Find the z-score for the which 50% of the distribution's area lies between -z and z

I'm guessing the equation should read something like

\(7(x^2+y^2) \,dx + 5xy \, dy = 0\)

or possibly with minus signs in place of +.

Multiply both sides by \(\frac1{x^2}\) to get

\(7\left(1 + \dfrac{y^2}{x^2}\right) \, dx + \dfrac{5y}x \, dy = 0\)

Now substitute

\(v = \dfrac yx \implies y = xv \implies dy = x\,dv + v\,dx\)

to transform the equation to

\(7(1+v^2) \, dx + 5v (x\,dv + v\,dx) = 0\)

which simplifies to

\((7 + 12v^2) \, dx + 5xv\,dv = 0\)

The ODE is now separable.

\(\dfrac{5v}{7+12v^2} \, dv = -\dfrac{dx}x\)

Integrate both sides. On the left, substitute

\(w = 7+12v^2 \implies dw = 24v\, dv\)

\(\displaystyle \int \frac{5v}{7+12v^2} \, dv = -\int \frac{dx}x\)

\(\displaystyle \dfrac5{24} \int \frac{dw}w = -\int \frac{dx}x\)

\(\dfrac5{24} \ln|w| = -\ln|x| + C\)

Solve for \(w\).

\(\ln\left|w^{5/24}\right| = \ln\left|\dfrac1x\right| + C\)

\(\exp\left(\ln\left|w^{5/24}\right|\right) = \exp\left(\ln\left|\dfrac1x\right| + C\right)\)

\(w^{5/24} = \dfrac Cx\)

Put this back in terms of \(v\).

\((7+12v^2)^{5/24} = \dfrac Cx\)

Put this back in terms of \(y\).

\(\left(7+12\dfrac{y^2}{x^2}\right)^{5/24} = \dfrac Cx\)

Solve for \(y\).

\(7+12\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}}\)

\(\dfrac{y^2}{x^2} = \dfrac C{x^{24/5}} - \dfrac7{12}\)

\(y^2= \dfrac C{x^{14/5}} - \dfrac{7x^2}{12}\)

\(y = \pm \sqrt{\dfrac C{x^{14/5}} - \dfrac{7x^2}{12}}\)

Answer:

y=x+2

Step-by-step explanation:

use the formula y=mx+c

first u find m which is the gradient 3-1/5-3 = 2/2=1

sub in any point to find the c

5=1(3)+c

c=2

y=1x+2

The vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.

To determine if a vector field is conservative, we need to check if it is the gradient of a scalar function (i.e., a potential function). We can do this by taking the partial derivatives of each component with respect to their respective variables and checking if they are equal:

∂f_x/∂y = 66xy^2
∂f_y/∂x = 66xy^2

Since these partial derivatives are equal, the vector field is conservative. We can then find a potential function by integrating each component with respect to their respective variable:

φ(x,y) = 11x^3y^2 + 11x^2y^2 + C

where C is the constant of integration.

Therefore, the vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.

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Answer:

x = √53

Use the pythagorean theorem to solve for x, which would be c in the equation a^2 + b^2 = c^2.

(a and b are the sides that meet up in a right triangle, c is the hypotenuse. In this case, you are solving for the hypotenuse.)

Step-by-step explanation:

1. Plug in the numbers in the pythagorean theorem.

2^2 + 7^2 = c^2 (remember, each variable is squared)

2. Simplify.

4 + 49 = 53

Since each variable in the pythagorean theorem is squared, the side value would be √53.

yes it's correct............

Answer:

The inequality that can be used to figure out how many cases Sandra is working on is: \(x + 8 > 29\)

Step-by-step explanation:

She is working on "x" cases, then she adds 8 more to that number, therefore it is "x + 8" and we also know that the total number of cases she's working is more than 29, in other words, it is greater than 29. With this in mind we can create the following inequality:

\(x + 8 > 29\)

The inequality that can be used to figure out how many cases Sandra is working on is: \(x + 8 > 29\)

Answer: y = ±√ 0.500 = ± 0.70711

Step-by-step explanation:

Solve  :    2y2-1 = 0  Add  1  to both sides of the equation :                       2y2 = 1 Divide both sides of the equation by 2:                     y2 = 1/2 = 0.500   When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:                        y  =  ± √ 1/2  

Answer:

Answer: y = ± √0.500 = ± 0.70711

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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Answer:

1. 70

2. 110

Step-by-step explanation:

The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.857 or 85.7%.

The random variable X represents the outcome of the first test, where it takes on a value of 1 if the student passes and 0 if the student fails.

Similarly, the random variable Y represents the outcome of the second test, taking on a value of 1 if the student passes and 0 if the student fails. Given that the joint probability of passing both tests is 0.6, we can interpret this as the probability of X=1 and Y=1.

