Rearrange the equation to solve for the variable p.
m (p + 7) = 11

Answer: 26

Step-by-step explanation:

42+10= 52 , 52-3=49

75-49= 26

To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

To determine the magnitude and direction of the force F and the reactions at points A and D in the given loaded truss, we need to analyze the equilibrium of forces. Based on the given information, the resultant force R is directed to the right with a magnitude of 12.4 kN. Here's how we can approach the problem:

Resolve Forces: Resolve the applied forces into their horizontal and vertical components. Let's label the forces as follows:Force at point A: F_A

Force at point B: F_B

Force at point C: F_C

Force at point D: F_D

Equilibrium in the Vertical Direction: Since the truss is in equilibrium, the sum of vertical forces must be zero.

F_A * cos(30°) - F_C = 0 (Vertical equilibrium at point A)

F_B - F_D = 0 (Vertical equilibrium at point D)

Equilibrium in the Horizontal Direction: The sum of horizontal forces must be zero for the truss to be in equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R (Horizontal equilibrium)

Determine the Reactions: Solving the equations obtained from the equilibrium conditions will allow us to find the values of F_A, F_B, and F_D, which are the reactions at points A and D.

Calculate Force F: Once we know the reactions at A and D, we can calculate the force F using the equation derived from the horizontal equilibrium.

F_A * sin(30°) + F_B - F_C * cos(60°) = R

The size of the structure is necessary to determine the forces accurately. The dimensions and geometry of the truss, along with the loads applied, affect the magnitude and direction of the reactions and the forces within the truss members. Without the size of the structure, it would be challenging to determine the accurate values of the forces and reactions.

To obtain precise calculations and solutions, it would be helpful to have the dimensions and geometry of the truss and any other relevant information provided in the problem statement or accompanying diagram.

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Answer:

x = 112°

Step-by-step explanation:

The missing two internal angles of the triangle measure:

\(180-126=54^{0}\)

\(180-58-54=68^{o}\)

then:

\(x=180-68=112^{o}\)

Hope this helps

To find the length of the arc on the circle determined by the central angle of 3 radians, we can use the formula  the length of the arc on the circle determined by the central angle of 3 radians is 3 centimeters.

Radian is a unit of measurement for angles. It is defined as the angle subtended at the center of a circle by an arc of the circle that is equal in length to the radius of the circle. In other words, an angle of 1 radian is the angle that corresponds to an arc length equal to the radius of the circle.Measurement is the process of assigning a numerical value to a physical quantity, such as length, volume, weight, or temperature, by using a suitable measuring instrument or technique. The result of a measurement is expressed in a unit of measurement, which is a standardized quantity used to quantify the physical quantity being measured. Common units of measurement include meters, liters, grams, and degrees Celsius. Accurate measurement is essential in many fields of science and engineering, as well as in everyday life.

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In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):

fy(a,b) = lim┬(y→b)⁡〖[f(a,y) - f(a,b)]/(y - b)〗

Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

To see why this is the case, consider the following argument:

Let L be the limit in the expression given above.

Let h = y - b be the change in the y-coordinate from b to y.

Then, we can rewrite the limit as:

fy(a,b) = lim┬(h→0)⁡〖[f(a,b + h) - f(a,b)]/h〗

This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].

As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).

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The set that contains all the roots of the polynomial is given by:

C. {-3/2, 0,1}

They are the values of x for which F(x) = 0.

In this problem, the polynomial is given by:

F(x) = 2x³ + x² - 3x.

Hence:

2x³ + x² - 3x = 0.

2x(x² + 0.5x - 1.5) = 0.

2x = 0 -> x = 0.

x² + 0.5x - 1.5 = 0 -> (x + 1.5)(x - 1) = 0.

Then, this means that the other two roots are:

Hence the correct option is:

C. {-3/2, 0,1}

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Answer:

I think H because it is the only one going vertical

Step-by-step explanation:

The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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Answer:

In order, top to bottom:

(-3,6)

(-2,1)

(0,-3)

(2,1)

(3,6)

Step-by-step explanation:

All you have to do is plug the X given into the equation provided to find Y, y=x^2-3.

