Random variable X is approximately normally distributed with mean 30 and standard deviation 6, and random variable Y is approximately normally distributed with mean 41 and standard deviation 8. If X and Y are independent, which of the following best described the distribution X-Y? Approximately normal with mean -11 and standard deviation 10 Approximately normal with mean -11 and standard deviation 14 Approximately normal with mean 11 and standard deviation 2 Approximately normal with mean 11 and standard deviation 10 Approximately normal with mean 11 and standard deviation 14

Answer:

63

Step-by-step explanation:

so y/3 - 9 = 12, add 9 on both sides and you get y/3 = 21. Then you multiply both sides by 3, y/3 * 3, the 3's cancel out, 21 * 3 = 63. You get y = 63

So basically just do + 9 on both sides then *3 on both sides (do it step by step)

Answer:

Hey! The answer would be 63.

Step-by-step explanation:

First, you have to simplify both sides of the equation.

Next, add 9 to both sides.

And finally, multiply both sides by 3.

following these steps will leave you to the answer:

Y= 63

hope this helps!

The difference of two Fractions can also be  a fraction,the result is always a rational number.

(a) The sum of two rational numbers is always true. When we add two rational numbers, the result is also a rational number. This is because rational numbers can be expressed as the ratio of two integers, and the sum of two fractions can be written as a fraction as well.

(b) The product of a rational number and an irrational number is sometimes true. The product of a rational number and an irrational number can result in either a rational or an irrational number, depending on the specific numbers involved. For example, if we multiply the rational number 2/3 by the irrational number √2, the result is (√2 * 2)/3 = (2√2)/3, which is an irrational number. However, if we multiply the rational number 1/2 by the irrational number √4, the result is (√4 * 1)/2 = 2/2 = 1, which is a rational number.

(c) The product of two rational numbers is always true. When we multiply two rational numbers, the result is always a rational number. This is because the product of two fractions can be written as a fraction as well.

(d) The difference between two rational numbers is always true. When we subtract one rational number from another, the result is always a rational number. This is because the difference of two fractions can also be expressed as a fraction.

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It will take 29.4 years for the population of Africa to be two times what it is today. This reflects: doubling time.

Doubling time is the time it takes for a particular amount of size or value to double at a given growth rate. By applying the 70 rules, we can find the doubling time of the exponentially increasing population. To do this, divide 70 by the growth rate (r).

Rule of 70 is a simplified way to determine the doubling time using the equation doubling time = 70 / r. Where r is the percentage growth rate of the population. For example, if the population of 10 species increases by 2 individuals per year, the r value will be 20%.

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Answer:

1) positive 2)negative 3)negative

Step-by-step explanation:

i hope thats what your asking

Answer:

250\(\pi\) which is around 785 cm  (C)

Step-by-step explanation:

Surface area of a cylinder can be found by finding the area of the two circles.

So the diameter of the circle is 10, meaning the radius is 5. (10/2)

\(2 * 5^2\pi\)  = 50\(\pi\)

Multiply by 2 because there are two of these circles.

Now to find the "long part", we find the circumfrence of the circle (\(\pi\)d or 2\(\pi\)r) and multiply it by the height (15)

10\(\pi\) * 15 = 150\(\pi\)

add these two up and you get...

250\(\pi\) which is around 785 cm. (C)

Answer:

Exactly one solution

Step-by-step explanation:

4x -2y = 8

2x +y = 2

Multiply the second equation by 2

4x +2y = 4

Add the two equations together

4x -2y = 8

4x +2y = 4

-------------------

8x = 12

x = 12/8

We know there will be one solution

The equation of the line is 2x - 3y = 19.

The standard form for linear equations is

ax+by = c

From the question, we have

y + 1 = (2/3)(x - 8)

⇒y + 1 = (2/3)x - (16/3)

Multiply by 3 in both sides, we get

⇒3y + 3 = 2x - 16

Subtract 2x from both sides, we get

⇒-2x + 3y + 3 = - 16

⇒-2x + 3y = -16-3

⇒2x - 3y = 19

Linear equations:

First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., only one variable).

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

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Answer:

Step-by-step explanation:

For an equivalent expression for \(18^{-7}\\\) * \(18^5\\\) it is option 4 that is correct that means the equivalent expression can be seen as \(\frac{1}{18} ^{2}\).

Expressions that can be considered are equivalent do the same thing even when they have distinct appearances. When we get to enter the same value(s) for the same variable, two algebraic expressions that are equivalent have the same value (s).

