Find the slope and y-intercept of the equation.

y = 1/2x + 12

m=

b=

Answer:

unooooooooooooooooooooooooooooooooooooooooooo

Step-by-step explanation:

Answer:

About .9332

Step-by-step

This tells us that the probability that a z value is less than or equal to 1.5 is about .9332. Thus, the shaded region is about 93.32% of the entire curve. Let's try another example.

Answer:

love jacobt tremblay

Step-by-step explanation:

If the best player makes 70% of all free throws, then this player would be expected to make 70% of the next 60 free throws, which is 42. (The equation that goes with this is \(\frac{70}{100}=\frac{x}{60}.\))

Similarly, the second-best player would make 65% of 60 throws, which is 39, and the third-best player would make 55% of 60 throws, which is 33.

The length of each side of the triangle is;

The trusses made by the manufacturer have the shape of an isoscelles triangle and as such two congruent sides (PQ ≅ PR) are equal and QR is the third side whose length is 4/3 of the congruent sides.

The perimeter of each truss is 70ft.

Let the length of each congruent side be x ft.

Therefore,

Therefore, Length of QR is; QR = (4/3) x

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Answer:

3/4 or 0.75

----------------------

Given expression

Find its value using logarithm rules:

The rules used above:

The equation of the tangent at the point (1/3, π) is y - π = (-√3/3)(x - 1/3)

Given sec(xy) = 2

We need to find the equation of the tangent to the curve at the point (1/3, π).

Differentiating both sides of the equation with respect to x and using the chain rule, we get

d/dx (sec(xy)) = d/dx (2) sec(xy) * d/dx (xy) = 0 sec(xy) * d/dx (xy) = 0

d/dx (xy) = 0

Using the product rule, we get d/dx (xy) = y + x * dy/dx

d/dx (xy) = y + x * (d/dx (y))

sec(xy) = 2 at (1/3, π) sec(1/3 * π) = 2sec(π/3) = 2

To find the slope of the tangent at the point (1/3, π), we substitutex = 1/3 and y = π in the expression for dy/dx.

dy/dx = y + x * (d/dx (y))= π + 1/3 * dy/dx(1/3, π) = π + 1/3 * (dy/dx)

Putting x = 1/3 and y = π, sec(xy) = sec(π/3) = 2, we get tan(theta) = 1/sec(theta)

tan(π/3) = √3/3

Slope of the tangent = -√3/3

Therefore, the equation of the tangent at the point (1/3, π) is y - π = (-√3/3)(x - 1/3)

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Answer:

1- The range of the runner's heart rate is 60 to 110.

2- The interval where the runner's heart rate is increasing is from second 0 to second 2.

3- The interval where the runner's heart rate is decreasing is not mentioned in the given information.

4- The interval where the runner's heart rate is staying the same is from second 2 to second 4.

5- To create an equation to represent the linear portions between 2 and 3 minutes, we need to first determine the slope of the line. The slope is the change in heart rate (y-value) divided by the change in time (x-value). In this case, the change in heart rate is 80 - 60 = 20 and the change in time is 2 - 0 = 2. Therefore, the slope of the line is 20/2 = 10.

To find the equation of the line, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1). In this case, y1 is the starting heart rate of 60 at time x1 = 0. Substituting these values into the equation, we get: y - 60 = 10(x - 0). Simplifying this equation, we get: y = 10x + 60.

To find the equation of the range between 3 and 4 minutes, we can use the same method. The starting heart rate at time x1 = 3 is 80 and the ending heart rate at time x2 = 4 is above 110. The change in heart rate is 110 - 80 = 30 and the change in time is 4 - 3 = 1. Therefore, the slope of the line is 30/1 = 30. Using the point-slope form of a linear equation, we get: y - 80 = 30(x - 3). Simplifying this equation, we get: y = 30x + 50.

6- It is difficult to determine what is causing the changes in heart rate without more information. Heart rate can be affected by many factors, including physical activity level, age, fitness level, and underlying medical conditions. It is possible that the runner's heart rate increased at the beginning of the interval due to the increased physical activity, and remained constant for the next two minutes because the activity level was sustained. The sudden increase in heart rate at the end of the interval could be due to a variety of factors, such as a burst of energy or a reaction to some external stimulus.

Solution

Firstly, we will find the third angles of both triangles,

The sum of angles in a triangle is 180 degrees.

