Find the length of the altitude to the hypotenuse. Round the answer to the nearest tenth. Solve for AD.

Answer: #x^3

Step-by-step explanation:

        x^3

note: An algebraic expression doesn't have an equal sign (=)

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The measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

Given data ,

The angles of the triangle ABC are

∠A = ( 2x + 10 )°

∠B = ( 4x + 2 )°

Let angle ∠C be y

The sum of ∠A + ∠B + ∠C = 180°  

So ,

( 2x + 10 )° + ( 4x + 2 )° + y = 180°   be equation (1)

Now , we can see that AD is a straight line and C is a point on the line AD

The total angle of C on the line AD is 180°

So , ( 5x + 27 )° + y = 180°

y = 180° - ( 5x + 27 )°   be equation (2)

Substituting the value of equation (2) in equation (1) , we get

( 2x + 10 )° + ( 4x + 2 )° + 180° - ( 5x + 27 )° = 180°

On Simplifying , we get

( 2x + 10 )° + ( 4x + 2 )° - ( 5x + 27 )° = 0

( 2x + 4x - 5x ) + ( 10 + 2 - 27 ) = 0

x - 15 = 0

Adding 15 on both sides , we get

x = 15°

Substituting the value of x in the ∠A , ∠B and ∠C equation , we get

∠A = ( 2x + 10 )°

     = 40°

∠B = ( 4x + 2 )°

     = 62°

∠C = 180° - ( ∠A + ∠B )

     = 180° - 102°

     = 78°

Therefore , the angles of the triangle ABC are 40° , 62° and 78°

The measure of ( 5x + 27 )° is

= ( 5 x 15 + 27 )°

= 102°

Hence , the measure of angles of ( 5x + 27 )° , ( 2x + 10 )° and ( 4x + 2 )° are 102° , 40° and 62° respectively

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Assume that the population has a normal distribution and the standard deviation is known to be σ = 0.6.There are a number of variables to keep in mind when constructing confidence intervals (CI). First and foremost, the wider the interval, the more confident we are that the actual mean is contained within the interval.

Second, the wider the interval, the less precise our estimation of the actual mean will be. There's an inherent trade-off between these two factors. To achieve a specific interval width at a certain level of confidence, we can change the sample size.

The formula to calculate the sample size can be represented as follows:

n = (Zσ/E)2,

where n is the sample size, Z is the Z-score corresponding to the confidence level, σ is the standard deviation, and E is the desired margin of error (interval width).

Therefore, we can now use the formula to calculate the sample size:

Z score corresponding to 95% confidence is 1.96

n = (1.96 * 0.6 / 1.5)2= (1.96 * 0.4)2= 0.7842= 0.6148

Hence, the sample size needed should be around 15.

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a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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Answer: -8/15

Step-by-step explanation:

-(2/15)/(1/4)

-[(2/15)/(1/4)]*(4/4)

= (-2/15)*(4/1)

= -8/15

Answer:

alex

Step-by-step explanation:

The probability for getting the different numbers when two dice are thrown is: 5/6.

The sample space formed by rolling two dice are: 6*6 = 36.

Total number of pairs having same number = (1,1), (2,2),(3,3),(4,4),(5,5),(6,6) = 6 samples.

Thus,

Number of outcomes having different numbers:

36 - 6 = 30

Probability (different numbers) = total number of different number / total outcomes.

Probability (different numbers) = 30 / 36

Probability (different numbers) = 5/6

Thus, the probability for getting the different numbers when two dice are thrown is: 5/6.

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Question: if n  balls are randomly placed into n cells, determine the probability that exactly one cell remains empty.

The probability that exactly one cell remains empty when n balls are randomly placed into n cells can be calculated as \((n-1)/n^n\).

Let's consider the scenario where n balls are randomly distributed into n cells. To determine the probability that exactly one cell remains empty, we need to calculate the number of favorable outcomes (arrangements where exactly one cell is empty) and divide it by the total number of possible outcomes.

The total number of possible outcomes is given by n^n since each ball has n choices (n cells) for placement, and there are n balls in total.

To calculate the number of favorable outcomes, we focus on the cell that remains empty. There are n choices for selecting the empty cell. For the remaining (n-1) cells, each ball has n-1 choices for placement, as it cannot be placed in the empty cell. Therefore, the number of favorable outcomes is (n-1)*(n-1)*(n-1)*...*(n-1) (n-1 repeated n-1 times).

Dividing the number of favorable outcomes by the total number of possible outcomes, we obtain \((n-1)/n^n\) as the probability that exactly one cell remains empty when n balls are randomly placed into n cells.