The marginal probability of failing the first test is 0.3, which can be represented as P(X=0). To find the conditional probability of passing the second test, given that the student passed the first test, we use the formula \(P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1).\)

Since we know that \(P(X=1 and Y=1) = 0.6, and P(X=1) = 1 - P(X=0) = 1 - 0.3 = 0.7\), we can substitute these values into the formula:
\(P(Y=1 | X=1) = 0.6 / 0.7\)

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The conditional probability of passing the second test, given that the student passed the first test, is approximately 0.8571 or 85.71%.

The conditional probability of passing the second test, given that the student passed the first test, can be calculated using the formula for conditional probability:

P(Y=1 | X=1) = P(X=1 and Y=1) / P(X=1)

We are given that the joint probability of passing both tests is 0.6, which means P(X=1 and Y=1) = 0.6.

To find P(X=1), we need to use the marginal probability of failing the first test, which is given as 0.3. Since the marginal probability of passing the first test is the complement of failing the first test (i.e., 1 - 0.3 = 0.7), we can say P(X=1) = 0.7.

Now we can substitute these values into the conditional probability formula:

P(Y=1 | X=1) = 0.6 / 0.7

Simplifying this expression, we have:

P(Y=1 | X=1) = 0.8571

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If 2 dice which are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3, then the probability that sum of numbers on them is 6 is 0.1389.

In order to find the probability of getting a sum of 6, we need to count the number of ways we can obtain a sum of 6 and divide by the total number of possible outcomes.

Let us first list all the possible outcomes of throwing these two dice:

The possible outcomes on the are : {(1,1) (1,1) (1,2) (1,2) (1,3) (1,3)

(2,1) (2,1) (2,2) (2,2) (2,3) (2,3)

(3,1) (3,1) (3,2) (3,2) (3,3) (3,3)

(4,1) (4,1) (4,2) (4,2) (4,3) (4,3)

(5,1) (5,1) (5,2) (5,2) (5,3) (5,3)

(6,1) (6,1) (6,2) (6,2) (6,3) (6,3)},

We can see that there are 36 possible outcomes in total.

Now we count the number of ways we can obtain a sum of 6:

The possible case , where sum is "6" are : {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1)},

There are 5 possible ways to obtain a sum of 6.

So, probability of obtaining a sum of 6 is:

P(sum of 6) = number of ways to get a sum of 6 / total number of possible outcomes

= 5/36

= 0.1389

Therefore, the required probability is 0.1389.

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The given question is incomplete, the complete question is

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are thrown and the sum of numbers on them is noted. Find the probability of getting sum 6.

Let's begin by listing out the given information:

Number of students (n) = 20

Amount (a) = $298

The equation that can be used to find the amount of money that each student must raise (m) is given below:

Hence, option D is the correct answer

Answer:

Step-by-step explanation:

Angle 2= 50

angle 1= 180-50= 130 degrees (linear pair (sum 180))

angle 3= 130 degrees (vertically oposite angles are equal)

angle 6= 130 degrees (alternate interior angles)

angle 5= 180-130= 50 degrees (linear pair)

i hope this helps :)

Answer:

n = 6

Step-by-step explanation:

2n - 32 = 10n - 80

2n - 10n = -80 + 32

-8n = -48

-48/-8 = 6

Answer:

mean is 3 median is 3 and mode is also 3

Step-by-step explanation:

brainliest helps

The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

  210 cm²

Step-by-step explanation:

The area of the triangle can be found using the triangle area formula:

  A = 1/2bh

  A = 1/2(12 cm)(35 cm) = 210 cm²

_____

Additional comment

The legs (short sides) of the right triangle are effectively the base and height of the triangle.

The area of the right angle triangle is 210 square centimeters if the side lengths are 12 cm, 35 cm, and 37cm

It is defined as a triangle in which one angle is 90 degrees and the other two angles are acute angles. In a right-angled triangle, the name of the sides are hypotenuse, perpendicular, and base.

We have a right angle triangle with side lengths of 12cm, 35cm, and 36cm

Here the base length b = 12 cm

The height of the right angle triangle h = 35 cm

We know the formula for the area of the right angle triangle is given by:

\(\rm A = \frac{1}{2} bh\)

\(\rm A = \frac{1}{2} \times 12\times 35\)

A = 210 square centimeters

Thus, the area of the right angle triangle is 210 square centimeters if the side lengths are 12 cm, 35 cm, and 37cm

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Answer:

length = 15 cm

Width = 12 cm

Step-by-step explanation:

Let width = w cm

Length = w + 3

Perimeter of rectangle = 54 cm

2 * (length + width) = 54

2 * (w+3 + w) = 54   {Add like terms}

2 *(2w + 3) = 54

2*2w + 2 * 3 = 54

4w + 6   = 54

Subtract 6 form both sides

4w = 54 - 6

4w = 48

Divide both sides by 4

w = 48/4

w = 12 cm

Length = 12 + 3= 15 cm

Answer:

Length = 15cm

Step-by-step explanation:

let width be x

length = x+3

Perimeter = 2(l + b)

Perimeter = 54cm

equating:

2(x + x + 3) = 54

2(2x +3) = 54

4x + 6 = 54

4x = 54 - 6

4x = 48

x = 48/4 = 12

width = x = 12cm

length = x +3 = 12 + 3 = 15cm

Answer:

7. (0, -3) (1,-4) (2,-2)

Answer:

ummmmmmmmmm 22

(kk it's 4)

hope this helped ur education btw

Therefore, Mario's winnings of 177 dollars is approximately 2.92 standard deviations below the mean.