For the first row, you're given -3 for X, so you plug that into the equation.

y=(-3)^2-3 So, -3^2 is just (-3) times (-3) which equals 9. Then you subtract 3 from 9 which gives you 6. So your Y=6 for the first row. And, you do the same thing for the rest of the rows. Just plug X in and solve. Anything raised to the second power is just that number multiplied by itself like I did with the -3.  

We can say that Raymond's claim of an average typing speed of 89 words per minute may be underestimated based on the sample data collected.

In this scenario, the term "average" refers to Raymond's claimed typing speed of 89 words per minute, while "sample" refers to the 15 trials that Raymond conducted during his practice session. To determine whether there is sufficient evidence to conclude that Raymond's mean typing speed is greater than 89 words per minute, we need to conduct a hypothesis test. Our null hypothesis (H0) is that Raymond's mean typing speed is equal to 89 words per minute, while our alternative hypothesis (Ha) is that his mean typing speed is greater than 89 words per minute. We can use a one-sample t-test to test this hypothesis. Using the sample data provided, we can calculate the t-statistic as follows:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is 95.5, the population mean (based on Raymond's claim) is 89, the sample standard deviation is unknown, and the sample size is 15. However, since we are assuming that the population standard deviation is unknown, we will use a t-distribution with 14 degrees of freedom.
Using a t-table (or calculator), we can find the critical t-value for a one-tailed test with 14 degrees of freedom and a 1% significance level to be 2.977. If our calculated t-statistic is greater than this critical value, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.
Plugging in the values from our sample data, we get:
t = (95.5 - 89) / (sample standard deviation / sqrt(15))
We don't know the sample standard deviation, but we can estimate it using the sample standard deviation formula:
s = sqrt(sum((xi - x)^2) / (n - 1))
where xi is the typing speed for trial i, x is the sample mean, and n is the sample size. Using the data provided, we get:
s = sqrt((sum((xi - 95.5)^2)) / (15 - 1))
s = 9.9
Plugging this value into our t-statistic equation, we get:
t = (95.5 - 89) / (9.9 / sqrt(15))
t = 3.57
Since this calculated t-statistic is greater than our critical t-value of 2.977, we can reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that Raymond's mean typing speed is greater than 89 words per minute. Therefore, we can say that Raymond's claim of an average typing speed of 89 words per minute may be underestimated based on the sample data collected.

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Answer:

6/35

Step-by-step explanation:

20/35 - 14/35= 6/35

Answer:

0.1214 or 6/35

Step-by-step explanation:

didn't know if they were whole numbers with division signs or fractions

Answer:

  3

Step-by-step explanation:

You want the greatest of three consecutive odd integers that have a sum of 3.

The average of the integers is their sum divided by their number:

  average = 3/3 = 1

This is the value of the middle of the three integers, so they are ...

  -1, 1, 3

The greatest of the three is 3.

Answer:

complex

Step-by-step explanation:

Answer:

pretty sure it's compound

Step-by-step explanation:

a) The area of the surface of the water in the pool is 100,000 square feet.

b) The pool holds 1,000,000 cubic feet of water when filled to the top.

a) To find the area of the surface of the water in the pool, we can simply multiply the length and width of the pool:

Area of surface of water = length x width

= 1,000 ft x 100 ft

= 100,000 square feet

So, the area of the surface of the water in the pool is 100,000 square feet.

b) To find how much water the pool holds, we need to calculate its volume. The volume of a rectangular prism (like a swimming pool) is calculated by multiplying its length, width, and height

Volume of pool = length x width x height

= 1,000 ft x 100 ft x 10 ft

= 1,000,000 cubic feet

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The given question is incomplete, the complete question is:

A large rectangular swimming pool is 1,000 feet long, 100 feet wide, and 10 feet deep. The pool is filled to the top with water.

a) What is the area of the surface of the water in the pool?

b) How much water does the pool hold?

