Line g passes through points (1, 1) and (10, 9). Line h is perpendicular to g. What is the
slope of line h?

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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Answer:

cubic-degree of 3

Step-by-step explanation:

its not the first two, because they have way more waves

Answer:

  {2, 3, 5, 7, 11, 13, 17, 19}

Step-by-step explanation:

You want the prime numbers between 1 and 20.

A prime number is whole number divisible only by 1 and itself.

2 is the first prime. It eliminates all even numbers from consideration.

3 is the second prime. It eliminates multiples of 3 from consideration, so we can exclude 9 and 15. (The other multiples of 3 in that range are even.)

The numbers that have not been eliminated so far are all prime. The full list is ...

  {2, 3, 5, 7, 11, 13, 17, 19}

__

Additional comment

When testing a number for primality, one only needs to check prime divisors up to the square root of the number. Here, all numbers less than 25 can be tested for primality by checking their divisibility by 2 and 3.

Answer:

The answer is 2163.57142857 rounded equals 2164 is the answer

Step-by-step explanation:

all you have to do is 15145 divided by 7 and you get your answer then round

Answer:

1 \(\frac{1}{6}\) pounds of candy

Step-by-step explanation:

Add together the fractions by creating a common denominator of 6:

\(\frac{5}{6} + \frac{1}{3}\)

\(\frac{5}{6} + \frac{2}{6}\)

= \(\frac{7}{6}\)

Simplify into a mixed fraction:

= 1 \(\frac{1}{6}\)

So, the girls had 1 \(\frac{1}{6}\) pounds of candy

The width of the original piece of sheet metal is (w^2 - l^2)/(3w + 3l), and the length is (l^2 - w^2)/(3w + 3l).

To solve this problem, we can use the formula for the volume of a rectangular box, which is V = lwh, where l is the length, w is the width, and h is the height.

First, let's find the height of the box. Since we cut squares from each corner, the height of the box is the length of the square that was cut out. Let's call this length x.

The width of the box is the original width minus the lengths of the two squares that were cut out, which is w - 2x.

Similarly, the length of the box is the original length minus the lengths of the two squares that were cut out, which is l - 2x.

Now we can write the volume of the box in terms of x, w, and l:

V = (w - 2x)(l - 2x)(x)

Expanding this expression, we get:

V = x(4wl - 4wx - 4lx + 8x^2)

Simplifying further:

V = 4x^3 - 4wx^2 - 4lx^2 + 4wlx

To find the dimensions of the original piece of sheet metal, we need to maximize this volume. We can do this by taking the derivative of the volume with respect to x and setting it equal to zero:

dV/dx = 12x^2 - 8wx - 8lx + 4wl = 0

Solving for x, we get:

x = (2wl)/(3w + 3l)

Now we can use this value of x to find the width and length of the original piece of sheet metal:

w - 2x = w - 2(2wl)/(3w + 3l) = (w^2 - l^2)/(3w + 3l)

l - 2x = l - 2(2wl)/(3w + 3l) = (l^2 - w^2)/(3w + 3l)

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The expression which is equivalent to (2 cubed) Superscript negative 5 is; (1/2¹⁵)

According to the question;

The expression is therefore; (2³)-⁵

Hence, upon evaluation; it follows that;

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Answer:

A

Step-by-step explanation:

Answer:

120 pizzas

Step-by-step explanation:

Answer:

all of them.

Step-by-step explanation:

Hope this helps!

<3

~nxmbus

Answer: did you ever get the answer?

Step-by-step explanation:

I need it too lol

Answer:

ok so the equation will be

35d+28=203

-28

35d=175

divide by 35

d=5

she drove to work 5 times

Hope This Helps!!!

it's:

\(5 \times {6}^{78} \)

The simplified fοrm οf the inequality is  -5x < -10.

The term "inequality" is used in mathematics tο describe a relatiοnship between twο expressiοns οr values that is nοt equal tο οne anοther. Inequality results frοm a lack οf balance. When twο quantities are equal, we use the symbοl '=', and when they are nοt equal, we use the symbοl. If twο values are nοt equal, the first value can be greater than (>) οr less than (), οr greater than equal tο () οr less than equal tο ().

