For a normal distribution mean is _______ to median.

Answer:

(0,0) is a saddle point

(-4,4) is a local maximum

Step-by-step explanation:

\(\displaystyle z=3x^3-36xy-3y^3\\\\\frac{\partial z}{\partial x}=9x^2-36y\\\\\frac{\partial z}{\partial y}=-36x-9y^2\)

Determine critical points

\(9x^2-36y=0\\9x^2=36y\\\frac{x^2}{4}=y\)

\(-36x-9y^2=0\\-36x-9(\frac{x^2}{4})^2=0\\-36x-\frac{9}{16}x^4=0\\x(-36-\frac{9}{16}x^3)=0\\\\x=0\\\\-36-\frac{9}{16}x^3=0\\-36=\frac{9}{16}x^3\\-64=x^3\\-4=x\)

When x=0

\(9x^2-36y=0\\9(0)^2-36y=0\\-36y=0\\y=0\)

When x=-4

\(9x^2-36y=0\\9(-4)^2-36y=0\\9(16)-36y=0\\144-36y=0\\144=36y\\4=y\)

So, we need to check what kinds of points (0,0) and (-4,4) are.

For (0,0)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(0))(-18(0))-(-36)^2\\\\H=-1296 < 0\)

Therefore, (0,0) is a saddle point since \(H < 0\).

For (-4,4)

\(\displaystyle H=\biggr(\frac{\partial^2 z}{\partial x^2}\biggr)\biggr(\frac{\partial^2 z}{\partial y^2}\biggr)-\biggr(\frac{\partial^2 z}{\partial x\partial y}\biggr)^2\\\\H=(18x)(-18y)-(-36)^2\\\\H=(18(-4))(-18(4))-(-36)^2\\\\H=(-72)(-72)-1296\\\\H=5184-1296\\\\H=3888 > 0\)

Because \(H > 0\) and since \(\frac{\partial^2z}{\partial x^2}=-72 < 0\), then (-4,4) is a local maximum

Answer:

167,772,160

Step-by-step explanation:

-Each term is multiplied by 2-

10, 20, 40, 80, 160, 320, 640, 1,280, 2,560, 5,120, 10,240, 20,480, 40,960, 81,920, 163,840, 327,680, 655,360, 1,310,720, 2,621,440, 5,242,880, 10,485,760, 20,971,520, 41,943,040, 83,886,080, 167,772,160

167,772,160 is the 25th term

Answer:

If I live in South Carolina then I live in Charleston

Step-by-step explanation:

Just switch them

The link between x and y in the paragraph is best illustrated by the equation y=-2x+3.

A formula that demonstrates the relationship between the expressions on either side of a sign. That typically has an equal sign and one variable. When it is necessary to combine two or more components in order to comprehend or adequately explain a situation, an equation is used. It can occasionally be challenging to distinguish between an equation and a formula since both contain equals signs. Calculations for specific purposes, such as converting from Fahrenheit and Celsius or vice versa, are known as formulas. No matter what values are used, a formula is also always accurate.

The graph shows that the line passes through points (0, 3) and (3/2, 0).

Assumption: y= kx + b

k=3-0/0-3/2=-2

b= 3

Therefore, y= -2x + 3

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Answer: 156!

Step-by-step explanation: i’m not going to lie, i guessed but, i ended up getting it right .

Answer:

∠WXY=72°

Step-by-step explanation:

2X-2=70+X

2X-X=70+2

X=72° ⇒ ∠WXY=72°

Answer:

152

Step-by-step explanation:

this is because there is 360 degrees in a circle and if you subtract 98 and 110 from 360 you get 152.

Answer:

the statement is false

Step-by-step explanation:

\(18x - 12 = 3(6x - 12) \\ 18x - 12 = 18x - 36 \\ \)

\( - 12 = - 36\)

A triangle can be formed with side lengths 4, 8, 11. Yes, because 4 + 8 > 11

According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides. The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

If the sum of any two sides is greater than the sum of the third, then the difference of any two sides is less than the sum of the third. The sum of any two sides must be greater than the sum of the third. The longest side in a triangle is the side opposite a larger angle.

