How to solve the function 4y+x=12

Answer:

a = 1.125

is your compleate full answer

Answer:

the factorised form is 4(8a+9)

Answer:

40   mark Brainliest please

Step-by-step explanation:

15/40

Let the missing number be x .

Then :-

\( \frac{3}{8} = \frac{15}{x} \)

\( 3 \times x = 8 \times 15\)

\(3x = 120\)

\(x = \frac{120}{3} \)

\(x = 40\)

The missing number is 40 .

Let us check it by doing cross multiplication :-

\(3 \times 40 = 15 \times 8\)

\(120 = 120\)

Hence proved the missing number is 40 .

\(therefore \: , \frac{3}{8} = \frac{15}{40} \)

The ODE in terms of u and x only is dx/du = 3tanh(3x)(u + 5)^6 - x^3(u + 5).To solve the given ordinary differential equation (ODE) using the substitution u = y - 5, we need to find an expression for dx/du in terms of u and x.

Starting with the given ODE:

dx/dy = 3tanh(3x)y^6 - x^3y.

We will first express dx/dy in terms of dx/du using the chain rule.

Using the chain rule, we have:

dx/dy = (dx/du) / (dy/du).

To find dy/du, we differentiate the substitution u = y - 5 with respect to u:

du/du = dy/du - 0,

1 = dy/du.

Substituting this into the expression for dx/dy, we have:

dx/dy = (dx/du) / 1,

dx/dy = dx/du.

Therefore, dx/dy can be written as dx/du.

Now, let's rewrite the original ODE using the substitution u = y - 5 and dx/du:

dx/du = 3tanh(3x)(u + 5)^6 - x^3(u + 5).

Thus, the ODE in terms of u and x only is:

dx/du = 3tanh(3x)(u + 5)^6 - x^3(u + 5).

This transformation allows us to solve the ODE in terms of the new variable u and the original variable x, simplifying the problem.

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There are 191 different patterns of mail delivery possible for the 19 houses on the northern side of the street, satisfying the given conditions.

To determine the number of different patterns of mail delivery in this scenario, we can use a combinatorial approach.

Let's consider the possible patterns based on the number of houses in a row that receive mail on the same day: If no houses in a row receive mail on the same day: In this case, all 19 houses would receive mail on different days. We have a single pattern for this scenario.

If one house in a row receives mail on the same day: We have 19 houses, and we can choose one house in a row that receives mail on the same day in 19 different ways. The remaining 18 houses would receive mail on different days. So, we have 19 possible patterns for this scenario.

If two houses in a row receive mail on the same day: We have 19 houses, and we can choose two houses in a row that receive mail on the same day in C(19, 2) = 19! / (2! * (19-2)!) = 171 different ways. The remaining 17 houses would receive mail on different days. So, we have 171 possible patterns for this scenario.

Therefore, the total number of different patterns of mail delivery in this scenario is: 1 (no houses in a row) + 19 (one house in a row) + 171 (two houses in a row) = 191 different patterns.

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The term used to describe events that have no outcomes in common is called "Mutually Exclusive."

Probability is a measure of how likely an event is to occur. The probability of an event ranges from 0 to 1, where 0 means that an event will not occur, and 1 means that an event will certainly occur.

In Mutually Exclusive events, the probability of both events happening at the same time is 0, which means that the outcome of one event completely eliminates the possibility of the outcome of the other event. The probability of getting heads and tails at the same time is 0, as it is impossible for the coin to show both heads and tails at the same time.

In mathematical terms, Mutually Exclusive events are represented by

=> P(A) + P(B) = P(A or B),

where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A or B) represents the probability of either event A or B occurring.

To summarize, Mutually Exclusive events are events that have no outcomes in common and have a probability of 0 of occurring simultaneously.

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Answer to part (A) is y = 42x+9

Answer to part (B) is 98

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

Explanation:

Part (A)

Let's plug x = 0 into the 1st derivative of f(x)

\(f'(\text{x}) = \cos(\pi \text{x}) + \text{x}^5 + 6\\\\f'(0) = \cos(\pi *0) + (0)^5 + 6\\\\f'(0) = 1 + 0 + 6\\\\f'(0) = 7\\\\\)

We'll use that later in the steps below, which show computing the derivative value of h(x) at x = 0.

\(h(\text{x}) = ( f(\text{x}) )^2\\\\h'(\text{x}) = 2( f(\text{x}) )*f'(\text{x}) \ \ \text{ ... chain rule}\\\\h'(0) = 2( f(0) )*f'(0)\\\\h'(0) = 2( 3 )*7\\\\h'(0) = 42\\\\\)

This is the slope of the tangent line to h(x) at x = 0.

