(28 POINTS) write the next three terms in the sequence.

Answer:

51

Step-by-step explanation:

1. Approach

One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.

One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).

2. Find the area of (ABC)

The formula to find the area of a triangle is the following:

\(A=\frac{b*h}{2}\)

Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:

\(A=\frac{b*h}{2}\)

Substitute,

\(A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9\)

3. Find the area of (ACDE)

The formula to find the area of a rectangle is as follows:

\(A=b*h\)

The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:

\(A=7*6\\\\A=42\)

4. Find the area of the total figure

To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:

\(9+42= 51\)

Answer:

B, negative

Step-by-step explanation:

When we look at lines on graphs, we see it from left to right. This can help you remember that if the line gets higher from left to right, it is positive. On the other hand, this line descends from left to right, meaning the slope is negative.

Answer:B

Step-by-step explanation:

The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA

Given original diameter do = 12 mm

Ao = \(\pi\)/4 x 12² = 113.097 mm²

Deformed diameter d =10mm

Ad = \(\pi\)/4 x 10² = 78.54 mm²

Degree of cold work %CW = (Ao - Ad/Ao)X 100

                                             =(113. 097 - 78. 54/113.097) x 100

                                             = 30.56%

% CW is 30.56 %

Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.

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When a thesis test is being performed for a population mean, the probability of a type II error isn't dependent on the sample mean. Option B is the right answer.

A type II error occurs when a null thesis isn't rejected despite it being incorrect. It's worth noting that the threat of making a type II error is affected by several factors, including the sample size, the true population mean, the position of significance, and the variability of the data.

As a result, the larger the sample size, the lower the threat of making a type IIerror.The true population mean also has an impact on the liability of a type II error. As the difference between the true mean and the hypothecated mean grows, the threat of a type II error decreases.

The position of significance is also pivotal in determining the threat of a type II error. As the significance position increases, the threat of a type II error decreases.

So, the correct answer is B

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Since the cost, c, of hiring a contractor to build a patio varies jointly as the area, A. in square feet, of the patio and the price, p. per square foot of the patio tiles, the value of p is: B. $3.25.

Mathematically, a proportional relationship or direct variation can be represented by the following equation:

y = kx

Where:

Based on the information provided, we have the following:

c ∝ Ap

c = kAp

In order to have a proportional relationship and equivalent ratios, the variables c, A, and P must have the same constant of proportionality:

Constant of proportionality (k) = c/AP

Constant of proportionality (k) = 2832/(80 × 2.95)

Constant of proportionality (k) = 12

For the value of p, we have:

p = c/kA

p = 4368/(12 × 112)

p = $3.25

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y= x²+2 x / x²+2

1. Domain: All real numbers

2. Points of Discontinuity: None

3. X-intercepts: x = 0 and x = -2

4. Y-intercept: (0, 0)

5. Removability of Discontinuities: No points of discontinuity

To find the domain, points of discontinuity, and x- and y-intercepts of the rational function y = (x² + 2x) / (x² + 2), we can analyze its different components.

Domain:

The domain of a rational function is the set of all real numbers except the values that make the denominator zero. In this case, the denominator is x² + 2. To find the domain, we set the denominator equal to zero and solve for x:

x² + 2 = 0

This equation has no real solutions since x² is always non-negative. Therefore, the domain of the rational function is all real numbers.

Points of Discontinuity:

In this case, the rational function has no points of discontinuity since the denominator x² + 2 is never zero for any real value of x.

X-intercepts:

To find the x-intercepts, we set the numerator equal to zero and solve for x:

x² + 2x = 0

Factoring out x, we have:

x(x + 2) = 0

Setting each factor equal to zero, we find two x-intercepts:

x = 0 and x = -2

Y-intercept:

To find the y-intercept, we substitute x = 0 into the function:

y = (0² + 2(0)) / (0² + 2)

= 0 / 2

= 0

Therefore, the y-intercept is (0, 0).

Removability of Discontinuities:

Since there are no points of discontinuity in this rational function, there are no removable discontinuities. All points in the domain are defined.

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Answer:

7 blue marbles

Step-by-step explanation:

because 3:7 equals red:blue so blue = 7

To find a parametric equation for the line of intersection of two planes, we need to solve a system of equations formed by the equation of the two planes.

To find a parametric equation for the line of intersection of two planes, we need to solve a system of equations formed by the equation of the two planes. The equation of a plane is given by Ax + By + Cz + D = 0, where A, B, C and D are constants. We can then form a system of equations by equating the coefficients of x, y and z from both equations. Solving the system of equations gives the parametric equation of the line of intersection of the two planes. The parametric equation can be written as x = x0 + at, y = y0 + bt, and z = z0 + ct, where x0, y0 and z0 are constants and a, b, and c are non-zero constants. This equation gives the coordinates of any point on the line of intersection of the two planes, which is determined by the constants x0, y0, z0 and a, b, c.