Calculating the equivalent expression,

\(18^{-7}\\\) * \(18^5\\\)

= \(18^{-7+5}\)

=\(18^{-2}\)

=  \(\frac{1}{18} ^{2}\)

An expression that can be considered equivalent to another phrase but then differs in appearance is the one that has the same value or worth. In algebra, we can say 2(2x – 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.

When two expressions can be reduced to a single thread expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. You can also determine whether two expressions are equivalent.

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A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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A linear equation is the equation of a line.The equation which is passing through the point (-1,6) and parallel to the line -2x+y=9 is -2x + y = 8.

A straight line on the coordinate plane is represented by a linear function.

A linear function is a function that varies linearly with respect to the changing variable.

A linear equation in slope y-intercept form is written as,

y = mx + c where m is the slope while c is the y-intercept.

Given equation is -2x+y=9

y = 2x + 9 so slope m is 2.

Since parallel lines have the same slope so equation will be,

y = 2x + c

Substitute,(-1,6)

6 = 2(-1) + c → c = 8

So,

y = 2x + 8 → -2x + y = 8.

Hence "A linear equation is the equation of a line. The equation which is passing through the point (-1,6) and parallels to the line -2x+y=9 is -2x + y = 8".

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The given question is incorrect correct question follows ;

Find the equation of the line passing through the point (-1,6) and parallel to the line -2x+y=9

The equation that shows the correct relationship between the measures of the angles of the two triangles is;

Option D: The measure of angle BCA = The measure of angle C prime A prime B prime

We are told that Triangle ABC is transformed to triangle A′B′C′.

Now,  the triangle ABC and A'B'C' are similar triangles and we know that similar triangles angles are congruent. Thus;

From the given coordinates, we can say that;

∠BAC = ∠B'A'C'

∠ABC = ∠A'B'C'

∠ACB = ∠A'C'B'

Thus, the equation that shows the correct relationship between the measures of the angles of the two triangles is;

The measure of angle BCA = The measure of angle C prime A prime B prime

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For the first series, we can use the Limit Comparison Test by comparing it to the series 1/n^2. Specifically, we will take the limit as n approaches infinity of the quotient of the two series:

lim_n->∞ [(n + 7)/(n^3 - 3n + 3)] / (1/n^2)

= lim_n->∞ [(n + 7)/(n^3 - 3n + 3)] * (n^2/1)

= lim_n->∞ [(n^3 + 7n^2)/(n^3 - 3n + 3)]

Since the numerator and denominator both have degree 3, we can apply L'Hopital's rule:

= lim_n->∞ [(3n^2 + 14n)/(3n^2 - 3)]

= lim_n->∞ [3 + 14/n] / [3 - 3/n^2]

= 3/3 = 1

Since the limit is positive and finite, and the series 1/n^2 is known to converge, the original series also converges.

For the second series, we can use the Limit Comparison Test by comparing it to the series 1/n^2. Specifically, we will take the limit as n approaches infinity of the quotient of the two series:

lim_n->∞ [(n^(k-1))/(n^(k+7))] / (1/n^2)

= lim_n->∞ (n^(k-1) * n^2) / (n^(k+7))

= lim_n->∞ n^(k+1) / n^(k+7)

= lim_n->∞ 1/n^6

Since the limit is positive and finite, and the series 1/n^2 is known to converge, the original series also converges.

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Answer:

70° , 70°

Step-by-step explanation:

The 2 angles are corresponding and are congruent, then

23x + 1 = 4 + 22x ( subtract 22x from both sides )

x + 1 = 4 ( subtract 1 from both sides )

x = 3

Then the angles are

23x + 1 = 23(3) + 1 = 69 + 1 = 70°

4 + 22x = 4 + 22(3) = 4 + 66 = 70°

Answer:

70° & 70°

Step-by-step explanation:

These angles are known as corresponding angles. This means they are congruent.

23x + 1 = 4 + 22x

23x + 1 - 22x = 4 + 22x - 22x

x + 1 = 4

x + 1 - 1 = 4 - 1

x = 3

Substitute the value for the variable.

23(3) + 1 = 70

4 + 22(3) = 70

A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.

A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).

The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.

However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.

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The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

Sampling Distribution: A sampling distribution is a probability distribution of a statistic that is obtained through repeated sampling of a specific population. It describes a range of possible outcomes for a statistic, such as the mean or mode of some variable, of a population.

Given that the sampling distribution of the population proportion is based on a binomial distribution.