Now plug x = 0 into the h(x) function itself, without any derivatives applied.

\(h(\text{x}) = ( f(\text{x}) )^2\\\\h(0) = ( f(0) )^2\\\\h(0) = ( 3 )^2\\\\h(0) = 9\\\\\)

This is the y intercept of the line, i.e. the b value.

We found that

We go from y = mx+b to y = 42x+9 as the equation of the tangent line.

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

Part (B)

In the previous part, we already calculated the first derivative. Differentiate that with respect to x to get the second derivative.

\(h'(\text{x}) = 2( f(\text{x}) )*f'(\text{x})\\\\h''(\text{x}) = \frac{d}{dx}\left[h'(x)\right]\\\\h''(\text{x}) = \frac{d}{dx}\left[2( f(\text{x}) )*f'(\text{x})\right]\\\\h''(\text{x}) = \frac{d}{dx}\left[2( f(\text{x}) )\right]*f'(\text{x})+2*f(\text{x})*\frac{d}{dx}\left[f'(\text{x})\right] \ \ \text{ ... product rule}\\\\h''(\text{x}) = 2f'(\text{x})*f'(\text{x})+2*f(\text{x})*f''(\text{x})\\\\h''(\text{x}) = 2\left(f'(\text{x})\right)^2+2*f(\text{x})*f''(\text{x})\\\\\)

The second derivative is useful to determine where the function is concave up or concave down. And also to determine points of inflection.

The h''(x) function involves f''(x), so we'll need to find the second derivative of the f(x) function.

\(f'(\text{x}) = \cos(\pi \text{x}) + \text{x}^5 + 6\\\\f''(\text{x}) = \frac{d}{dx}\left[\cos(\pi \text{x}) + \text{x}^5 + 6\right]\\\\f''(\text{x}) = -\pi\sin(\pi \text{x}) + 5\text{x}^4\\\\\)

Then plug in x = 0

\(f''(\text{x}) = -\pi\sin(\pi \text{x}) + 5\text{x}^4\\\\f''(0) = -\pi\sin(\pi *0) + 5(0)^4\\\\f''(0) = 0\\\\\)

We have enough info to find h''(0) finally.

\(h''(\text{x}) = 2\left(f'(\text{x})\right)^2+2*f(\text{x})*f''(\text{x})\\\\h''(0) = 2\left(f'(0)\right)^2+2*f(0)*f''(0)\\\\h''(0) = 2\left(7\right)^2+2*3*0\\\\h''(0) = 98\\\\\)

Side notes:

Answer:  205,209

Step-by-step explanation:

We want to find a perfect cube that is closest to the number N = 205,632

A perfect cube number is a number such that the square root is a whole number.

Now, to search this number we must take the square root of N:

n = √(205,632) = 453.47

Now, we can round it down or up and get whole numbers, and the squares of those whole numbers will be perfect squares that are near 205,632, lets start with rounding down.

n = 453

the square of 453 is:

453^2 = 205,209

If instead we round up the  453,47, we would get:

n = 454

and the square will be

n = 454^2 = 206,116

Now, to see which one is closser to N, we can take the differences:

205,632 -  205,209 = 423

206,116 - 205,632 = 484

so if we take n = 453 we are closser no N, then the perfect square that is closest to 205,632 is 205,209

Answer:

The probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.

To solve this problem, we first need to find the expected number of people who will show up on the flight. Since the airline estimates that 96% of people booked will actually show up, we can estimate that 0.96 x 70 = 67.2 people will show up.

Next, we need to find the probability that the number of people who show up will exceed the capacity of the plane, which is 65. To do this, we can use the normal distribution with a mean of 67.2 and a standard deviation of √(70 x 0.96 x 0.04) = 1.63.

We want to find the probability that the number of people who show up is greater than 65. To do this, we can standardize the value of 65 using the formula z = (x - mu) / sigma, where x is the value we want to standardize (65), mu is the mean (67.2), and sigma is the standard deviation (1.63).

z = (65 - 67.2) / 1.63 = -1.35

Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than -1.35 is 0.0885. Therefore, the probability that the number of people who show up will exceed the capacity of the plane is approximately 0.0885, or 8.85%.

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Answer:

I think is The little (D) -12.4.

The number of cups of fruit punch will be equal to 16.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a recipe calls for 3 cups of orange juice for every 4 cups of fruit punch. For 12 cups of orange juice.

Since now the cups of orange juice ratio has been altered, the cups of fruit punch ratio needs to be equally altered as well.

(3 / 4) = ( 12 / x)

x = 48 / 3

x = 16

Now that they are equally altered, the new ratio would be 12:16.

Therefore, the number of cups of fruit punch will be equal to 16.