We can calculate the number of standard deviations that Mario's winnings of 177 dollars is from the mean using the formula:

z = (x - μ) / σ

where x is the value we want to convert to standard deviations, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, Mario's winnings of 177 dollars is the value we want to convert to standard deviations, the mean is μ = 323 dollars, and the standard deviation is σ = 50 dollars. Substituting these values into the formula, we get:

z = (177 - 323) / 50

= -2.92

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Answer:

second one just se that cuse I think it is it a fuse fore me

Answer: 500 female students. 2:5 ratio for males means 200 male students. 500 female plus 200 male equals 700 students total. There are three teachers for every 35 students, so 700/35 multiplied by three equals 60 teachers.

Answer:

x=5 or x = -8

Step-by-step explanation:

|2x+3|=13

There are two solutions to this problem, one positive and one negative

2x+3 =13   and 2x+3 = -13

Subtract 3 from all sides

2x+3-3 = 13-3     2x+3-3 = -13-3

2x = 10                2x = -16

Divide each side by 2

2x/2=10/2           2x/2 = -16/2

x = 5                    x = -8

Answer:

answer is $819

Step-by-step explanation:

I did 1073+1108+x/3=1000 Let me know if this is wrong please !

Answer:

alternate interior angles

Step-by-step explanation:

We are looking at angles <3 and <6

which are on opposite sides of a transversal (line crossing through 2 parallel lines)

meaning that those 2 angles are congruent and are alternate interior angles are they are on the inside of this figure.

*Can we see the answer choices?  I'm not sure what they are, meaning I cannot fully help you*

Hope this helps a little! :)

In conclusion Since the coefficient a can be any nonzero constant, there are infinitely many possible graphs of f(x) that satisfy the given conditions.

How to find?

Since the zeros of the polynomial function are 3 - i/4 and 3 + i/4, we know that the function can be factored as:

f(x) = a(x - 3 + i/4)(x - 3 - i/4)

where a is a constant.

To simplify the expression, we can multiply the two factors in the parentheses:

f(x) = a[(x - 3)²2 - (i/4)²2]

Now, we can use the fact that i²2 = -1 to simplify further:

f(x) = a[(x - 3)²2 + 1/16]

This is the vertex form of a quadratic function with vertex (3, 1/16) and minimum value 1/16. Since the coefficient a can be any nonzero constant, there are infinitely many possible graphs of f(x) that satisfy the given conditions.

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Therefore, the probability of finding the first defective apple on or before the fourth trial is approximately 0.475 (rounded to 3 decimal places).

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is the measure of the likelihood or chance that a particular event will occur. Probability is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In probability theory, an event is a set of possible outcomes of an experiment or a process. The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability theory is widely used in various fields such as statistics, physics, economics, finance, computer science, and many others. It provides a powerful tool for making predictions, analyzing data, and making decisions under uncertainty.

Here,

This is an example of a geometric distribution, since we are interested in the number of trials required to achieve the first success (finding a defective apple). Let p be the probability of success (finding a defective apple) on any given trial, which is 0.18 in this case.

The probability of finding the first defective apple on the k-th trial is given by:

P(X = k) = \((1 - p)^{(k-1)} ^\) * p

Therefore, the probability of finding the first defective apple on or before the fourth trial is:

P(X ≤ 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - p)⁽¹⁻¹⁾ * p + (1 - p)⁽²⁻¹⁾ * p + (1 - p)⁽³⁻¹⁾ * p + (1 - p)⁽⁴⁻¹⁾ * p

= (0.82)⁰ * 0.18 + (0.82)¹ * 0.18 + (0.82)² * 0.18 + (0.82)³ * 0.18

≈ 0.475

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When four teachers share three boxes of ninety-six pencils apiece, they each receive seventy-two pencils.

A mathematical "operation" is the process of calculating a value with operands and a math operator. The math operator symbol has predefined rules that must be applied to the given operands or numbers. Addition, subtraction, multiplication, and division are commonly regarded to be the fundamental mathematical operations.

Given

First, we must determine the total number of pencils. This is accomplished by multiplying the number of pencils per box by the number of boxes.

= 96 × 3

= 288

The total number of pencils must then be divided by the number of teachers to calculate how many pencils each teacher will receive.

=288/4

= 72

When four teachers share three boxes of ninety-six pencils apiece, they each receive seventy-two pencils.

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Answer:

42 mi

Step-by-step explanation:

To find the perimeter, just add up all the side lengths.

13 + 14 + 15 = 42

Note this is mi and not mi² since this is not area.

Answer:

i think i know. . if its asking for the perimeter, its talking about around the triangle soooo C

Step-by-step explanation:

I'm sorry if you get it wrong. .