The conditions that must be met to use the normal approximation for the confidence level are np>5 and n(1-p)>5

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Answer:

C. sides of 3, 4 and 7

can't form a triangle.

the longest side (7) must be shorter than the sum of the other 2 sides.

Step-by-step explanation:

To find the exact length of the curve defined by the parametric equations x = 5t^2 and y = 3t^3, where 0 ≤ t ≤ 3, we can use the arc length formula for parametric curves.

The arc length formula for a parametric curve defined by x = f(t) and y = g(t) over the interval [a, b] is given by:

L = ∫[a,b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt

In this case, we have x = 5t^2 and y = 3t^3, with the parameter t ranging from 0 to 3.

First, we need to find the derivatives of x and y with respect to t:

dx/dt = d/dt (5t^2) = 10t

dy/dt = d/dt (3t^3) = 9t^2

Next, we substitute these derivatives into the arc length formula:

L = ∫[0,3] √[ (10t)^2 + (9t^2)^2 ] dt

L = ∫[0,3] √(100t^2 + 81t^4) dt

Now, we can integrate the expression inside the square root with respect to t:

L = ∫[0,3] √(100t^2 + 81t^4) dt

L = ∫[0,3] t√(100 + 81t^2) dt

Unfortunately, this integral does not have a simple closed-form solution. We would need to evaluate it numerically using numerical integration techniques or computer software.

So, the exact length of the curve cannot be determined algebraically. However, it can be approximated using numerical methods.

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The expression that is equivalent is 6(y + 1) and 6y + 6.

The expression that are not equivalent are 3(x + 3) and 3x + 6 and x(x + 4) and x² + 4.

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent algebraic expressions are those expressions which on simplification give the same resulting expression.

Now, let's check if the expression are equivalent by simplifying it.

3(x + 3) and 3x + 6

3x + 9 and 3x + 6

Therefore, the expressions are not equivalent.

6(y + 1) and  6y + 6

6y + 6 and 6y + 6

They are equivalent expression.

x(x + 4) and x² + 4

x² + 4x and x² + 4

They are not equivalent expression.

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f(-a) is the remainder when f(x) is divided by (x+a). This can be obtained by remainder theorem for polynomials.

Given that f(x) is divided by (x+a) and leaves a reminder

Using the remainder theorem for polynomials we get,

f(x) = (x+a)·g(x) + r, where g(x) is the quotient and r is the remainder.

Put x = -a, then

f(-a) = (-a+a)·g(-a) + r

f(-a) = (0)·g(x) + r

f(-a) = r

f(-a) is the remainder.

Hence f(-a) is the remainder when f(x) is divided by (x+a).

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Answer:

The coordinates of the vertices of the original triangle are (-4, 2), (2, 4), and

(-2, -2).

To obtain the new triangle, subtract 2 from each x-coordinate, and subtract 4 from each y-coordinate. So the coordinates of the vertices of the new triangle are (-6, -2), (0, 0) and (-4, -6). Draw the new triangle.

Answer:

hi sh Sheet sh I monorailg Jericho improve Odom Ybor

Answer:

To make such a frequency distribution table, first, write the class intervals in one column. Next, tally the numbers in each category based on the number of times it appears. Finally, write the frequency in the final column. A frequency distribution table drawn above is called a grouped frequency distribution table.

Answer:

-8

Step-by-step explanation:

5(-4)-(4)+8

-20+4+8

-20+12

-8

Answer:

(-8)

Step-by-step explanation:

Question :

5x - x + 8

First you can solve the equation simply like this.

5x - x + 8

4x + 8

Now they've given that,

x = (-4)

Now, you have to put -4 instead of x and solve the equation.

Let us solve now.

4 x + 8

4 × (-4) + 8

-16 + 8

(-8)

Hope this helps you :-)

Let me know if you have any other questions :-)

See attachment for math work and answer.

Answer: 3

Step-by-step explanation: 2 * 3 equals 6 and 6+4=10

Hopefully I did that right I am sorry if I didn't

Answer:

x = \(\frac{3}{4}\)

Step-by-step explanation:

Given

\(\frac{3}{4(x+2)}\) = \(\frac{x}{x+2}\)

multiply numerator/ denominator of \(\frac{x}{x+2}\) by 4, thus

\(\frac{3}{4(x+2)}\) = \(\frac{4x}{4(x+2)}\)

Since the denominators are common , equate the numerators, that is

4x = 3 ( divide both sides by 4 )

x = \(\frac{3}{4}\)