference of a circle

circumference of a circle = \(\pi d\)  (where d is the diameter)

Given diameter = 19 ft

⇒ circumference = 19\(\pi\) = 59.69 ft (nearest hundredth)

Answer:

$31.50

Step-by-step explanation:

3j = $94.50

 j = 94.50 / 3

 j = $31.50

Step-by-step explanation:

a. (13, 6) = (1, 2)

b. (-13, 6) = (2, 2)

c. (13, -6) = (1, 3)

d.(-13, -6) = (2, 3)

Answer:

(13 , 6) in 1st Quadrant

(-13, 6) in 2nd Quadrant

(13 , -6) in 4th Quadrant

(-13, -6) in 3rd Quadrant

-TheUnknownScientist

The glycerin should be used in preparing 5 gallons of the lotion is 3548.4 g. Thus, option D is correct.

According to the statement

we have given that the a vehicle contains 15% v/v of glycerin. and we have to find that the How much glycerin should be used in preparing 5 gallons of the lotion.

So, For this purpose, we know that the

15% v/v means that there will be 15 ml of glycerin in every 100 ml of lotion.

And The conversion would be :

We know that the

In 1 gallon = 3784 ml

5 gallons x 3784 ml = 18,920 ml

And

18,920 ml x 15 ml glycerin/100 ml = 2838 ml of glycerin

And the

Density of glycerin = 1.26 g/ml

So,

2838 ml x 1.26 g/ml = 3548.4 g glycerin.

So, The glycerin should be used in preparing 5 gallons of the lotion is 3548.4 g. Thus, option D is correct.

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Answer:

Step-by-step explanation:

The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.

Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:

Regression 1: y = -5.8x - 6.5, r = -0.7621

Regression 2: y = 2.4x - 14.7, r = 0.809

Regression 3: y = -7.4x - 17.4, r = -0.233

Regression 4: y = -3.4x - 8.5, r = -0.6121

Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.

Answer:

3-\(\frac{1}{3}\)k

Step-by-step explanation:

when using the distributive property multiply 1/3 into everything inside the parentheses.

So your first step is to multiply 1/3 to 9.

\(\frac{1}{3}\) x \(\frac{9}{1}\) keeping in mind that all numbers are divisible by one.

then you get your answer of \(\frac{9}{3}\) which equals 3.

From there you want to distribute the \(\frac{1}{3}\) into k but you don't know what "k" is so you'll have an answer of  \(\frac{1}{3}\)k meaning that k whatever it is. Is being multiplied by the \(\frac{1}{3}\).

12. MATLAB code: `f = (-3*t.^2 + 5*t + 20).*(t < 0) + (3*t.^2 + 5*t).*(t >= 0)`

13. MATLAB function: `function random_values = UniGen(n, a, b); random_values = (b - a) * rand(n, 1) + a; end`

MATLAB code to calculate f(t) using the given equation:

t = -9:0.5:9; % Generate values of t from -9 to 9 in steps of 0.5

f = zeros(size(t)); % Initialize f(t) vector

for i = 1:numel(t)

   if t(i) < 0

       f(i) = -3*t(i)^2 + 5*t(i) + 20;

   else

       f(i) = 3*t(i)^2 + 5*t(i);

   end

end

% Display the results

disp('t    f(t)');

disp('--------');

disp([t' f']);

```

This code generates values of `t` from -9 to 9 in steps of 0.5 and calculates `f(t)` based on the given equation. The results are displayed in a tabular format showing the corresponding values of `t` and `f(t)`.

13. MATLAB function UniGen to generate uniformly distributed random values:

function random_values = UniGen(n, a, b)

   % n: Number of random values to generate

   % a: Start of the interval

   % b: End of the interval

   random_values = (b - a) * rand(n, 1) + a;

end

This MATLAB function named `UniGen` generates `n` random values that are uniformly distributed on the interval `[a, b]`. It utilizes the `rand` function to generate random values between 0 and 1, which are then scaled and shifted to fit within the specified interval `[a, b]`. The generated random values are returned as a column vector.

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Answer: The new car will cost her less the new car will cost her about 11000 The used car will cost her about 3000

Step-by-step explanation:

Answer: The 90% confidence interval for the population mean of the length of text messages is a range of values that is likely to contain the true population mean with a probability of 0.90 (or 90%). Based on the given information, we can calculate the confidence interval as follows:

Standard error of the mean (SE) = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size, and sqrt denotes the square root.

SE = 3 / sqrt(22) ≈ 0.639

Margin of error (ME) = t(α/2, df) × SE

where t(α/2, df) is the critical value from the t-distribution with df degrees of freedom, and α is the level of significance (1 - confidence level).

For a 90% confidence level and 21 degrees of freedom (df = n - 1), the critical value is approximately 1.717.

ME = 1.717 × 0.639 ≈ 1.098

The confidence interval can be calculated as:

CI = sample mean ± ME

= 31 ± 1.098

= (29.902, 32.098)

Therefore, we can say that we are 90% confident that the true population mean of the length of text messages falls between 29.902 and 32.098 characters. In other words, if we were to repeat the sampling process many times and construct a 90% confidence interval for each sample, we would expect 90% of the intervals to contain the true population mean. Additionally, we can interpret the margin of error as the maximum amount that the sample mean is expected to differ from the true population mean, with a probability of 90%.

Step-by-step explanation:

Step-by-step explanation:

To find probability ratio wise

Sports Cars: Total Cars

3 + 3 + 2 = 8 total cars

2 sports cars

Ratio is 2:8

Reduces to 1:4

Answer:

Step-by-step explanation:

probability of an event: number of events that satisfy the criteria/ total number of events

number of events that satisfy the criteria (in this case the number of families with three people)= 200

total number of events= 1000

200/1000= 20%