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When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:

If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.

A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.

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The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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Answer:

Integrate( sqrt(9-x^2) from x=-3 to x=3)

Step-by-step explanation:

The equation for a full circle is (x-h)^2+(y-k)^2=r^2 where (h,k) is center and radius is r.

Your center, your (h,k) is (0,0). Your radius, your r, is 3.

So your equation is (x-0)^2+(y-0)^2=3^2 or more simply x^2+y^2=9.

We also must consider we don't have full circle.

Solving for y will give us the circle in terms of top half if we take positive values and bottom half if we take negative values. Since y is positive in the picture, you only see top half, we will only take the positive cases for y.

Subtracting x^2 on both sides gives: y^2=9-x^2

Square root both sides: y= sqrt(9-x^2)

(I did not choose -sqrt(9-x^2) because again y is positive).

So the x's in the picture range from -3 to 3.

The integral is therefore,

Integrate( sqrt(9-x^2) from x=-3 to x=3)

We need to determine the score a student must achieve to place in the top 5% of all students taking the SAT Verbal test with an N(\(515, 109\)) distribution, which came out to be \(695\) marks.

Identify the mean (μ) and standard deviation (σ) of the distribution: In this case, µ \(= 515\) and σ\(= 109\).

Determine the percentile rank: To place in the top \(5%\)% of students, we need to find the score corresponding to the \(95th\) percentile, as this represents the point where \(95\)% of students have a lower score.

Use a standard normal (Z) table or calculator to find the Z-score corresponding to the \(95th\) percentile: A Z-score represents the number of standard deviations a data point is from the mean.

For the \(95th\) percentile, the Z-score is approximate \(1.645\).

Apply the Z-score formula to find the required SAT score: \(X =\) µ \(+ Z*\) σ. In this case, \(X = 515 + (1.645 *109)\).Calculate the result: \(X = 515 + (1.645 *109)\)

\(=515 + 179.305 = 694.305\).

Round up to the nearest whole number: Since a student's SAT score must be a whole number, round up to \(695\). A student must score \(695\) or higher on the SAT Verbal test to place in the top \(5\)% of all students taking the test, given the N(\(515, 109\)) distribution.

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~ Use the distance formula to measure the lengths of the sides.

~ Use the slope to check whether sides are perpendicular and form right angles.

~ Use the slope to check whether the diagonals are perpendicular to each.

I hope this helps ^-^

The triangle ABC, the angle x is 36°.

Given that,

In the picture, we have triangles ABC.

We have to find the angle x.

The sides of the triangle are AB=3cm and AC=5cm.

We have the angle B is 90°.

We use the sine law.

In trigonometry, there are six fundamental ratios that are used to establish a connection between a right triangle's side-to-angle ratio and its angle. If the angle created by the base and hypotenuse of a right-angled triangle is, then

Perpendicular/hypotenuse = sin θ

base/hypotenuse = cos θ

tan θ = Base/Perpendicular

The three additional functions' values, cot, sec, and cosec, are dependent on the values of tan, cos, and sin, as shown below.

cot θ= perpendicular/base

sec θ=hypotenuse/base

cosec θ=hypotenuse/perpendicular

So,

Sin x=opposite side/hypothesis

Sin x=3/5

Sin x= 0.6

x= sin⁻¹(0.6)

x=36.86°

Approximately, x=36°

Therefore, The angle x is 36°.

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Answer:

a. y-intercept: 6.85

b. m = 2.95

c. 4 grandchildren

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Our equation is f(c) = 6.85 +2.95c

a. The y-intercept is 6.85

b. m = 2.95

c. We put 18.65 in to solve

18.65 = 6.85 + 2.95c

11.8 = 2.95c

c = 4 grandchildren

So, Mrs. Franklin took 4 grandchildren to the buffet.

The equation of the plane tangent to the surfacer=3u2i+(5u−v2)j+3v2kr=3u2i+(5u−v2)j+3v2kat the point P that is P(12,9,3).z(x,y)=z(x,y)= 90x + 1296y + 810z = 14218.