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By forming and solving equations, we know that the speed of the runner is 4 miles per hour.

So, we need to form an equation to get the speed of the runner:

'x' is the speed of the runner. Now, solve for x as follows:

Therefore, by forming and solving equations, we know that the speed of the runner is 4 miles per hour.

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The expression for area of triangle is 1/2x² + 3x.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Area = 1/2 × base × height

and, length is 6 inches greater than the height.

let the height of the triangle is x

length of triangle = x + 6

So, The Area of triangle

= 1/2 x base x height

= 1/2(x)(x+ 6)

= 1/2x² + 3x

Hence, the expression for area of triangle is 1/2x² + 3x.

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Answer:-32

Step-by-step explanation:

p=-32

7Answer:

-7

-Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

There are 15 students who take Latin, and 10 students who take both.

Therefore:

15+10 =25 total students taking Latin

25 students / 50 total students = 1/2

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Therefore, the equation of the line passing through (-3, -5) and parallel to the line 2x + 3y = 15, in slope-intercept form, is y = (-2/3)x - 7.

To find the equation of a line parallel to the line 2x + 3y = 15 and passing through the point (-3, -5), we need to determine the slope of the given line and use it to construct the equation in slope-intercept form (y = mx + b).

The given line is in the form Ax + By = C, where A = 2, B = 3, and C = 15. To find the slope of this line, we can rearrange the equation to isolate y:

2x + 3y = 15

3y = -2x + 15

y = (-2/3)x + 5

The slope of the given line is -2/3.

Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the line passing through (-3, -5) will also be -2/3.

Now, we can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

Substituting the values of (-3, -5) and -2/3 for (x1, y1) and m, respectively:

y - (-5) = (-2/3)(x - (-3))

y + 5 = (-2/3)(x + 3)

To convert this equation into slope-intercept form, we can simplify and rearrange:

y + 5 = (-2/3)x - 2

y = (-2/3)x - 2 - 5

y = (-2/3)x - 7

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Probability of

=0.0403.

The probability that exactly two of the 14 students selected with replacement will wear wrist watches is 3/30 * 2/29 * 27/28 * 26/27 = 0.0437.

The probability that exactly two of the 14 students selected without replacement will wear wrist watches is 3/30 * 2/29 * 26/28 * 25/27 = 0.0403.

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Answer:

28"

Step-by-step explanation:

the length of the other non-hypotenuse side =

√(53² - 45²) =√(2809-2025) =√784 = 28"

Using Pythagorean theorem

\(\\ \rm\longmapsto P^2=H^2-B^2\)

\(\\ \rm\longmapsto P^2=53^2-45^2\)

\(\\ \rm\longmapsto P^2=2809-2025\)

\(\\ \rm\longmapsto P^2=784\)

\(\\ \rm\longmapsto P=\sqrt{784}\)

\(\\ \rm\longmapsto P=28\)

14 it will be (x + 14) it's not the answer I don't know what it would be

A threshold effect is when a small change in one variable results in a noticeable change in another variable. In this example, a small 8% increase in salt content of the chips is enough to produce a noticeable change in the saltiness of the chips to the sample of consumers.

The snack manufacturer can calculate the increase in salt content of their chips needed to produce the threshold effect by first determining the baseline salt content of the chips. Once this is known, they can then calculate what percentage increase to the salt content is needed by multiplying the baseline salt content by 8%. For example, if the baseline salt content of the chips is 10%, then the 8% increase in salt content would be calculated as 10% x 8% = 0.8%. This means that the snack manufacturer needs to increase the salt content of their chips by 0.8% to reach the threshold effect desired by the sample of consumers.

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17) \(x+2x+1+3x=\boxed{6x+1}\)

18) \(17-a+5a-1+4ab=\boxed{4ab+4a+16}\)

19) \(2(3y-5+y+2)=\boxed{8y-6}\)

20) \(k^2 +k+k^2 -9k+23+k^2 +k+2k^2 -17=\boxed{5k^2 -7k+6}\)

If the "arithmetic-sequence" which has "first-term" as 25, then it's 13th term will be -71.

The first-term of the "arithmetic-sequence" is denoted as "a₁" is 25,

The common-difference denoted as "d" is -8,

We can use the formula for the nth term of an arithmetic sequence to find the 13th term. The formula is : aₙ = a₁ + (n - 1)d;

where, n is = number of the term we want to find,

We have to find the 13th term, so, n is = 13,

Substituting the values,

We get;

a₁₃ = 25 + (13 - 1)(-8)

a₁₃ = 25 + 12(-8)

a₁₃ = 25 - 96

a₁₃ = -71

Therefore, the 13th term of arithmetic sequence is -71.