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Answer:the slope is 2

Step-by-step explanation:

rise over run 2/1

Answer:

2

Step-by-step explanation:

The line rises by 2 and runs by 1.

this equation is error because of -7and 4y two this is not have + or - that's why

The term is dimension reduction.

Dimensionality reduction:

The process of transforming data from a high-dimensional space into a low-dimensional space with the goal of keeping the low-dimensional representation as close as possible to the inherent dimension of the original data is known as dimension reduction. Working with high-dimensional spaces can be undesirable for a variety of reasons, including the fact that the data analysis is typically computationally intractable and that the raw data are frequently sparse as a result of the curse of dimensionality. Dimensionality reduction is frequently used in disciplines like signal processing, speech recognition, neuroinformatics, and bioinformatics that deal with huge numbers of observations and/or variables.

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In inferential statistics, the objective is to determine the probability of the alternative hypothesis being true or the null hypothesis being true.

This involves using sample data to make inferences and draw conclusions about a larger population. By analyzing the data and performing statistical tests, we assess the likelihood of the alternative hypothesis or the null hypothesis being accurate.

The alternative hypothesis represents a claim or statement that contradicts the null hypothesis and suggests that there is a significant relationship or difference between variables. To determine its probability, statistical methods such as hypothesis testing and p-values are employed. These methods evaluate the strength of evidence against the null hypothesis and support the alternative hypothesis when the evidence is substantial.

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The equation of the tangent plane to the surface at the point (4, -4, -144) is z = 6x - 13y - 24.

To find the equation of the tangent plane to the surface z = 1x²+4xy-6y² at the point (4, -4, -144), follow the following steps:

Step 1: Calculate the partial derivative with respect to x.

This gives 2x + 4y.

Step 2: Calculate the partial derivative with respect to y.

This gives 4x - 12y.

Step 3: Plug in the values (4, -4) to find the gradient vector.

So, gradient vector = <12, -52>.

Step 4: Use the formula z - z₀ = ∇f(a, b) · (x - a, y - b)

To find the equation of the tangent plane where,

(a, b) = (4, -4) and ∇f(a, b) = <12, -52>.z - (-144) = <12, -52> · (x - 4, y +4) Simplifying gives z = 6x - 13y - 24.

Therefore, the equation of the tangent plane to the surface at the point (4, -4, -144) is z = 6x - 13y - 24.

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8 less than 3 times a number is at most 30 can be written as 8 < 3N ≤ 30

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation

Since 8 less than 3 times a number is at most 30

Let the number be N

Thus, 8 less than 3 times a number is at most 30 can be written as:

8 < 3×N  ≤ 30

8 < 3N ≤ 30

Note: at most means less than or equal (≤)

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Answer:

y= -1/3x-6

Step-by-step explanation:

The slope is rise over run

The y-intercept is the point where the line crosses the y-axis.

If this helped please consider giving brainliest.

Answer: y=.25x-6

Step-by-step explanation: find the slope with \(m=\frac{y2-y1}{x2-x1}\) and make it \(m=\frac{-6+7}{0-4} =1/4\) or .25

then, convert to y=mx+b form which would be \(y=\frac{1}{4}x-6\) or \(y=.25x-6\)

b standing for y intercept and m standing for slope.

Answer:

443.28

Step-by-step explanation:

Subtract 42.24 from 570.3 three times.

Answer:

1.) 2/3

2.)2 3/17

3.) 16/27

4.)8

5.)1/2

6.)3 3/32

7.) 20/31

8.)1/7 0r 0.142857

Step-by-step explanation:

Answer:

9 quarters

Step-by-step explanation:

From the question

Jesse has $3.40 in quarters and nickels

Quarters = q = number of quarters

1 quarter = $0.25

nickels = n = number of nickels

1 nickel = $0.05

Hence,

0.25q + 0.05n = $3.40 .......Equation 1

The number of nickels is 5 more than 2 times the number of quarters.

n = 2q + 5

0.25q + 0.05n = $3.40 .......Equation 1

0.25q + 0.05(2q + 5) = 3.40

0.25q + 0.10q + 0.25= 3.40

0.35q = 3.40 - 0.25

0.35q = 3.15

q = 3.15/0.35

q = 9

Therefore, Jessie has 9 quarters.

Step-by-step explanation:

so the rate (or ratio) between both currencies is

0.0071 / 1

as you can see, such a rate of ratio is actually a fraction in appearance and handling.

now if we multiply one side by a factor, we need to multiply also the other side by the same factor to keep the value of the fraction overall unchanged.

in our case the right (or bottom) side is multiplied by 5000, as the exchange of 1 Yen is done 5000 times when changing 5000 Yen.

so, we need to multiply also the other side by 5000 to give us the amount of Pound needed to keep the rate (or ratio) unchanged.

so, we get

0.0071/1 × 5000/5000 = 35.5 / 5000

that means he gets £35.5 for his 5000 JPY.

