The dimensions of a cylindrical are shown in the diagram. Find the total surface area of the can in terms of pi
R=3
h=4.5

The length of XW from the given triangle XYZ is 671.16 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in ΔXYZ, ∠X=17° and ∠Y=82°. ∠XWZ=90° and XY=700.

By using angle sum property,

∠X+∠Y+∠Z=180°

17°+82°+∠Z=180°

99°+∠Z=180°

∠Z=180°-99°

∠Z=81°

Now, YZ/sinX=XZ/sinY=XY/sinZ

YZ/sin17°=XZ/sin82°=700/sin81°

XZ/0.9902=700/0.9876

XZ/0.9902=708.78

XZ=701.83

Now, cos17°=XW/701.83

0.9563=XW/701.83

XW=0.9563×701.83

XW=671.16

Therefore, the length of XW is 671.16 units.

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Answer:671

Step-by-step explanation:

Given piecewise function has a jump discontinuity at 0 or x=0 i.e. B.

What exactly is a piecewise function?

A piecewise function is one that has multiple definitions in different x intervals. A piecewise function's graph is divided into parts that correspond to each of its definitions. A very excellent example of a piecewise function is the absolute value function. Let us investigate why it is thus named. We know that an absolute value function is defined as f(x) = |x|.

f(x)=(x if x≥0 ,

     -x  if x><0)

This piecewise function should be interpreted as

When x is higher than or equal to 0, f(x) equals x.

When x is less than zero, f(x) equals -x.

Now,

As jump discontinuity is defined as where the endpoint of one segment and the start of the following segment may have the same x coordinate but have different values of f(x). In the piecewise linear function, such a difference is known as a jump discontinuity.

and in the given graph that happened at x=0 or 0.

Hence,

         Given piecewise function has a jump discontinuity at 0.

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Answer:

h = 10.0708 cm

Area of shaded region = 8.1841 [tex]cm^{2}[/tex]

Step-by-step explanation:

r = radius of circle

 = 14 cm

h = perpendicular height of triangle

Use SinФ trigonometric function to determine h

SinФ = [tex]\frac{Opposite}{Hypotenuse}[/tex]

Sin46° = [tex]\frac{h}{14}[/tex]

Cross-multiplication is applied:

∴h = (14)(Sin46°)

   h = 10.0708 cm (Rounded to four decimal places)

Area of sector = [tex]\frac{AngleOfSector}{360^{o}}[/tex] × ([tex]\pi r^{2}[/tex])

                         = [tex]\frac{46}{360}[/tex] × [tex]\pi (14^{2})[/tex]

                         = [tex]\frac{9016}{360} \pi[/tex] [tex]cm^{2}[/tex]
                         = 78.68 [tex]cm^{2}[/tex]

Area of triangle = [tex]\frac{1}{2}[/tex] × (Base of triangle) × h

                           = [tex]\frac{1}{2}[/tex] × (14 cm) × [(14)(sin46°)]
                           = (98)(sin46°)

                           = 70.50 [tex]cm^{2}[/tex]

∴Area of yellow shaded region = Area of sector - Area of triangle

           = {[[tex]\frac{9016}{360} \pi[/tex]] - [(98)(sin46°)]} [tex]cm^{2}[/tex]

           = 8.1841 [tex]cm^{2}[/tex]  (Rounded to four decimal places)

The probability of a defect units is 0.3174 by calculating the z-score of the greater than and less than value.

When the distribution is normal, we use the z-score formula.

Z = (X - μ)/σ

We have σ = 0.15 and units with weights less than 9.85 or greater than 10.15 ounces will be classified as defects.

μ = 10.15 - 0.15 = 9.85 + 0.15 = 10

Now, the probability that a unit is defective.

P(X ≥ 10.15)

1 subtracted by the pvalue of Z when X = 10.15

[tex]Z = \frac{10.15-10}{0.15}[/tex]

Z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

P(X ≤ 9.85)

[tex]Z = \frac{9.85-10}{0.15}[/tex]

Z = -1  has a pvalue of 0.1587

P = P(X ≥ 10.15) + P(X ≤ 9.85)

P = 0.1587 + 0.1587

P = 0.3174

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The area of the rectangle is 200 square centimeters

The area of a rectangle can be found by multiplying its length and width. In this case, the width is given as w and the length is given as 2w.

