What is the measure of angle z in this figure?
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The given statement (1/cotx)+cotx = (1/sinxcosx) is true.

What is Trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles, and the functions based on these relationships. It is widely used in various fields such as engineering, physics, architecture, and navigation to calculate distances, heights, angles, and other geometric properties.

Starting with the left-hand side of the equation:

1/cot(x) + cot(x)

= cos(x)/sin(x) + sin(x)/cos(x) [Using the reciprocal identity]

= (cos²(x) + sin²(x))/(sin(x)cos(x))

= 1/(sin(x)cos(x)) [Using the identity sin²(x) + cos²(x) = 1]

Now, we have shown that the left-hand side simplifies to 1/(sin(x)cos(x)).

Now, we can simplify the right-hand side of the equation using the identity sin(2x) = 2sin(x)cos(x):

1/(sin(x)cos(x))

= 1/(1/2 × 2sin(x)cos(x))

= 2/(2sin(x)cos(x))

= 2/sin(2x)

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

= (sin(x)cos(x))/(sin(x)cos(x)×sin(2x)) + (sin(x)cos(x))/(sin(x)cos(x)×sin(2x))

= (cos(x))/(sin(2x)) + (sin(x))/(sin(2x))

= (cos(x) + sin(x))/(sin(2x))

= (cos²(x) + 2sin(x)cos(x) + sin²(x))/(2sin(x)cos(x))

= (1 + cos(2x))/(2sin(x)cos(x)) [Using the identity cos(2x) = cos²(x) - sin²(x)]

Thus, we have shown that the right-hand side simplifies to (1 + cos(2x))/(2sin(x)cos(x)).

Since we have shown that the left-hand side simplifies to 1/(sin(x)cos(x)) and the right-hand side simplifies to (1 + cos(2x))/(2sin(x)cos(x)), we can see that the given identity is true.

Therefore,1/cot(x) + cot(x) = 1/(sin(x)cos(x)) = (1 + cos(2x))/(2sin(x)cos(x)).

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By applying the the variance formula to obtain the value of Var(10X + 1) is 1000.

Let's start by using the definition of the expected value of a discrete random variable. Given that E(X) = 2, it means that the average value of X is 2.

Now, we are given that E(2X(X - 1)) = 16. To find the variance of 10X + 1, we need to calculate E((10X + 1)²), where E represents the expected value.

Expanding the square term, we have:

E((10X + 1)²) = E(100X² + 20X + 1)

= 100E(X²) + 20E(X) + E(1)

Using the formula for variance, Var(X) = E(X²) - [E(X)]², we can rearrange it as follows:

E(X²) = Var(X) + [E(X)]²

= Var(X) + 2² = Var(X) + 4

Substituting this value back into our expression, we get:

E((10X + 1)²) = 100(E(X²) + 4) + 20(2) + 1

= 100E(X²) + 400 + 40 + 1

= 100E(X²) + 441

Now, we know that E(2X(X - 1)) = 16, so we can rewrite it as follows: E(2X(X - 1)) = 16 2E(X² - X)

= 16 2E(X²) - 2E(X)

= 16 2E(X²) - 4

= 16 2E(X²)

= 20 E(X²) = 10

Plugging this value into the previous expression, we have:

E((10X + 1)²) = 100(10) + 441 = 1000 + 441 = 1441

Finally, to find Var(10X + 1), we use the variance formula:

Var(10X + 1) = E((10X + 1)²) - [E(10X + 1)]²

= 1441 - [E(10X) + 1]²

= 1441 - [(10E(X)) + 1]² = 1441 - (20 + 1)²

= 1441 - 21² = 1441 - 441 = 1000

Therefore, Var(10X + 1) = 1000.

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The angles that make up a kite are 1, 2, 3, 4, 5, 6, and 7. Angle 1 is the interior angle between sides 1 and 2. Angle 2 is the interior angle between sides 2 and 3.

Angle 3 is the interior angle between sides 3 and 4. Angle 4 is the exterior angle between sides 4 and 1. Angle 5 is the interior angle between sides 1 and 3. Angle 6 is the exterior angle between sides 2 and 4. Angle 7 is the interior angle between sides 2 and 4.