To find the equation of the plane tangent to the surface at point P(12, 9, 3), we first need to find the partial derivatives of the surface with respect to u and v:

∂r/∂u = 6ui + 5j

∂r/∂v = -2vj + 6vk

Next, we can evaluate these partial derivatives at the point P(12, 9, 3) to get:

∂r/∂u = 6(12)i + 5j = 72i + 5j

∂r/∂v = -2(9)j + 6(3)k = -18j + 18k

Using these partial derivatives, we can find the normal vector to the tangent plane at point P by taking their cross product:

n = (∂r/∂u) x (∂r/∂v) = (72i + 5j) x (-18j + 18k)

= -90i - 1296j - 90k

Since the tangent plane passes through point P, its equation can be written in the form:

-90(x - 12) - 1296(y - 9) - 90(z - 3) = 0

Simplifying this equation gives:

-90x + 12960 - 1296y - 810z + 1458 = 0

or

90x + 1296y + 810z = 14218

Therefore, the equation of the plane tangent to the surface at point P is 90x + 1296y + 810z = 14218.

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Answer:

240

Step-by-step explanation:

maybe

Answer:

240

Step-by-step explanation:

3/5 of the people try it use it again.

so, it you divid you would get 3/2000 which is wrong.

but, if you multiply you would get 240.

3/5 x 400 = 240

Answer:

B.)    2 / 15

Step-by-step explanation:

: )

The given series Σ((n² - 2)/(n² + 1)) is divergent. To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we need to analyze the given series: Σ((n² - 2)/(n² + 1))

Let's break it down and analyze each part separately.

Now, let's consider the ratio of the terms:

En = ((n² - 2)/(n² + 1))

To determine the convergence or divergence of the series, we can analyze the limit of the ratio as n approaches infinity.

η = lim(n→∞) ((n² - 2)/(n² + 1))

We can simplify the ratio by dividing both the numerator and denominator by n²:

η = lim(n→∞) ((1 - 2/n²)/(1 + 1/n²))

As n approaches infinity, the terms involving 1/n² tend to zero. Therefore, we have:

η = lim(n→∞) ((1 - 0)/(1 + 0)) = 1

The ratio η is equal to 1, which means the ratio test is inconclusive. It does not provide enough information to determine the convergence or divergence of the series.

To determine whether the series is absolutely convergent, conditionally convergent, or divergent, we need to explore other convergence tests.

Since the ratio test is inconclusive, let's try using the integral test to determine the convergence or divergence.

If the integral of the absolute value of the series converges, then the series is absolutely convergent.

Let's consider the integral of the absolute value of the series:

∫[1, ∞] |(n² - 2)/(n² + 1)| dn

Simplifying the absolute value, we have:

∫[1, ∞] ((n² - 2)/(n² + 1)) dn

We can calculate this integral to determine if it converges.

∫[1, ∞] ((n² - 2)/(n² + 1)) dn = ∞

The integral diverges since it results in infinity. Therefore, the series is not absolutely convergent.

    2. Conditional Convergence:

To determine if the series is conditionally convergent, we need to investigate the convergence of the series without considering the absolute value.

Let's consider the series without taking the absolute value:

Σ((n² - 2)/(n² + 1))

To analyze the convergence of this series, we can try applying the limit comparison test.

Let's compare it to a known series, the harmonic series: Σ(1/n).

Taking the limit as n approaches infinity:

lim(n→∞) ((n² - 2)/(n² + 1)) / (1/n)

We simplify this limit:

lim(n→∞) ((n² - 2)/(n² + 1)) * (n/1)

This simplifies further:

lim(n→∞) ((n³ - 2n)/(n² + 1))

As n approaches infinity, the dominant term in the numerator is n³, and the dominant term in the denominator is n².

Therefore, the limit becomes:

lim(n→∞) (n³/n²) = lim(n→∞) n = ∞

The limit is divergent, as it approaches infinity. This implies that the given series also diverges.

In conclusion, the given series Σ((n² - 2)/(n² + 1)) is divergent.