Therefore, the area of the rectangle can be found using the expression 2w^2.

If the width of the rectangle is 10 centimeters, we can substitute this value into the expression for the area to find the area in square centimeters.

Area = 2w^2

= 2(10)^2

= 2(100)

= 200 square centimeters

Therefore, the area of the rectangle is 200 square centimeters

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Answer:

Step-by-step explanation:

Based on the information given, we can calculate the change in the depth of the river between the years 1846, 1847, and 1848.

Change in depth between 1846 and 1847:

The depth of the river dropped from 5 feet in 1846 to 4.9 feet in 1847. The change in depth can be calculated as:

Change in depth = 4.9 - 5 = -0.1 feet

So, the depth of the river dropped by 0.1 feet between 1846 and 1847.

Change in depth between 1847 and 1848:

The depth of the river rose from 4.9 feet in 1847 to 6.4 feet in 1848. The change in depth can be calculated as:

Change in depth = 6.4 - 4.9 = 1.5 feet

So, the depth of the river increased by 1.5 feet between 1847 and 1848.

Answer:

below

Step-by-step explanation:

12m=6km

divide both by 6

2m=1km

how many km is equal to 18m?

18m=9km

how many m are equal to 42km?

42km=64m

never gonna give you up, never gonna let you down

After rounding off the numbers product of the given numbers is 27000.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The given number are 88 and 304.

Rounding each number to the nearest 10

That is, 88 to 90 and 304 to 300

Now, 88×304 can be written as

90×300

= 27000

Therefore, after rounding off the numbers product of the given numbers is 27000.

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The value of x and y in the equations are as follows:

x = -8

y = -1

System of equation can be solved using different method such as elimination method, substitution method and graphical method. Therefore, let's use elimination method to solve the equation.

Therefore,

8x - 8y = -8

-3x + 4y = -4

multiply equation(ii) by 2

8x - 8y = -8

-6x + 8y = -8

add the equations

2x = -16

x = -16 / 2

x = -8

Let's find y

-8y = -8 - 8x

-8y = -8 - 8(-8)

-8y = -8 + 16

-8y = 8

y = 8 / -8

y = -1

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Answer:

6

Step-by-step explanation:

F = 4 x 6 / 2^2

= 6

The measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.

What is the angle measurement?

A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.

If the measure of angle x needs to be increased by 200, we can simply add 200 to the original measure of angle x to find the new angle.

So, if the original measure of angle x is, for example, 30 degrees, the new angle would be:

New angle = 30 degrees + 200 degrees

New angle = 230 degrees

Therefore, if the measure of angle x needs to be increased by 200, the new angle would be the original measure of angle x plus 200 degrees.

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A graph of the resulting image after the given triangle is rotated 90° counterclockwise about the origin is shown in the image below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle ABC, the coordinates of the vertices of the image are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (-5, 7) → Ordered pair A' = (-(7), -5) = (-7, -5).

Ordered pair B  = (-8, 3) → Ordered pair B' = (-(3), -8) = (-3, -8).

Ordered pair C  = (-2, 6) → Ordered pair C' = (-(6), -2) = (-6, -2).

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The value of x from the right triangle is x = 3√11

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°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDBC

Now , BD is perpendicular to AC

So , the triangles ΔABC and ΔDBC are similar

The measure of BD = x

The measure of AD = 9

The measure of DC = 20

Now , AD / AB = AB / DC

Substituting the values in the equation , we get

9/a = a/20

On simplifying the equation , we get

a² = 180

So , a = 3√20

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Now , the measure of x = √ ( 3√20 )² - ( 9 )²

So , the measure of x = √ ( ( 180 ) - 81 )

The measure of x = √ 99

The measure of x = 3√11

Hence , the measure of x of triangle is 3√11

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A yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

To convert a yearly salary to an hourly rate, you need to divide the annual salary by the number of working hours in a year.

Assuming a typical workweek of 40 hours and 52 weeks in a year, the total number of working hours in a year is:

40 hours/week x 52 weeks/year = 2,080 hours/year

To calculate the hourly rate for a yearly salary of $47,000, you can divide the annual salary by the total number of working hours in a year:

$47,000 / 2,080 hours = $22.60 per hour

Therefore, a yearly salary of $47,000 is equivalent to an hourly rate of approximately $22.60 per hour.

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In the given figure , the measure of angle p is 41 degrees.