An angle is a figure formed by two lines that meet at a common point. The lines are called the arms of the angle, and the common point is called the vertex. Angles are usually measured in degrees, with a full circle being 360°.

A kite is a four-sided geometric shape with two pairs of adjacent equal-length sides. The missing values for each angle in the kite can be calculated using the formula:

Angle 1 + Angle 2 + Angle 3 + Angle 4 + Angle 5 + Angle 6 + Angle 7 = 360 degrees

For example, if angle 1 is 60 degrees, then angle 2 = 120 degrees, angle 3 = 120 degrees, angle 4 = 60 degrees, angle 5 = 120 degrees, angle 6 = 60 degrees, and angle 7 = 60 degrees.

In general, the sum of the interior angles of a kite will equal 360 degrees, and each interior angle will be equal to the sum of the exterior angles. Therefore, if the values of four of the angles are known, the remaining angles can be calculated by subtracting the known angles from 360 degrees.

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Answer:

Standard deviation = 5.1

Mean = 13

Median = 14

Step-by-step explanation:

The sample standard deviation measures the spread of a data distribution of the sample. It is usually used to estimate the population standard deviation

The mean of a set of numbers is the sum divided by the number of terms.

Arrange the data in an ascending order and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.

Answer:

39.63

Step-by-step explanation:

If the number after the place you are rounding to is 4 or lower, then you round down. If it is 5 or higher round up.

Answer:

the answer is: 39.63 and that is the answer

Option B is the correct answer, The set of correlations which correctly shows the highest to lowest degree of relation is -0.91, +0.83, +0.10, -0.03.

What is correlation?

In statistics, the correlation is a technique used to determine the relationship between the two variables. The correlation's range is from -1 to +1. There are three primary categories of correlation: no correlation, positive correlation, and negative correlation. When the correlation value is zero, there is no association; the correlation value that is closest to zero indicates the weakest degree of relationship.

We must select the set of correlations in the question that accurately displays the highest to the lowest degree of relation.

Option B is the best choice since we must take the absolute value into account in order to determine the relationship's degrees. Here, the absolute values drop from 0.91 to 0.03.

Option A is incorrect since the absolute values decline from 0.91 to 0.03 and then climb to 0.10 in this situation.

Because the absolute values are not listed in decreasing order, Option C is incorrect.

Because the absolute values in this situation are not ordered in decreasing order, Option D is also a incorrect choice.

Therefore, option B, is the correct option.

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Answer:

With the discounts, you saved a total of $4.90. You still owe $29.10.

Step-by-step explanation:

Shoes:

10% of 24 is 2.4

The shoes cost 21.60  with the 10% discount and before tax.

Belt:

25% of 10 is 2.5

The belt cost $7.50 with the 25% discount and before tax.

Total:

You still owe 29.10 for the belt and shoes before tax.

You saved $2.4 on the shoes and $2.5 on the belt (total of $4.90)

Answer:

A, or Triangle DEC

Step-by-step explanation:

Answer:

the two is in the thousandths place

Step-by-step explanation:

the eight is in the tenths, and the one is in the hundredths

Answer:

.8 tenths

.01 hundredths

.002 thousandths

so the value of 2 would be 2 thousandths or .002 thousandths

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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The answer will be 1374.2 m/s using root mean square.

What is  root mean square?