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The constant of proportionality will be 9.5. Then the correct option is A.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table shows the corresponding connection between the cost for a specific number of cans of golf balls at a driving reach.

Buckets                         3               5             7

Price (dollars)            28.50       47.50      66.50

The constant of proportionality is calculated as,

⇒ 25.8 / 3

⇒ 9.5

The constant of proportionality will be 9.5. Then the correct option is A.

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Answer:

9.5

Step-by-step explanation:

I took the exam and got it right

Answer:

100mi

Step-by-step explanation:

The first law of thermodynamics, mathematically expressed as:

ΔU = Q - W

Where:

ΔU represents the change in internal energy of the system,

Q represents the heat added to the system, and

W represents the work done by the system.

The first law of thermodynamics, also known as the law of energy conservation, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The term "internal energy" (ΔU) refers to the total energy possessed by the system, including the kinetic and potential energy of its molecules. It is a measure of the system's thermal energy.

The term "heat" (Q) represents the transfer of energy between the system and its surroundings due to temperature difference. It is a form of energy transfer that occurs spontaneously from higher temperature regions to lower temperature regions.

The term "work" (W) represents the energy transfer resulting from forces applied to the system, causing displacement. It can take different forms, such as mechanical work, electrical work, or expansion work.

For different scenarios, the explicit form of the energy balance equation can be derived by considering the specific types of work and heat involved in the system. By drawing appropriate schematics, one can identify the relevant forms of work and heat transfer. Examples include:

Adiabatic Process: In this scenario, no heat transfer occurs (Q = 0). The energy balance equation simplifies to ΔU = -W, where the work done by the system contributes to the change in internal energy.

Isothermal Process: In this case, the temperature remains constant (ΔU = 0). The energy balance equation becomes Q = W, indicating that the heat added to the system is fully converted into work.

Isobaric Process: Here, the pressure remains constant. The energy balance equation can be written as ΔU = Q - PΔV, where P is the constant pressure and ΔV is the change in volume. This equation accounts for both heat transfer and work done against the constant pressure.

Therefore, by applying appropriate schematics and considering the specific conditions of a given scenario, one can deduce the explicit form of the energy balance equation and understand the interplay between heat, work, and the change in internal energy.

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Answer:

C. $17.50

Step-by-step explanation:

your first point (3, 52.5) states that Garth made $52.5 for 3 hats, so we divide 52.5 by 3

\(\frac{52.5}{3} = 17.5\)

if you're still skeptical look at the graph and look at where the point lines up perfect with the number of caps sold and income. Our next point would be  (10, 175)

\(\frac{175}{10} = 17.5\)

Answer:

30

Step-by-step explanation:

The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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-4.5,1.5),(0,-2),(-1.2,0)

Answer:

Could you give a more detailed question and or picture

Answer:

A. \(\frac{\frac{1}{4} mile }{22.5 seconds} = 40 mph\)

Step-by-step explanation:

Miles per hour can be written like this:

\(MPH=\frac{miles}{hour}\)

So, the correct way to write this question would be:

\(\frac{\frac{1}{4} mile }{22.5 seconds} = 40 mph\)

If you multiply 22.5 by 4 you get 90, which is 1.5 minutes.

So, a hyena can run a mile in 1.5 minutes.

Divide 60 by 1.5 and you find that the hyena runs 40 miles in 1 hour.

It can't be 90mph. The hyena can't run 60mph because it doesn't run a mile a minute.

Therefore, your answer is A.

I hope this helps!!

- Kay :)

Answer:

Step-by-step explanation:

Answer:

They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.

Step-by-step explanation:

The greatest possible length of time will be "1020 min".

Given:

The average length of time,

= 960

For all 3 computers,

The minimum length of time,

= 930

Let,

Now,

→     \(\frac{930+930+930+x}{3} = 960\)

→  \(\frac{930+930+930}{3} +\frac{x}{3} =960\)

→           \(\frac{3\times 930}{3} +\frac{x}{3} =960\)

→              \(930+\frac{x}{3}=960\)

→                        \(\frac{x}{3} = 960-930\)

→                        \(x = 30\times 3\)

→                        \(x = 90\)

hence,

The greatest possible length of time will be:

=  \(930+x\)

=  \(930+90\)

=  \(1020 \ min\)

Thus the above is the appropriate answer.

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Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.