Here the given inequality is,

=> 7-2( x + 2) <-4 - 3(1 – x)

Nοw simplifying the inequality then,

=> 7-2( x + 2) <-4 - 3(1 – x)

=> 7-2x-4 < -4-3+3x

=> 3-2x < 3x-7

=> -2x -3x < -7-3

=> -5x < -10

Hence the simplified fοrm οf the inequality is  -5x < -10.

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Answer:

SOLUTION??? And btw thanks for free pts...

Step-by-step explanation:

To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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Answer:

n = -4

Step-by-step explanation:

\((\frac{5}{3} )^2^n^+^1 * (\frac{5}{3} )^5 = (\frac{5}{3})^n^+^2\)

in multiplication if the base are same u can add there exponent.

\((\frac{5}{3})^2^n^+^1^+^5 = (\frac{5}{3})^n^+^2\)

base of both sides are equal so their exponent will be equal

2n + 1 + 5 = n + 2

2n + 6 = n + 2

2n - n = 2 - 6

n = -4

It is 8%

Hope I helped

Answer:

8%=0.08 because 0.08 is 8/100 and 8% is also 8/100

Step-by-step explanation:

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The solution to a system of the type x2=A+f(t) must be 22 and is given in:

(a) Eigenvalues: λ = -2, 11. Eigenvectors: (1, 1), (-1, 1).

(b) Particular solution: \(\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)\)

(c) General solution: \(\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}\)

(d) Second linearly independent solution: x = 22t - 23.

Here is the explanation :

(a) The system is of the form x' = Ax + f(t), where A is a 2x2 matrix and f(t) is a 2x1 vector-valued function. The characteristic equation of A is |A - λI| = 0, which in this case gives us λ² + λ - 22 = 0. The eigenvalues are λ = -2 and λ = 11. The eigenvectors corresponding to these eigenvalues are (1, 1) and (-1, 1), respectively.

(b) The particular solution to the system in (a) is given by \(\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + f(t)\).

The function f(t) must satisfy the initial conditions x(0) = (1, -6) and x'(0) = (-2, 1). Using these initial conditions, we can find \(c_1\) and \(c_2\) as follows:

\(\begin{equation}c_1 = \frac{1 - 6}{-2 - 11} = -\frac{1}{13}\)

\(\begin{equation}c_2 = \frac{-2 + 1}{-2 - 11} = \frac{1}{13}\)

Therefore, the particular solution to the system is

\(\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)\)

(c) The general solution to the system is given by \(\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + u\), where u is a particular solution to the system. In this case, we have already found \(\begin{equation}u = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}\).

Therefore, the general solution to the system is \(\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}\).

(d) The system has a repeated eigenvalue of -1, and Fire is one solution to the system. The second linearly independent solution can be found using the method of variation of parameters. In this method, we assume that the second solution is of the form x = vt + w, where v and w are constants to be determined. Substituting this into the system gives us the following equations:

-2v + w = -21

v + 11w = -1

Solving these equations gives us v = 22 and w = -23. Therefore, the second linearly independent solution is x = 22t - 23.

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Work Shown:

a = change in distance = 492-300 = 192 miles

b = change in time = 12 weeks

c = a/b = rate of change of distance over time = speed of growth

c = (192 miles)/(12 weeks)

c = (192/12) miles per week

c = 16 miles per week

In other words, each time a week goes by, Ryan has walked another 16 miles.

For a related math concept, check out the slope formula. The slope represents the rate of change. It's useful for graphing linear equations.

Answer:

y - 1 = (-2/3)(x + 9)

Step-by-step explanation:

Here you are given a point on a line and the slope of the line.  You'll need to apply the "point-slope" formula

y - k = m(x - h) (Memorize this)

Then m = slope = -2/3, h = -9 and k = 1.

Making the appropriate substitutions, we get:

y - 1 = (-2/3)(x + 9)

Answer:

63 mins

Step-by-step explanation:

84 mins ÷ 8 miles = 10.5 mins per mile

6 miles × 10.5 mins = 63 mins

Answer:

the unit cost per rubber tile is $$$$$$$$$$$$$6

Step-by-step explanation:

..