The root mean square formula provides the square root of the sum of all squares for each observation's data. The arithmetic mean of the squares of a set of values is known as the root mean square, or RMS, and is denoted by the abbreviation. Quadratic mean is another name for it. An integral of the squares of the instantaneous values during a cycle can be used to define the root mean square value for a function for a function that is continuously changing. The root mean square formula is used to determine the square root of the arithmetic mean of the square of the function that characterises the continuous waveform in this case.

mass of He is = 4 / 6.023*10²³

So Root mean square velocity is = √(3RT/m)

v = √(3*8.31*10³*303/4)

v = 1374.2 m/s

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Answer:

c > 9

Step-by-step explanation:

\(\frac{2c}{3} +1 > 7\)

To solve this, first subtract 1 from both sides

\(\frac{2c}{3} +1 > 7\\\frac{2c}{3} > 6\)

multiply both sides by 3

2c > 18

divide both sides by 2

c > 9

Hope this helps! :)

Answer:

c > 9

Step-by-step explanation:

Answer:

3 three point baskets

9 two point baskets

4 one point baskets

Step-by-step explanation:

Since you cannot have a 1/3 or 2/3 of a three point basket, finding multiples of threes for the initial two point baskets is the easiest way to start.

Answer:C

Step-by-step explanation:

288 divided by 4 equals 72

Option C is correct, y=72x is the equation which represents the number of times her heart beats per minutes.

A division is a process of splitting a specific amount into equal parts.

The equation that represents the relationship between the number of times Lupe's heart beats per minute and the time (in minutes) is:

y = 72x

where y is the number of times Lupe's heart beats per minute, and x is the time in minutes.

We can see this by dividing the total number of heart beats by the time in minutes:

y = (288 beats / 4 minutes) = 72 beats/minute

Hence, y=72x is the equation which represents the number of times her heart beats per minutes.

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The vector-valued function at each given value of t  is :

a) i

b)  1/√2i+9/√2j

c)−cos(θ)i+9sin(θ)j

d)  −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

The given problem is related to trigonometric Ratios of Angle, where there are six trigonometric ratios sine, cosine, tangent, cotangent, cosecant, and secant. Since it is given that a  vector valued function:

r(t)= cos(t)i + 9 sin(t)j

r(t)=cos(t)i+9sin(t)j

so ,  r(0)=  cos(0)i+9sin(0)j = i ( sine cos0 =1 and sin0 =0)

r(π/4) =  cos(0)i+4sin(0)j = cos(π/4)i+9sin(π/4)j

           = 1/√2i+9/√2j

r(θ−π)= cos(θ−π)i+9sin(θ−π)j= −cos(θ)i+9sin(θ)j

(π/6+△t)−r(π/6)= cos(π/6+△t)i+9sin(π/6+△t)j−cos(π/6)i−9sin(π/6)j

=  cos(π/6+△t)i−cos(π/6)i+9sin(π/6+△t)j−9sin(π/6)j

= −2sin(π/6+△t/2)sin(△t/2)i+18cos(π/6+△t/2)sin(△t/2)j

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Evaluate (If possible) the vector-valued function at each given value of t. (If an answer does not exist, enter DNE.)

r(t)=cos(t)i+9sin(t)jr(t)

a)r(0)=?

b)r(π/4)=?

c)r(θ−π)=?

d)r(π/6+△t)−r(π/6)=?

Answer:

y= -1.5x-7 is the equation of the perpendicular line

Here's why:

when we convert 2x-3y=8 to standard form, we get y= 2/3x-8/3. This means the perpendicular line will have a slope of the negative reciprocal of the original one, so the perpendicular slope is -1.5. When we substitute the points (-2,-4) into the equation y=-1.5x+b, we get a b value of -7. So the perpendicular line equation is y= -1.5x-7. You can't the parallel line equation with the points (-2,-4) as it is part of the line 2x-3y=8.

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer: 18 litres

Step-by-step explanation:

In 4 litre pink paint, red paint constituted 3 litres. In percentage therefore, it was:

= 3/4 * 100%

= 75% of the mixture.

In a 24 litre therefore, it will occupy the same percentage which will be:

= 75% * 24

= 18 litres

The points A(2, -1, 4), B(3, 1, 2), C(0, 5, 6), and D(-1, 3, 8) form a parallelogram. The area of the given parallelogram is 12 square units.  It is not a rectangle.

To verify if the given points form a parallelogram, we need to check if both pairs of opposite sides are parallel.

The vectors formed by the sides AB and CD are AB = (1, 2, -2) and CD = (-1, -2, 2). The vectors formed by the sides BC and AD are BC = (-3, 4, -4) and AD = (-3, 4, -4).