Answer:

M = 3

Step-by-step explanation:

slope formula = change in y/change in x

(10-7)/(2-1) = 3/1

3/1 = 3

slope = 3

The statistical formula to determine degrees of freedom is quite simple. It states that degrees of freedom equal the number of values in a data set minus 1, and looks like this:

df = N-1

N is the number of values in the data collection, in this case (sample size). View the illustration of the computation.

If there are four data sets, then N = 4.

Create a list with the values for each data and give the data set the name X.

Set X for this example data consists of: 15, 30, 25, 10.

The mean, or average, for this set of data is 20. By combining the values and dividing by N, find the mean:

(15+30+25+10)/4= 20

The degrees of freedom would be determined using the formula as follows: df = N-1:

In this case, it appears that df = 4-1 = 3.

This demonstrates that three numbers in this set of data are flexible as long as the mean stays constant at 20.

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Considering the confidence interval given, the likely difference is given by:

\(\frac{0.064 + (-0.014)}{2} = 0.025\)

Given an interval (a,b), the point estimate is the mean of the bounds, that is:

p = (a + b)/2.

In this problem, the interval is (-0.014, 0.064), hence the expression for the likely difference is given by:

\(\frac{0.064 + (-0.014)}{2} = 0.025\)

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Answer:

The answer is 9

Step-by-step explanation:

The answer is 9

By multiplying Equation 2 by 6, Yumiko ensures that the coefficient of "x" in both equations is 12, allowing her to add the equations and eliminate the "x" variable.

To eliminate a variable when adding the equations, Yumiko needs to multiply both sides of the other equation by a factor that will make the coefficients of one of the variables the same in both equations. Let's consider the system of equations:

Equation 1: 2x - 3y = 12

Equation 2: ax + by = c

Since Yumiko multiplied Equation 1 by 6, it becomes:

6(2x - 3y) = 6(12)

12x - 18y = 72

To eliminate the variable "x" when adding these equations, we need the coefficient of "x" in Equation 2 to be 12. Therefore, the factor by which Yumiko should multiply both sides of Equation 2 is 6.

6(ax + by) = 6(c)

6ax + 6by = 6c

Now, when we add Equation 1 and the modified Equation 2, the "x" terms will eliminate each other:

(12x - 18y) + (6ax + 6by) = 72 + 6c

(12x + 6ax) + (-18y + 6by) = 72 + 6c

(12 + 6a)x + (-18 + 6b)y = 72 + 6c

By multiplying Equation 2 by 6, Yumiko ensures that the coefficient of "x" in both equations is 12, allowing her to add the equations and eliminate the "x" variable.

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note the full question may be:

A carpenter is building a rectangular table with a length of 4 feet and a width of 3 feet. If the carpenter wants to increase the dimensions of the table by a factor of 2, what should be the new length and width of the table?

Answer:

20.62 feet

Step-by-step explanation:

The ladder propped against a building forms a right angle triangle

Height of the ladder (hypotenuse) = 21 feet

Base of the ladder from the building (adjacent) = 4 feet

Height of the building (opposite) = x feet

Hypotenuse ² = opposite ² + adjacent ²

21² = x² + 4²

21² - 4² = x²

441 - 16 = x²

425 = x²

x = √425

= 20.62 feet

Answer: 20.62 ft or rounding it to 20.6 ft

Step-by-step explanation:

Answer:

Time in air is 7.5 s.

Step-by-step explanation:

initial height, h = 0.125 feet

initial velocity, u = 80 ft/s

final height, h' = 5 ft

acceleration due to gravity, g = 32 ft/s^2

Let the time is t to reach the maximum height.

v = u - gt

0 = 80 - 32 t

t = 2.5 s

Let the time is t' from top to ground.