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CD is the perpendicular bisector of another line AB which can be proven below.

Perpendicular bisector is a line that divides another line into two equal halves in such a way that it creates an angel of 90°.

To proof that CD is the perpendicular bisector of another line AB the following is carried out;

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Answer:

heres what i got

Step-by-step explanation:

2.  definition of a perpendicular bisector

5. reflexive property of congruence

11. definition of square root

Step-by-step explanation:

a=32(alternate angles are equal)

b=a=32

c=17(all sides of rhombus are equal in length)

d=17(all sides of rhombus are equal in length)

e=90

f=90(diagonals intersect at right angles)

Answer:

The answer is 380.8

Step-by-step explanation:

476 is 125% of 380.8

Answer: 380.8

Step-by-step explanation: 125 % of 380.8 is 476 . This means 380.8 is the total because in percentage what comes after the word of is the total . PLEASE GIVE BRAINLIEST .THANKS HOPE IT HELPS .

Answer:

1) \(m\)∠JKL = 145°

2) \(m\)∠IHG = 164°

3) \(m\)∠NME = 50°

4) \(m\)∠TUV = 178°

I hope this helps! (✿◠‿◠)

Answer:

Sunni Muslims accept all four leaders, including Abu Bakr and Ali, as the rightful successors of Muhammad. Shi'a Muslims, also called 'the party of Ali', believe that Muhammad chose Ali as his successor rather than having a bloodline successor.

Imamate is the Shi'a belief that all modern imams should be spiritual descendants of the Prophet Muhammad. Shi’a Muslims believe that imams protect the religion and help to guide Muslims along the right path. Today, Shi'a Muslim communities are led by imams, who are seen as having been chosen by God. Shi’a Muslims believe that imams are exemplary individuals who obey all teachings. Shi’a Muslims believe that imams are inspired by God, are without sin and are infallible, which means that they can interpret the teachings of the Qur’an without making any errors.

Today, Shi’a Muslim communities are led by imams, who are seen as having been chosen by God. Imams should be exemplary individuals who obey all teachings.

Origins of Imamate

After the Prophet Muhammad died, the Muslim community had to choose a successor. Abu Bakr, who was Muhammad’s father-in-law and closest friend, became the leader of the Sunni Muslim community.

Sunni Muslims, who make up around 90 per cent of the global Muslim population, agree that the rightful successor to Muhammad was Abu Bakr, Muhammad’s father-in-law. They recognise two further leaders who came after Abu Bakr. They then recognise a fourth leader, Ali (Muhammad’s cousin). Sunni Muslims accept all four leaders, including Abu Bakr and Ali, as the rightful successors of Muhammad.

Shi’a Muslims, also called ‘the party of Ali’, believe that Muhammad chose Ali as his successor rather than having a bloodline successor. After Ali’s death, Shi’a Muslims were led by twelve imams, whom they believe were spiritual successors to the Prophet Muhammad rather than having any family connection to him. This was the beginning of the Imamate. Shi’a Muslims make up around 10 per cent of the global Muslim population.

Hope this helps..!

Step-by-step explanation:

The dimensions of the picture are 5 inches by 5 inches.

Let's denote the side length of the square picture as "x".

The frame is 2 inches wide, which means the dimensions of the entire picture and frame are increased by 2 inches on each side. Therefore, the total dimensions of the picture and frame would be (x + 4) by (x + 4).

The area of the picture and frame is given as 81 square inches. So we can set up the equation:

(x + 4) * (x + 4) = 81

Expanding and rearranging the equation, we get:

x^2 + 8x + 16 = 81

x^2 + 8x - 65 = 0

Now we can solve this quadratic equation for "x". Factoring or using the quadratic formula, we find:

(x - 5)(x + 13) = 0

This gives us two potential solutions: x = 5 or x = -13. Since we are dealing with dimensions, we discard the negative value and conclude that the side length of the picture is 5 inches.

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The classical probability density for a particle in an infinite square well is uniform within the well and zero outside. The classical averages for position and momentum are proportional to the size of the well.

(a) The classical probability density describing a particle in an infinite square well can be derived by considering the time the particle spends in each interval. In the classical framework, the probability for finding a particle in a particular interval is proportional to the time it spends in that interval.

For an infinite square well of dimension L, the particle is confined to the region between 0 and L. Assuming the particle has a constant velocity, the time it takes to travel from 0 to L is given by L/v, where v is the velocity. Therefore, the probability of finding the particle in the interval [a, b] is proportional to the time it spends in that interval, which is (b - a)/v.

