Find the x - and y-intercepts of the graph of the linear equation 3x + 6y = 24.​

Answer:

1. D. Teorema.

2. A. Axioma.

Step-by-step explanation:

En matemáticas, un conjunto de proposiciones que deben estar respaldadas por una prueba adecuada basada en el razonamiento se denomina teorema. Se puede demostrar plenamente que todos los teoremas matemáticos son verdaderos mediante el razonamiento.

Sin embargo, un axión es evidente por sí mismo y no necesita ser probado. Es un hecho ya establecido.

Answer:

1. D. Teorema.

2. A. Axioma.

Step-by-step explanation:

Espero que esto ayude

Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

Answer:

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

Number of eggs purchased:

Cost of eggs:

Number of eggs sold:

Money made:

Profit or loss?

Percent loss:

A graph of the equation y = 2x + 3 is shown in the image attached below.

In order to use the given linear function to complete the table, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = -2, the linear function is given by;

y = 2x + 3

y = 2(-2) + 3

y = -1.

When the value of x = -1, the linear function is given by;

y = 2x + 3

y = 2(-1) + 3

y = 1.

When the value of x = 0, the linear function is given by;

y = 2x + 3

y = 2(0) + 3

y = 3.

When the value of x = 1, the linear function is given by;

y = 2x + 3

y = 2(1) + 3

y = 5.

When the value of x = 2, the linear function is given by;

y = 2x + 3

y = 2(2) + 3

y = 7.

When the value of x = 3, the linear function is given by;

y = 2x + 3

y = 2(3) + 3

y = 9.

In this exercise, we would use an online graphing calculator to plot the given linear function with data points as shown in graph attached below.

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The solution to the equation 3(2 + 3 + 5), 13(9 + 6 - 3), (9 + 6 - 3) ÷ 3, 3(2. 3. 5) and 3 ÷ (9 + 6 - 3)  is 30, 156, 4, 90 and 1/4 respectively

An equation is an expression that shows the relationship between two or more numbers and variables.

a) 3(2 + 3 + 5)

= 3(10) = 30

b) 13(9 + 6 - 3)

= 13(12) = 156

c) (9 + 6 - 3) ÷ 3

= 12 ÷ 3 = 4

d) 3(2. 3. 5)

= 3(30) = 90

e) 3 ÷ (9 + 6 - 3) = 3 ÷ 12 = 1/4

The solution to the equation 3(2 + 3 + 5), 13(9 + 6 - 3), (9 + 6 - 3) ÷ 3, 3(2. 3. 5) and 3 ÷ (9 + 6 - 3)  is 30, 156, 4, 90 and 1/4 respectively

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Answer:

Circumference is about 182.21

Step-by-step explanation:

Use the distance formula to find the radius of the circle with the two coordinates given. The radius of this circle is 29. Plug 29 into the formula 2(pi)r to find the Circumference. The answer is 182.21

The equation of the circle is \(\rm(x-3)^2+(y+2)^2=29^2\).

The equation of the circle is given by;

\(\rm (x-h)^2+(y-k)^2=r^2\)

Where r is the radius and h and k are the centre of the circel.

The radius of the circle is;

\(r=\sqrt{(23-3)^2+(19-(-2))^2} \\\\r=\sqrt{(20)^2+(21)^2} \\\\r=\sqrt{400+441}\\\\r =\sqrt{841}\\\\r=29\)

The equation of the circle is;

\(\rm (x-h)^2+(y-k)^2=r^2\\\\\rm (x-3)^2+(y-(-2))^2=29^2\\\\ (x-3)^2+(y+2)^2=29^2\)

Hence, the equation of the circle is \(\rm(x-3)^2+(y+2)^2=29^2\).

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To calculate the point estimate of a population proportion, collect a representative sample, determine the number of individuals with the characteristic of interest, divide it by the sample size, and the resulting value is the point estimate of the population proportion.

The point estimate of a population proportion is a single value that represents an estimate of the proportion of a certain characteristic in a population based on a sample. To calculate the point estimate, follow these steps:

Collect a representative sample from the population of interest. The sample should be randomly selected to ensure it is unbiased and reflects the population.