If we know that two angles of one triangle are 112° and 39°

Let the third angle be x

The third angle is 29 degrees

And two angles of another triangle are 39° and 29°

Let the third angle be y

The third angle is 112 degrees

Two triangles are similar if their corresponding angles are equal.

Since, their corresponding angles are equal

Hence, then the two triangles must be similar (option d)

Answer:

He would be 41

Step-by-step explanation:

Maths go brrrr

Answer:

41

Step-by-step explanation:

Answer:

-5.44

I took the test.

Step-by-step explanation:

=======================================================

Explanation:

The general form of an exponential function is

y = a*b^x

where 'a' is the initial starting amount and b helps determine if we have exponential decay or exponential growth, and how much of it.

We have a = 330 as the initial amount. Since b = 1.06 is larger than 1, this means we have exponential growth. If 0 < b < 1, then we would have exponential decay.

Solving 1+r = 1.06 leads to r = 0.06 = 6%, showing we have a growth rate of 6%

This means that if we started with say 100 people, and the population grew by 6%, then at the end of the time unit (say 1 year), then we'd have 106 people.

The argument to be proven is Δ: ~(x)(Bx ⊃ Dx). This can be demonstrated using a proof by contradiction, assuming the negation of Δ and deriving a contradiction.

To prove Δ: ~(x)(Bx ⊃ Dx), we will use a proof by contradiction. We assume the negation of Δ, which is ((x)(Bx ⊃ Dx)). By double negation, this can be simplified to (x)(Bx ⊃ Dx).

Next, we will introduce a new assumption, let's call it γ, which states (∃x)(Bx • ~Dx). We will aim to derive a contradiction from this assumption.

By using the existential elimination (∃E) rule, we can introduce a specific variable, say c, such that (Bc • ~Dc) holds.

Now, we can apply the universal elimination (∀E) rule to the assumption (x)(Bx ⊃ Dx) using the variable c, which gives us Bc ⊃ Dc.

Using modus ponens, we can combine Bc ⊃ Dc with Bc • ~Dc to derive a contradiction, which negates the assumption γ.

Having derived a contradiction, we can conclude that the negation of Δ: ~(x)(Bx ⊃ Dx) is true, leading to the validity of Δ itself: ~(x)(Bx ⊃ Dx).

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The argument to be proven is Δ: ~(x)(Bx ⊃ Dx). This can be demonstrated using a proof by contradiction, assuming the negation of Δ and deriving a contradiction.

To prove Δ: ~(x)(Bx ⊃ Dx), we will use a proof by contradiction. We assume the negation of Δ, which is ((x)(Bx ⊃ Dx)). By double negation, this can be simplified to (x)(Bx ⊃ Dx).

Next, we will introduce a new assumption, let's call it γ, which states (∃x)(Bx • ~Dx). We will aim to derive a contradiction from this assumption.

By using the existential elimination (∃E) rule, we can introduce a specific variable, say c, such that (Bc • ~Dc) holds.

Now, we can apply the universal elimination (∀E) rule to the assumption (x)(Bx ⊃ Dx) using the variable c, which gives us Bc ⊃ Dc.

Using modus ponens, we can combine Bc ⊃ Dc with Bc • ~Dc to derive a contradiction, which negates the assumption γ.

Having derived a contradiction, we can conclude that the negation of Δ: ~(x)(Bx ⊃ Dx) is true, leading to the validity of Δ itself: ~(x)(Bx ⊃ Dx).

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To find the least squares polynomials of degrees 1 and 2 for the given data points (-2, 0), (0, -2), (2, 1), and (4, 2), we can use the method of least squares regression.

1. Degree 1 Polynomial (Linear):

We need to find the equation of the form y = mx + b. Using the given data points, we can set up a system of equations:

-2m + b = 0

0m + b = -2

2m + b = 1

4m + b = 2

Solving this system of equations, we get m = 0.5 and b = -1.

Thus, the equation of the linear polynomial is y = 0.5x - 1.

2. Degree 2 Polynomial (Quadratic):

We need to find the equation of the form y = ax^2 + bx + c. Using the given data points, we can set up a system of equations:

4a - 2b + c = 0

0a + 0b + c = -2

4a + 2b + c = 1

16a + 4b + c = 2

Solving this system of equations, we get a = 0.25, b = -0.5, and c = -1.

Thus, the equation of the quadratic polynomial is y = \(0.25x^2 - 0.5x - 1.\)

To compute the total error in each case, we calculate the sum of the squared differences between the predicted values from the polynomials and the actual data points.