Since the probability density is defined as the probability per unit length, we can express it as follows:

ρ(x) = k, if 0 ≤ x ≤ L,

      = 0, otherwise,

where k is a constant. This implies that the probability density is constant within the well and zero outside of it. Thus, the classical probability density for a particle in an infinite square well is uniform within the well and zero outside.

(b) Using the classical probability density derived in part (a), we can determine the classical averages and for a particle confined to the well. The classical average position is given by:

<x> = ∫ xρ(x) dx,

and the classical average momentum is given by:

<p> = ∫ pρ(x) dx.

Since the classical probability density is uniform within the well, the integrals become:

<x> = k ∫ x dx, from 0 to L,

<p> = k ∫ p dx, from 0 to L.

Evaluating these integrals yields:

<x> = k(L²/2),

<p> = k(Lp/2),

where Lp is the linear momentum. These results indicate that the classical averages for position and momentum are proportional to the size of the well. Comparing these classical results with the quantum results obtained from Example, we observe that the quantum averages are not proportional to the size of the well. s, especially in systems with confinement and discreteness. When compared to the quantum results, we observe deviations from the classical predictions, indicating the limitations of classical mechanics in describing confined quantum systems. This deviation is in line with the correspondence principle, which states that classical mechanics is a limiting case of quantum mechanics for large quantum numbers or systems.

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Answer:

\(\int\limits^1 _\frac{1}{2} {\frac{-1}{u} } \, du\)

General Formulas and Concepts:

Pre-Algebra

Calculus

Step-by-step explanation:

Step 1: Define

\(\int\limits^\frac{-\pi}{2} _\frac{-2\pi}{3} {\frac{sin(x)}{1+cos(x)} } \, dx\)

Step 2: Evaluate

Step 3: Evaluate Further

Answer: Range = 22 IQR = 13

Step-by-step explanation:

To find the range of a data set, subtract the largest value of the data set from the smallest value. 45 is the largest value and 23 is the smallest, and 45-23 is 22, so the range is 22. To find the IQR, you must subtract the upper quartile and the lower quartile. We can find this after finding the mean by re-arranging all the values in order from lowest to greatest, and finding the middle value. Once we do so, we get 33.5. Then, we find the median of all the numbers below and after the median to get the lower and upper quartiles. Then, we subtract them to get the IQR 13.

The inequality \($uv^2 \leq (uv)^2$\) holds for any vectors u and v in \(R^2\). Equality holds when the vectors u and v are collinear or when one of them is the zero vector.

To prove the inequality \($uv^2 \leq (uv)^2$\), we can start by expressing the dot product of u and v in terms of their components. Let u = (\(u_1, u_2\)) and v = (\(v_1, v_2\)).

Then, the dot product of u and v is given by\(uv = u_1 v_1 + u_2 v_2\).

Now, consider the squared length of the projection of u onto v.

This can be calculated as \((uv)^2\) / \(||v||^2\), where ||v|| represents the length of vector v.

Since ||v||^2 = vv, we have \((uv)^2\) /\(||v||^2\) = \((uv)^2\) / (\($v \cdot v$\)).

On the other hand, the squared length of vector u can be expressed as \(u\cdot u = u1^2 + u2^2\).

Now, we can compare the two expressions: \(uv^2\) and \((uv)^2\) / (vv).

By substituting the expression for uv, we get \(uv^2\) = \((u_1 v_1 + u_2 v_2)^2\), and by substituting the expressions for \(||v||^2\) and uu, we get \((uv)^2\) / (vv) = (\(u_1^2 v_1^2 + u_2^2 v_2^2\)) / (\(v_1^2 + v_2^2\)).

It can be shown that \((u_1 v_1 + u_2 v_2)^2 \geq (u_1^2 v_1^2 + u_2^2 v_2^2)\) for any real numbers \(u_1, u_2, v_1, v_2\). Therefore, \(uv^2\) ≤ \((uv)^2\) / \((vv)\), which implies \(uv^2\) ≤ \((uv)^2\).

Equality holds in the inequality \($uv^2 \leq (uv)^2$\) when the vectors u and v are collinear or when one of them is the zero vector.

Geometrically, this inequality represents the fact that the squared length of the projection of vector u onto vector v is always less than or equal to the squared length of the projection of u onto v.

When the vectors are collinear, their projections coincide and the inequality becomes an equality. Similarly, when one of the vectors is the zero vector, its projection onto any other vector is zero, resulting in equality as well.

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