If Itsuki exchanges ¥5,000 JPY at the current exchange rate of £0.0071 GBP to ¥1 JPY, he will receive £35.50 GBP.

If the current exchange rate is £0.0071 GBP to ¥1 JPY, then for every ¥1, you will receive £0.0071. If Itsuki exchanges ¥5,000 JPY, he will receive 5,000 x 0.0071 = £35.50 GBP.

To put it concisely, if Itsuki exchanges ¥5,000 JPY at the current exchange rate of £0.0071 GBP to ¥1 JPY, he will receive £35.50 GBP.

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Confidence intervals are used to estimate the range of values in which a true population parameter is likely to lie.

One example where confidence interval must be used for statistical inference is when we want to estimate the mean or proportion of a population based on a sample.

For instance, if we want to estimate the average weight of adult females in a city, we can take a random sample of 100 women and calculate the sample mean and standard deviation.

We can then construct a 95% confidence interval for the population mean weight using the sample data and statistical formulas.

This interval provides us with a range of plausible values for the population mean weight with a 95% level of confidence. Hypothesis testing is used to determine whether a given hypothesis about a population parameter is supported by the sample data or not.

One example where hypothesis testing must be used for statistical inference is when we want to compare two population means or proportions based on their sample estimates.

For instance, if we want to test whether there is a significant difference in the mean salary between male and female employees in a company, we can take a random sample of 50 male and 50 female employees and calculate their sample means and standard deviations.

We can then use a t-test or z-test to test the null hypothesis that the population means are equal versus the alternative hypothesis that they are not equal.

If the p-value of the test statistic is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference between the two population means at that level of significance.

P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true.

It measures the strength of evidence against the null hypothesis and is used to make a decision about whether to reject or fail to reject the null hypothesis.

A smaller p-value indicates stronger evidence against the null hypothesis and supports the alternative hypothesis.

Typically, a significance level of 0.05 or less is used to determine whether the p-value is statistically significant or not.

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The neutral isotope of selenium (Se) with a mass number of 78 has 34 protons and 44 neutrons.

To determine the number of neutrons, protons, and electrons in a neutral isotope of selenium (Se) with a mass number of 78, we need to consider the atomic structure of selenium.

The atomic number (Z) of an element represents the number of protons in its nucleus. The mass number (A) represents the sum of protons and neutrons in the nucleus. Since selenium has an atomic number of 34 (Z = 34), we know it has 34 protons.

To find the number of neutrons, we subtract the atomic number (protons) from the mass number:

Number of neutrons = Mass number (A) - Atomic number (Z)

= 78 - 34

= 44

Therefore, the neutral isotope of selenium (Se) with a mass number of 78 has 34 protons and 44 neutrons.

In a neutral atom, the number of electrons is equal to the number of protons. Hence, this neutral isotope of selenium with 34 protons will also have 34 electrons.

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The expression 9x2/3 can be written in fraction form as, 18/3

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

9 times 2/3 can be calculated by first converting 9 to a fraction and then multiplying that fraction by 2/3. To convert 9 to a fraction, we write it over 9/1 x 2/3

Next, we multiply the two fractions by multiplying the numerators (the top numbers) together and the denominators (the bottom numbers) together:

⇒ (9/1) x (2/3)

⇒ (9 x 2) / (1 x 3)

⇒ 18/3

So, 9 times 2/3 as a fraction is 18/3.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

A(n) Descriptive statistic allows researchers to represent large amounts of data with just one (or a few) numbers

Descriptive statistics are used to summarize data and make it easier to understand. They can be used to describe the central tendency, variability, and shape of a distribution.

Descriptive statistics can be used to describe data in a variety of ways. For example, they can be used to describe the average height of a group of people, the distribution of grades on a test, or the number of people who voted for each candidate in an election.

Hence, the missing phrase is descriptive.

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Answer:

Step-by-step explanation:

d=rt

d= 55x5.5

d=302.5 mph

Tom travels 302.5 miles at 55 miles/hour for 5.5 hours.

Speed is the rate at which an object is moving with no specified direction and hence it is a scalar quantity.Speeds are generally measured in miles per hour or kilo meters per hour.

According to the given question distance equals rate times time which is

d = rt.

If Tom is moving at a rate of 55 mi/h for 5.5 h find the distance he travelled.

To find the distance he travelled we just have to use the given formula.

∴ d = (55 × 5.5)

d = 302.5 miles.

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