Answer:

8.175$

Step-by-step explanation:

If we do 23+25+(3.25)×2

The sum of all the bought

It will equal to 54.5

So if we do as the waiter planned

We must to 54.5×15%=8.175$

Answer: 63

Step-by-step explanation:

tan(B) = 10/5

B = tan^-1 (10/5)

B = 63.43 ≈ 63

To be 94% confident that the true mean IQ is within 2 points of the sample mean, you must obtain a sample of at least 199 individuals.

To determine how large a sample must be obtained to be 94% confident that the true mean IQ is within 2 points of the sample mean, we will use the following terms: confidence level, margin of error, and standard deviation. We will also need the z-score corresponding to the desired confidence level.

Step 1: Identify the confidence level, margin of error, and standard deviation
Confidence level: 94%
Margin of error: 2 points
Standard deviation (σ): Since it's not provided, we will use a common value for IQ, which is 15 points.

Step 2: Find the z-score corresponding to the 94% confidence level
A 94% confidence level has a z-score of approximately 1.88 (you can find this value in a z-score table or using a calculator).

Step 3: Use the formula for sample size
n = (z * σ / E\()^2\)
n = (1.88 * 15 / 2\()^2\)
n = (28.2 / 2\()^2\)
n = \((14.1)^2\)
n ≈ 198.81

Step 4: Round appropriately
Since we can't have a fraction of a person in a sample, round up to the nearest whole number. In this case, the sample size should be 199.

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a. There are 10 kg salt in the tank after t minutes

b.  After 30 minutes, the amount of salt in the tank is still 10 kg.

a) After t minutes, the amount of salt in the tank can be found by the formula:

Amount of salt = initial amount of salt + (rate of salt in - rate of salt out) x time

The initial amount of salt is 10 kg, and the rate of salt in is 0.01 kg/L x 15 L/min = 0.15 kg/min. The rate of salt out is also 0.01 kg/L x 15 L/min = 0.15 kg/min, because the solution is kept thoroughly mixed. Therefore, the amount of salt in the tank after t minutes is:

Amount of salt = 10 + (0.15 - 0.15) x t = 10 kg

b) After 30 minutes, the amount of salt in the tank is still 10 kg. This is because the rate of salt in and the rate of salt out are equal, and so the amount of salt in the tank remains constant. Therefore, the answer is the same as part (a), which is 10 kg

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(a)The antiderivative of f(x) = 1/x with C=0 is ln|x|.

(b)The antiderivative of g(x) = 5/x with C=0 is 5 ln|x|.

(c)The antiderivative of h(x) = 4 - 3/x with C=0 is 4x - 3 ln|x|.

a. To find the antiderivative of f(x) = 1/x^b, we use the power rule of integration. The power rule states that if f(x) = x^n, then the antiderivative of f(x) is (1/(n+1))x^(n+1) + C. Applying this rule, we get:

∫(1/x^b) dx = x^(-b+1)/(-b+1) + C

Simplifying the above expression, we get:

∫(1/x^b) dx = (-1/(b-1))x^(1-b) + C

Therefore, the antiderivative of f(x) = 1/x^b with C=0 is (-1/(b-1))x^(1-b).

b. To find the antiderivative of g(x) = 5/x^c, we again use the power rule of integration. Applying this rule, we get:

∫(5/x^c) dx = 5/(1-c)x^(1-c) + C

Simplifying the above expression, we get:

∫(5/x^c) dx = (5/(c-1))x^(1-c) + C

Therefore, the antiderivative of g(x) = 5/x^c with C=0 is (5/(c-1))x^(1-c).

c. To find the antiderivative of h(x) = 4 - 3/x, we split the integral into two parts and use the power rule of integration for the second part. Applying the power rule, we get:

∫(4 - 3/x) dx = 4x - 3 ln|x| + C

Therefore, the antiderivative of h(x) = 4 - 3/x with C=0 is 4x - 3 ln|x|.

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