Determine the number of individuals in the sample who possess the characteristic of interest. Let's denote this as "x".

Calculate the sample proportion by dividing "x" by the sample size, denoted as "n". The sample proportion is the estimated proportion of the characteristic in the sample.

Sample Proportion (p-hat) = x / n

The point estimate of the population proportion is equal to the sample proportion. Therefore, the point estimate is the value calculated in step 3.

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The point estimate of a population proportion is calculated by dividing the number of successes in the sample by the sample size.

To calculate the point estimate of a population proportion, you need to follow these steps:

Mathematically, the formula for calculating the point estimate is:

Point Estimate = (Number of Successes in Sample) / (Sample Size)

Remember that the point estimate is just an estimate and may not be exactly equal to the true population proportion. The accuracy of the point estimate depends on the sample size and the variability in the population.

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The function represents exponential decay, meaning that the population is decreasing over time.

Exponential growth and decay are mathematical concepts that describe the increase or decrease of a quantity over time.  

Exponential decay occurs when the rate of decrease of a quantity is proportional to the current value of the quantity.

The formula for exponential decay is given:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the decay rate, and t is the time.

Here we have

The population of a country is modeled by the function

f(x) = 375(1 − 0.002)x.

The given function is f(x) = 375(1 − 0.002)x,

which can be written in form f(x) = a(1 + r)x,

where a = 375 and r = -0.002.

The formula a(1 + r)x represents exponential growth if r is positive and exponential decay if r is negative.

In this case, r = -0.002, which is negative.

Therefore,

The function represents exponential decay, meaning that the population is decreasing over time.

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Answer:

Step-by-step explanation:

The answer would be D. exponential decay

The given function is f(x)=375(1-0.002)^x

It's being raised to a power making it exponential and it's a decay because the function has a -0.002 and not +0.002

The problem involves finding the distance from a given point (12, 14, 1) to the y-z plane. The distance can be determined by finding the perpendicular distance from the point to the plane.

The equation of the y-z plane is x = 0, as it does not depend on the x-coordinate. We need to calculate the perpendicular distance between the point and the plane.

To find the distance from the point (12, 14, 1) to the y-z plane, we can use the formula for the distance between a point and a plane. The formula states that the distance d from a point (x₀, y₀, z₀) to a plane Ax + By + Cz + D = 0 is given by the formula:

d = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)

In this case, since the equation of the y-z plane is x = 0, the values of A, B, C, and D are 1, 0, 0, and 0 respectively. Substituting these values into the formula, we can calculate the distance from the point to the y-z plane.

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The graphs and their inequalities are

The inequalities are given as:

2x - 7y ≤ 14

7x + 2y ≥ 14

2x - 7y ≥ 14

3x + 4y < 6

4x - 3y > 6

3x + 4y > 6

To represent the inequalities on a graph, we use the following guides:

Using the above as a guide, we have:

Graph 1 ⇒ 3x + 4y > 6

Graph 2 ⇒ 2x - 7y ≥ 14

Graph 3 ⇒ 3x + 4y < 6

Graph 4 ⇒ 7x + 2y ≥ 14

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Answer: В. Same distance and same direction

Step-by-step explanation:

A translation is a  rigid transformation that maps each point of the original figure to a new position by the same distance and in the same direction.

It does not change the size or shape of the image.

Thus the correct statement relates to translation is "Same distance and same direction"

Hence, the correct option is B.

Answer:

0.75 cents

Step-by-step explanation:

quarter is 25 cents and nickels are 5 cents so add 25+25+25=75

Step-by-step explanation:

Hope it helps you in your learning process.

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Answer:

0.19148936170212766

Step-by-step explanation:

18/94 = 0.19148936170212766

Answer:

30%

Step-by-step explanation:

the first solution -30% will be 45% and the second solution added by 30% will be 45%

An which direction does heat move?

From an object with a cool temperature to another object with a cool temperature.

From an object with a higher temperature to an object with a lower temperature.

with a lower temperature to an object with a higher temperature.

From an object with a warm temperature to another object with a warm temperature.

Step-by-step explanation:

One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.

Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.

Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.

By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.

With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.