For the linear polynomial:

Total error = \((0 - (-1))^2 + (-2 - (-1.5))^2 + (1 - 0)^2 + (2 - 0.5)^2\) = 1 + 0.25 + 1 + 2.25 = 4.5

For the quadratic polynomial:

Total error =\((0 - (-1))^2 + (-2 - (-1.5))^2 + (1 - 0)^2 + (2 - 0.5)^2\) = 1 + 0.25 + 1 + 2.25 = 4.5

To graph the data and the polynomials, you can plot the data points (-2, 0), (0, -2), (2, 1), and (4, 2) on a graph, and then plot the linear polynomial y = 0.5x - 1 and the quadratic polynomial y =\(0.25x^2 - 0.5x - 1\).

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To create the desired subplot configuration and plot the given functions, you can use the subplot command along with the plot and title commands in MATLAB. Here's the code:

% Define the x values

x = 0:0.1:2*pi;

% Calculate the y values for each function

y1 = sin(2*x);

y2 = cos(2*x);

y3 = sin(x) + cos(x);

% Create the figure window with subplots

figure;

% Left subwindow

subplot(1,3,1);

plot(x, y1);

title('y1 = sin(2x)');

% Middle subwindow

subplot(1,3,2);

plot(x, y2);

title('y2 = cos(2x)');

% Right subwindow

subplot(1,3,3);

plot(x, y3);

title('y3 = sin(x) + cos(x)');

This code will split the graph window into three subwindows and plot the functions y1 = sin(2x), y2 = cos(2x), and y3 = sin(x) + cos(x) in their respective subwindows. Each subwindow will have a title indicating the corresponding function. The x-axis will range from 0 to 2π with a step size of 0.1.

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Answer:

8/17

Step-by-step explanation:

Cosine is adjacent over hypotenuse (CAH as in SOH CAH TOA) so the ratio would be 8/17

Answer:

672 sq km

Step-by-step explanation:

Area of a regular polygon
\(A = \dfrac{P}{2} \times a\)

P = perimeter of the polygon

a = apotherm which is defined as
The distance from the center of a regular polygon to the midpoint of a side.

The given polygon has 8 sides and each side is 12 km
So the perimeter P = 12 x 8 = 96 km

The apotherm is given as 14 km

So area
\(A = \dfrac{96}{2} \times 14 = 672 \text { sq km}\)

Answer:

This is impossible.

Step-by-step explanation:

The interior angle of a regular polygon is equal to

\( \frac{180(n - 2)}{n} \)

where n is the number of sides.

Setting this equal to 180°,

\( \frac{180(n - 2)}{n} = 180 \\ \\ \frac{n - 2}{n} = 1 \\ \\ n = n - 2 \\ \\ 0 = - 2\)

which is false.

Answer:

The larger van has 23 seats

Step-by-step explanation:

Create a system of Equations:

1. Define variables.

> let x=small van and y=larger van

2. create 2 equations based on the information given.

> y = 6 + x

> 2x + y = 57

3. Use any method to solve

Substitution: 2x + (6 + x) = 57. x=17

                      now plug x in to the original equation to solve for y (the larger van)

                      y = 6 + 17 and y = 23

Elimination: 2y = 12 + 2x

                     y = 57 - 2x

         3y = 69  and y = 23

Answer:

h = 41.25 foot

Step-by-step explanation:

Given that,

Height of a street light = 7.5 feet

It casts a 3-foot-long shadow.

A nearby flagpole casts a 16.5 foot long shadow. We need to find the height of the flag pole. Let the height be h. It can be calculated as :

\(\dfrac{\text{height of street light}}{\text{height of shadow of street light}}=\dfrac{\text{height of flagpole}}{\text{height of shadow of the flag pole}}\\\\\dfrac{7.5}{3}=\dfrac{h}{16.5}\\\\h=\dfrac{7.5\times 16.5}{3}\\\\h=41.25\ foot\)

So, the height of the flag pole is equal to 41.25 foot.

The height of the flag pole is 41.25 feet tall.

Word problems in mathematics are methods used to solve real-life cases. They usually follow a logical approach with the use of arithmetic operations when solving them.