\(s = u t + 0.5 gt^2\\\\5 = 80 t - 16 t^2\\\\16 t^2 - 80 t + 5 = 0 \\\\t = \frac{80\pm\sqrt{6400 - 320}}{32}\\\\t = \frac{80\pm78}{32}\\\\t = 5 s or 0.0625 s\)

So the tie is 5 s

The time in air is

T = 2.5 + 5 = 7.5 s  

Answer: a) 26.2 cm

Step-by-step explanation:

Perimeter of rectangle = 2 (l + w)

2 (l + w) = 2 (9 + 4.1) = 2 (13.1) = 26.2 cm

Hope this helps!

Answer: The y-intercept is 1

Step-by-step explanation:

On a graph, the y-intercept is the point where the line intersects the y-axis. The corresponding x-coordinate is always 0. ... When a linear equation is written in slope-intercept form (y=mx+b), the slope is represented by the variable m. It is the coefficient to x in the equation.

Y intercept

The point on y axis at which the line intersects the y axis is called the y intercept of line

Here

The point is (0,1)

So y intercept=1

Answer:

C. $17.00

Step-by-step explanation:

The mathematicians credited with developing the mathematical models that predict population growth in each of two competing species are Rosenzweig and MacArthur(OPTION A).

These two scientists developed a theory known as the "competitive exclusion principle," which states that two species competing for the same resources cannot coexist indefinitely. Instead, one species will eventually outcompete and displace the other species.
Rosenzweig and MacArthur's model is based on the Lotka-Volterra equations, which are a set of differential equations that describe the dynamics of predator-prey relationships. They extended this model to include two competing species and developed the concept of the "ecological niche" – the specific set of environmental conditions under which a species can survive and reproduce.
Their model predicts that the two species will reach a stable equilibrium, where their populations remain relatively constant over time. However, the exact outcome of the competition depends on several factors, including the initial population sizes of the two species, the relative strengths of their ecological niches, and the availability of resources.
Overall, Rosenzweig and MacArthur's mathematical model has been influential in the field of ecology, providing a framework for understanding how competing species interact and how ecosystems evolve over time.

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Answer:

a) - 10m

b) - $5000

c) - 40°

d) + $2000

Step-by-step explanation:

I hope this help you

Answer:

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

Why?

Point slope form is written as (y-y1) = m(x-x1) with y1 being the value of y at a certain point, x1 being the value of x at a certain point, and m being slope. y1 and x1 are given to us by the point (-3, -2) letting us know that y1=-2 and x1=-3. The only thing left to find is slope. Parallel lines have the same slope. If the line we are trying to find is parallel to the one given in the question, we just need to find the slope of the equation given. That equation is given in slope-intercept form which is y = mx + b. m is still slope so we can see that the slope is 1/2. Now we can plug m, x1 and y1 into the point slope form equation to get y + 2 = 1/2(x + 3)

The area of the triangle is 5/2 square units

The area of a shape is the amount of space on the shape

For most regular quadrilaterals, you multiply the side lengths to determine the area

The coordinates of the triangle are given as

P(1, 1), Q(-2, 1) and  R(-1, -4)

The area of the triangle is calculated as

Area = 1/2 * |Px(Qy - Ry) + Qx(Py - Ry) + Rx(Py - Qy)|

So, we have

Area = 1/2 * |1 * (1 + 4) - 2(1 + 4) - 1(1 - 1)|

Evaluate

Area = 1/2 * 5

This gives

Area = 5/2

Hence, the area of the triangle is 5/2 square units

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The solution of v = (17 - b) / (a + 4)

1. Start with the given equation: av + 17 = -4v - b.

2. Move all terms containing v to one side of the equation: av + 4v = -17 - b.

3. Combine like terms: (a + 4)v = -17 - b.

4. Divide both sides of the equation by (a + 4) to solve for v: v = (-17 - b) / (a + 4).

5. Simplify the expression: v = (17 + (-b)) / (a + 4).

6. Rearrange the terms: v = (17 - b) / (a + 4).

Therefore, the solution for v is (17 - b) / (a + 4).

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