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Answer:

Step-by-step explanation:

o solve the compound inequality, we'll start by solving each inequality separately, and then find the intersection of their solutions.

For the first inequality: 8r - 3 ≥ 7r - 7

Adding 7r to both sides: 8r - 3 + 7r ≥ 7r - 7 + 7r

Combining like terms: 15r - 3 ≥ 14r

Subtracting 14r from both sides: 15r - 14r - 3 ≥ 0

Combining like terms: r - 3 ≥ 0

Adding 3 to both sides: r ≥ 3

For the second inequality: 2r + 4 ≤ r - 3

Subtracting 2r from both sides: 2r + 4 - 2r ≤ r - 3 - 2r

Combining like terms: 4 ≤ -r - 3

Adding r and 3 to both sides: 4 + r + 3 ≤ -r

Combining like terms: 7 ≤ -r

Multiplying both sides by -1: r ≤ -7

The solution to the compound inequality is the intersection of the solutions to each inequality, which is the range of r that satisfies both conditions. So, the solution is 3 ≤ r ≤ -7.

To graph the solution, we can plot the two inequalities on the number line, and shade the region between 3 and -7:

Corresponding angles: the angles which occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal (from Dictionary)

It's basically a line crossed two parallel lines and the angles formed in the same place are called corresponding angles. Also they share the same angle only if the two lines are paralleled.

Answer:

Start at any point on the graph. Move up 1 space and right 2 spaces, and then plot a point.

Explanation:

Look at the coordinates (4, 2) and (6, 3) that I graphed on the chart. If you move 1 space up, and 2 spaces to the right, it leads to the coordinates (6, 3)

Answer: The answer is 1/4.

Step-by-step explanation:

Answer:
45.2x0.784

Step-by-step explanation:

This problem equals 35.4368, which has four decimal points

Answer:

1/9

Step-by-step explanation:

Probability  =  Expected outcome/Total outcome

From the given pi chart,

Total outcome = 360degrees (since the total angle in a circle is 360 degrees)

Since we to find the probability of scoring a 5, we can see that the angle when he scores a 5 is 40degrees, hence;

Expected outcome = 40degrees

Pr(scoring a 5) = 40/360

Pr(scoring a 5) = 1/9

Hence the probability of scoring a 5 is 1/9

Answer:

1/9

Step-by-step explanation:

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Divide the number of events by the number of possible outcomes.

y = x + 3

as x increases by 1, y increases by 1 (Slope)

when x equals 0, y equals 3 (y-intercept)

Answer:

D. 9.28 units

Step-by-step explanation:

DF is the hypotenuse of the triangle.

\(\frac{sin(A)}{a} =\frac{sin(B)}{b}\)

\(\implies \frac{sin(55)}{7.6} =\frac{sin(90)}{DF}\)

\(\implies DFsin(55) =7.6sin(90)\)

\(\implies DF =\frac{7.6sin(90)}{sin(55)}\)

\(\implies DF =9.277886875...\)

\(\implies DF =9.28\ \textsf{units (nearest hundredth)}\)

Answer:

jbhbchbhvbbhcbrhfbcbhshshbhsvhbhv;b;rvbhbhcrbihcbhc

Step-by-step explanation:

A study that uses both manipulated and measured variables in a factorial design is called a(n)  option b. IV X PV design.

In this design, there are two or more independent variables (IVs) that are manipulated by the researcher.

And one or more measured variables, also known as participant variables (PVs), that are measured but not manipulated.

Factorial designs are used to investigate the effects of multiple independent variables on a dependent variable.

As well as the interactions between the independent variables.

The IV X PV design is a specific type of factorial design.

That includes at least one measured variable in addition to the manipulated independent variables.

Option A is incorrect because mixed repeated measures and independent groups are types of designs .

That describe how participants are assigned to different groups in a study, whereas the IV X PV design describes the types of variables that are used in a study.

Option C describes a specific type of 2x2 factorial design, which includes two independent variables, each with two levels.

Option D describes a design that is used to investigate the relationship between multiple measured variables and a single dependent variable.

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