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The graph of a proportional relationship is a line through the origin or a ray whose endpoint is the origin

3. No because it's a line that doesn't go through the origin

4. Yes because it's a line through the origin

5. Yes because 1/3 = 2/6 = 3/9 = 4/12

6. No because 4/2 isn't equal to 8/5

7. Draw a graph just like 4., but change the y-axis

8. a. Let the equation be y = ax. 27 = 3a. a = 9. Therefore the equation is y = 9x.

8. b. 9

8. c. 9 * 5 = 45

9. a. The car travels 25 (> 18) miles per gallon of gasoline.

9. b. 25 * 8 - 18 * 8 = 7 * 8 = 56

Answer:

(a) The best answer for residuals plot (a) is:

A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.

A fanned pattern in the residuals plot suggests that the linear model is not appropriate because the variability of the residuals increases as the values of the explanatory variable increases. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

(b) The best answer for residuals plot (b) is:

B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear.

A curved pattern in the residuals plot suggests that the linear model is not appropriate because the relationship between the variables is not linear. This indicates that the linear model is not capturing all the important features of the data and may not be the best fit for the data.

about 91 % of the players are weighing 245 kg or less than 245kg.

Total number of students = 40 players

Minimum weight = 152 pounds

Third quartile (Q3) = 245

We have to find the percentage of students that are weighing 245 kg or less than it.

About 10 of the intervals out of the 11-coverage interval of the box plot fall between 152 and 254; so,

= (10 / 11) * 100

= 90.90

= about 91 % of the total students are weighing 245 kg or less than it.

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Answer:

4.0

Step-by-step explanation:

In a 30-60-90 right triangle, the ratio of the lengths of the sides is

short leg : long leg : hypotenuse

      1        :      √3    :         2

7 is the long leg.

x is the short leg.

1/√3 = x/7

x√3 = 7

x = 7/√3

x = 4.0

Answer: i think it’s D

Step-by-step explanation:

a. The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30). b. The number of successes (136) and the number of failures 265 should be at least 10. In this case, both criteria are satisfied. c. The z is 2.048. d. If the p-value is larger than the significance level, it would suggest that there is not enough evidence to reject the null hypothesis and conclude that the proportion has not significantly changed.

a. The hypotheses to test if the proportion of genetic abnormalities has increased in recent years can be stated as follows:

Null hypothesis (H₀): The proportion of genetic abnormalities in recent years is equal to or less than the proportion believed in the 1990s (p ≤ 0.30).

Alternative hypothesis (Ha): The proportion of genetic abnormalities in recent years is greater than the proportion believed in the 1990s (p > 0.30).

b. To conduct the hypothesis test, we need to verify if the conditions for performing the test are met. The conditions are as follows:

Random Sample: The study states that the 401 children were randomly selected, so this condition is met.

Independence: The sample should consist of independent observations. If the children were selected randomly and their genetic abnormalities are unrelated to each other, then the independence condition is likely satisfied.

Large Sample Size: For hypothesis tests involving proportions, it is recommended to have a large enough sample size to ensure the sampling distribution is approximately normal. There is no specific threshold, but as a guideline, both the number of successes (136) and the number of failures (401 - 136 = 265) should be at least 10. In this case, both criteria are satisfied.

c. To find the p-value, we need to perform a hypothesis test based on the given data. Since the sample size is large, we can use the normal approximation for the binomial distribution. We calculate the test statistic, which is the z-score for proportions, and then find the p-value.

The formula for the z-score for proportions is:

z = (\(\hat p\) - p₀) / √((p₀ * (1 - p₀)) / n)

where \(\hat p\) is the sample proportion, p₀ is the proportion under the null hypothesis, and n is the sample size.

In this case, \(\hat p\) (sample proportion) = 136 / 401 = 0.339, p₀ (proportion under the null hypothesis) = 0.30, and n (sample size) = 401.

Calculating the z-score:

z = (0.339 - 0.30) / √((0.30 * (1 - 0.30)) / 401)

z = 2.048

To find the p-value associated with this z-score, we look up the area to the right of the z-score in the standard normal distribution table or use statistical software.

d. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or more extreme) assuming the null hypothesis is true. In this case, since we are testing if the proportion of genetic abnormalities has increased, the p-value is the probability of observing a sample proportion as large as or larger than 0.339, given that the true proportion is equal to or less than 0.30.