How to illustrate the exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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The question is incomplete. The complete question is :

A sine function that has an amplitude of 16 units, a period of 5 units,a vertical displacement of 3 units up and a phase shift of 2.5 units left. Graph this function and show each step.

Solution :

The standard form of the sine function is

y = a sin (bx - c) + d

Here given :

Amplitude, a = 16

Period :   \($\frac{2 \pi}{|b|} = 5$\)

            ⇒ \($b = \frac{2\pi}{5}$\)

Phase shift :  \($\frac{c}{b} = 2.5$\)

                   \($\Rightarrow \frac{c}{2 \pi/5}=\frac{5}{2}$\)

                  ∴ \($c = - \pi$\)

The vertical displacement : d = 3 units up

Now substituting a, b, c and d values in the standard form gives :

\($y = 16 \sin \left( \frac{2 \pi}{5}x -(- \pi)\right) + 3$\)

\($y = 16 \sin \left( \frac{2 \pi}{5}x + \pi\right) + 3$\)

The graph is attached below.

Answer:

a ray must be named by its endpoint first then an another point it that the ray goes through

Step-by-step explanation:

a ray has 1 endpoint and it goes through an infinite number of points but you name a ray by naming it's endpoint than a other point which the ray goes through hopes this helps have a nice day and good luck

A) Yes, the sample provides enough evidence to conclude that self - esteem scores for these adolescents are significantly different from those of the general population.

B) The size of the difference measure is 0.22

C)The effect of those activities is small.

The information available from the question:

General population mean (null): \(\mu\) = 50

Population standard deviation : σ =15

Sample mean : (x bar) = n53.8

Sample size n = 100

Level of significance: \(\alpha\) = 0.05

(A) Yes, the sample provides enough evidence to conclude that self - esteem scores for these adolescents are significantly different from those of the general population. This was determined by conducting a one- sample t - test:

The hypotheses are:

\(H_0:\mu=50\\\\H_\alpha :\mu\neq 50\)

Obtain the value of the standard error:

\(SE=\frac{s}{\sqrt{n} }\)

\(SE =\frac{15}{\sqrt{100} }\)

SE = 15/10

SE = 1.5

Apply the value for the standard error to the formula for the t- test statistic:

\(z=\frac{\mu_1-\mu_0}{SE}\\ \\z= \frac{53.8-50}{1.5}\\ \\z=\frac{3.8}{1.5}\\ \\z=2.5333\)

To determine if our test statistic is significant, we must obtain a critical value for comparison. To do so, consult a table for the z - distribution associated with an alpha level of 0.05 for a two - sided test. this should give you a value of 1.96

P(Z< -1.96) + P(Z > 1.96) = 0.05

As our test statistic was more extreme than the critical value, we can confidently reject the null hypothesis.

B)To calculate Cohens d, apply the following formula for a one sample test:

\(d=\frac{\mu_1-\mu_0}{s}\)

\(d=\frac{53.3-50}{15} \\\\d=0.22\)

The resulting value for Cohens d indicates a small effect size.

C) Significant differences were found between the mean of the sample and the mean in the population, allowing us to reject the null hypotheses. Thus, childhood participation in sports, cultural groups, and youth groups does appears to be related to improved self-esteem for adolescents. With a Cohen's d value of 0.22, we conclude, however, that the effect of those activities is small.

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The ball will land 67.381 feet away.

Thus, option (B) is correct.

Given:

v = 62 feet / second

\(\theta\) = 15

h = 2.2 feet

Using the formula

Horizontal range = \(\dfrac{v \;cos\; \theta\; [v \;sin\;\theta + \sqrt{v^2\;sin\;\theta + 2gh]}}{g}\)

Substituting the value back into the formula as

Horizontal range = \(\dfrac{62 \;cos\; (15)\; [62 \;sin\;(15)+ \sqrt{(62\;sin\;(15))^2 + 2g*2.2]}}{g}\)

                            = 67.381 feet

Therefore, the distance is 67.381 feet.

Thus, option (B) is correct.

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The question attached here seems to be incomplete, the complete question is:

A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15", from a height of 2.2 feet. How far away does the ball land in feet? (5 points)

56.372 feet

67.381 feet

60.646 feet

47.293 feet

The required equation can be given as

y = 25 - 0.5x

For the football game marking the school's homecoming, Carly is making flags. Every flag needs 0.5 yards.

Carly purchased 25 yards of fabric in total.

So, Each flag requires 0.5 yards of fabric, and Carly bought 25 yards of fabric.

Also given

The quantity of flags Carly has made, x, determines the number of yards that are left to be covered, y.

The required equation can be given as

y = 25 - 0.5x

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