From the parameters given:

Let the height of the flag pole be = x

∴

To determine the height of the flag pole, we have:

\(\mathbf{x = \dfrac{7.5 feet \ tall \times 16.5 \ foot \ long} {3 \ foot \ long} }\)

x = 41.25 feet tall

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Answer:50 %

Step-by-step explanation:

Given

There are 4 girls and 6 boys in a club

Probability of choosing 1 girl and 2 boys is

\(=\dfrac{\text{No of ways of choosing 1 girl and 2 boys }}{\text{No of ways of choosing 3 member out of 10 member}}\)

No of ways of choosing 1 girl and 2 boys\(=^4C_1\times ^6C_2\)

\(P=\dfrac{^4C_1\times ^6C_2}{^{10}C_3}\)

\(P=\dfrac{4\times 15}{10\times 3\times 4}\)

\(P=\dfrac{15}{30}=\frac{1}{2}\)

i.e. \(50\%\)

The probability that one girl and two boys will be chosen from the Spanish club is 50%.

Probability is used to determine the odds that an event would happen. If the event would happen with certainty, it would have a value of 1. If it is certain the event would not happen, it would have a value of 0.

The probability = number of ways of choosing 1 girl and two boys / number of ways of choosing 3 people

(4x15) / (10 x 3 x 4) = 15/30 = 1/2 = 50%

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Answer:

The factors of 27 are 1, 3, 9, and 27 (๑・ω-)～♥”

Answer:

The factor of 27 are: 1, 27, 3, 9

Step-by-step explanation:

Answer:

x + y = 0, so y = -x

3x - 2y = 10, so 3x - 2(-x) = 10

5x = 10

x = 2, so y = -2

Answer:

see explanation

Step-by-step explanation:

The sequence has a common difference between consecutive terms

14 - 18 = 10 - 14 = - 4

This indicates it is an arithmetic sequence with common difference - 4

The given sequence is in arithmetic sequence with common difference -4.

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The sequence is,

⇒ 18, 14, 10,..

Now,

Since, The sequence is,

⇒ 18, 14, 10,..

So, The commo difference is find as;

⇒ 14 - 18 = - 4

⇒ 10 - 14 = - 4

Thus, The common difference is same.

Hence, The sequence is an Arithmetic sequence.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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The value of A that makes the equation true for all values of x is A = \(2x^2\). Answer (E).

To begin, consider the following equation:

\(2^(x/12) = A/12x^2\)

We must determine the value of A that makes this equation true for all x values.

To begin, we can take the natural logarithm of both sides of the equation:

\(2(x/12) = 2(A/12x2)\)

We can simplify the left side of the equation by using the logarithm property that states log(ab) = b*log(a):

(x/12)

\(ln(2) = 2ln(x) - ln(A) (12)\)

Then, on one side of the equation, we can isolate ln(A):

ln(A) = (x/12)

\(2ln(x) + ln(2) + ln (12)\)

With base e, we can now exponentiate both sides of the equation:

A is equal to \(e((x/12)ln(2) + 2ln(x) + ln(12)).\)

To simplify even further, we can use exponent properties to combine the terms with ln:

\(A = 2^(x/12) * (x^2) * 12\)

Simplifying:

\(A = 2x^2\)

Therefore, the value of A that makes the equation true for all values of x is \(A = 2x^2\). Answer (E).

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a. The elasticity at P=18 is -0.6. b. The elasticity at P=18 would decrease if the demand curve shifts parallel to the right.

a. To find the elasticity at P=18, we need to calculate the derivative of Q with respect to P and then evaluate it at P=18.

The demand curve is given by P = 50 - 0.5Q. Solving for Q, we have Q = 100 - 2P.

Taking the derivative of Q with respect to P, we get dQ/dP = -2.

To find the elasticity at P=18, we use the formula: Elasticity = (dQ/dP) * (P/Q).

Plugging in the values, Elasticity = (-2) * (18 / (100 - 2*18)) = -0.6.

Therefore, the elasticity at P=18 is -0.6.

b. If the demand curve shifts parallel to the right, it means that the quantity demanded increases at each price level. In this case, the elasticity at P=18 would decrease in absolute value (become less negative or move towards zero).

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Answer:

5 liters

Step-by-step explanation:

Let x represent the number of liters of the 17% solution, and represent the percentages as decimal values:

0.1(2) + (0.17)(x) = 0.15(x + 2)

Simplify:

0.2 + 0.17x = 0.15x + 0.3

Solve for x:

0.17x = 0.15x + 0.1

0.02x = 0.1

x = 5

So, you would need 5 liters of a 17% solution to get a 15% solution

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5