Without the actual p-value, it is not possible to provide a specific interpretation. However, if the p-value is smaller than the significance level (commonly chosen as 0.05), it would indicate that there is strong evidence to reject the null hypothesis and conclude that the proportion of genetic abnormalities has increased in recent years.

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In the given boundary-value problem, we are asked to set up the set of equations required to solve the problem using the finite difference method. The equation is y" = 2x²y + xy + 2, and we are given the boundary conditions y(1) = -1 and y(4) = 4.

To solve the problem using the finite difference method, we can approximate the second derivative y" using the central difference formula: y" ≈ (yₙ₊₁ - 2yₙ + yₙ₋₁) / h². Substituting this approximation into the original differential equation, we obtain the finite difference equation: (yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2.

For the given boundary conditions, y(1) = -1 and y(4) = 4, we can use these values to form additional equations. At x₀ = 1, we have the equation y₀ = -1. At xₙ = 4, we have the equation yₙ = 4.

In summary, the set of equations required to solve the boundary-value problem by the finite difference method, with the given boundary conditions, would be:

(y₂ - 2y₁ + y₀) / h² = 2x₁²y₁ + x₁y₁ + 2,

(y₃ - 2y₂ + y₁) / h² = 2x₂²y₂ + x₂y₂ + 2,

...

(yₙ₊₁ - 2yₙ + yₙ₋₁) / h² = 2xₙ²yₙ + xₙyₙ + 2,

y₀ = -1,

yₙ = 4.

These equations form a system of equations that can be solved numerically to obtain the solution to the boundary-value problem.

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Answer:

One, Buff Billy's, has a joining cost of $80 and charges $25 a month. The other, Shredded Eddie's, has no joining cost but charges $35 a ...

Step-by-step explanation:

Answer:

2 Ounces.

Step-by-step explanation:

Each rocket must weigh 4 pounds or less.

Therefore: 4 Pounds =16 X 4=64 Ounces

Since Hectors rocket weighs 62 ounces and he cannot exceed 64 Ounces, the weight of the most paint he can use is:

64-62=2 Ounces.

He can use paint that weights at most 2 Ounces.

The answer to the given question is option c) The blocks in this design are the four different litters.

In a block design, the experimental units are grouped into homogeneous sets or blocks based on one or more characteristics that are expected to affect the response variable. The purpose of blocking is to reduce the variability of the response variable by reducing the differences between the experimental units within each block. In this experiment, the four different litters are the blocks. The pigs within each litter are expected to be more similar to each other than to pigs from other litters, so the blocks will reduce the variability of the response variable (e.g. weight gain, feed consumption) by accounting for the differences between the litters. The three different dietary supplements are the treatments that are being compared, and the 24 identical pens are the locations where the treatments are applied.

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The rate of change of the area of the rectangle is 80 mm²/s when the width is 8 mm and the length is increasing at a rate of 10 mm/s.

Let's first recall the formula for the area of a rectangle:

A = l × w

where A is the area, l is the length, and w is the width.

We are given that the length of the rectangle is increasing at a rate of 10 mm per second, and the width is constant at 8 mm. To find the rate of change of the area, we can use the chain rule of differentiation:

dA/dt = (dA/dl) × (dl/dt)

Since the width is constant, we can treat it as a constant and differentiate only the length with respect to time:

dA/dt = w × (dl/dt)

Substituting the given values, we have:

dA/dt = 8 × 10 = 80 mm²/s

Therefore, the rate of change of the area of the rectangle is 80 mm²/s when the width is 8 mm and the length is increasing at a rate of 10 mm/s.

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Answer:

<AEB = 51.2

Step-by-step explanation:

Remark

A straight line has a degree value of 180. There are 3 angles. One of them is 90. The other two must add to 90

Equation

2.7x + 8 + 3.8x - 22 = 90      combine like terms on the left.

6.5x - 14 = 90                        add 14 to both sides

6.5x = 90 + 14

6.5x = 104                              Divide by 6.5

x = 104/6.5

x = 16

<AEB = 2.7*16 + 8

<AEB = 51.2