Comparing these vectors, we can see that AB and CD are parallel, as are BC and AD. This indicates that the given points A, B, C, and D form a parallelogram.

To find the area of the parallelogram, we can use the cross product of the vectors AB and AD (or BC and CD) to find the area of the corresponding parallelogram. The magnitude of the cross product of AB and AD is |AB × AD| = 12.

Since the area of a parallelogram is equal to the magnitude of the cross product of its adjacent sides, the area of the given parallelogram is 12 square units.

To determine if the parallelogram is a rectangle, we can check if any of its angles are right angles. However, since the given points do not have any indication of angles, we cannot determine if the parallelogram is a rectangle based on the information provided.

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Answer:

There are no tables, but... I made a quick graph.

Step-by-step explanation:

y=2x-1 means that you start at (0,-1), one down from the origin (0,0). From there, you go up 2 and right one (1, 2), as well as down 2 and left 1 (-1, -2), since the slope is 2 (or \(\frac{2}{1\\}\)). The lines continues in both directions, of course.

The table for the equation is y = 2x - 1

x y

0 -1

1 1

2 3

To determine which table represents the equation y = 2x - 1, we substitute the values of x into the equation and check if the resulting y values match those given in the table.

Substitute the values 0, 1, and 2 into the equation y = 2x - 1 and calculate the corresponding y-values:

For x = 0:

y = 2(0) - 1

y = 0 - 1

y = -1

For x = 1:

y = 2(1) - 1

y = 2 - 1

y = 1

For x = 2:

y = 2(2) - 1

y = 4 - 1

y = 3

The corresponding y-values for x = 0, 1, and 2 are -1, 1, and 3, respectively.

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Answer:

angle y = 60

Step-by-step explanation:

They are equal due to the rule that vertical angles are always equal

"A pair of vertically opposite angles are always equal to each other."

hope this helps

Step-by-step explanation:

please mark me as brainlest

Answer:

89010

Step-by-step explanation:

1978 times 45 will equal 89010 its very simple step wise.

Answer:

89010

Step-by-step explanation:

Three problems would arise if the frequency of scrum was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

Scrum is a project management framework that was initially focused on software development, while it has now been applied to other areas such as research, sales, marketing, and cutting-edge technology.

It is intended for groups with ten or fewer members who divide their work into tasks that can be finished in sprints, which are time-boxed iterations that can be done in as little as one month and most frequently two weeks.

If the frequency was reduced to every two or three days, there would be three issues.

(A) The chances to review and modify the Sprint Backlog may be missed.

(B) The Sprint plan becomes imprecise; obstacles are raised and removed more slowly.

(C) Too much time is spent before meetings updating the scrum board.

Therefore, three problems would arise if the frequency was lowered to every two or three days.

(A) There may be missed opportunities to examine and amend the sprint backlog.

(B) The Sprint strategy deteriorates; barriers are raised and taken down more slowly.

(C) Too much time is spent updating the scrum board prior to meetings.

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Answer:

59

Step-by-step explanation:

i hope this halp

Answer:

Step-by-step explanation:

-0.5

Using the normal distribution, it is found that he needs a score of 605 in exam b in order to do equivalently well as he did on exam a.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For the z-score for exam a, we have that the parameters are given as follows:

\(X = 22, \mu = 40, \sigma = 10\)

Hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{22 - 40}{10}\)

Z = -1.8.

Then, for the equivalent grade X in exam B, we have that:

\(Z = -1.8, \mu = 650, \sigma = 25\)

Then:

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.8 = \frac{X - 650}{25}\)

X - 650 = -1.8 x 25

X = 605.

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Answer:

Commutative property of Addition

Step-by-step explanation:

Commutative property of addition:

Changing the order of addends does not change the sum.

Answer:

The property is the Commutative property.

Step-by-step explanation:

The Commutative property is almost like a mirror, it will look like the equation is being flipped.  This is how you know it is the Commutative property.

around 85 degrees. I did it with a protractor.

Answer:

nobody can see the question(s)