A quadrilateral is a closed figure that has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

It is given that the kite is shares a side with an equilateral triangle to form a new quadrilateral.

The side of kite which is attatched to triangle contains an angle of 79 degree.

the other end of side which is attatched to the triangle contains angle of 120 degree because it is attatched to the side of triangle which makes a straight line and the triangle is having each angle of 60 degrees.

So, the angle opposite to it will also be of 120 degrees.

Now in the kite, the angles are,

79+120+p+120=360

p=360-319

p=41 degrees

Hence, the measure of angle p is 41 degrees.

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Based on degree, polynomials can be classified as follows:

Then for number of terms, there are monomials with a single term, binomials with two terms, trinomials with three terms and multinomials with more than three terms.

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Note that if m/3 = 54°, then the measure of each missing angle are given as follows:

a. m<1= 36°

b. m<2= 90°

c. m<4= 36°

d. m<5= 90°

e. m<6= 45°

f. m<7= 126°

g. m<8= 54°

h. m<9= 126°

i. m<10= 45°

j. m<11 = 36°

k. m<12 = 144°

l. m<13 = 36°

m. m<14 = 144°

We are given three clues from which we solve the missing angles.

Clue 1: m∠3 given as 54°

Clue 2: m∠ 2 given as 90°

The two lines that (are now labeled AB and CD are parallel to one another. Thus:

a) ∠1, ∠2, and ∠3 are complimentary, ∠1 = 180 - (90+54) = 36°

b) ∠2 = 90° (given)

c) ∠4 = 36° (Opposite angles) ∠1 ≅ ∠4

d) ∠5 =90°  (Opposite angles) ∠2 ≅ ∠5

e) ∠6 = 54°  (Opposite angles) ∠13≅ ∠6

f) ∠7 = ∠1+∠2 (since Line EF is perpendicular to GH, (∠1+∠2) are corresponding angles to ∠7
g) ∠8 = 54° (∠3 and ∠8 are corresponding angles)

h) ∠9 = 126° (∠9 corresponds to ∠5 and ∠4; an alternate explanation is the angle on straight line (∠8 and ∠9) (180-54 = 126°)

i) ∠10 = 54° (∠6 and ∠10 are corresponding angles)

j) ∠11 = 36° (∠11 and ∠1 are corresponding angles)

k) ∠12 = 144° (∠12 corresponds to (∠2+∠3)

l) ∠13 = 36° ( ∠12 and ∠13 are supplementary angles)

m) ∠14 = 144° (∠12 and ∠14 are opposite angles)

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Answer: A quarter is worth $0.25 and a dime is worth $0.10, so the total amount of money Alonso has can be represented by the expression 0.25x + 0.1y. To find one possible solution to the system of inequalities, we need to find the values of x and y that satisfy both the inequality 0.25x + 0.1y ≥ 3.60 and the inequality y ≥ 0.

The inequality 0.25x + 0.1y ≥ 3.60 represents all points (x, y) that are on or above the line 0.25x + 0.1y = 3.60. The inequality y ≥ 0 represents all points (x, y) that are above or on the x-axis. The intersection of these two regions is the solution set of the system of inequalities, which represents all points (x, y) that satisfy both inequalities.

To graph the solution set, we can start by plotting the line 0.25x + 0.1y = 3.60 and shading the region above the line. Then, we can plot the x-axis and shade the region above the x-axis. The intersection of the two shaded regions is the solution set.

One possible solution to the system of inequalities is the point (14, 4). This means that Alonso has 14 quarters and 4 dimes, which total $3.60. However, there may be other solutions to the system of inequalities that would also satisfy the conditions.

Step-by-step explanation:

The required probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

Normal distributions can be altered to standard normal distributions by the formula:

Z = (X - μ)/σ

The difference in diameter between the lid and cup, D = L - C, is also a normal distribution with mean μ(D) = μ(L) - μ(C) = 3.98 - 3.96 = 0.02 inches and standard deviation σ(D) = √(σ² (L)+ σ²(C)) = 0.03 inches.

The probability that a randomly selected lid will fit on a randomly selected cup is the probability that D is between 0 and 0.06 inches. To find this probability, we can standardize D using the z-score formula and find the corresponding area under the standard normal curve.

Let z = (D - μ) / σ.
Then, the required probability is,
P(0 < D < 0.06) = P(0 < z < (0.06 - 0.02) / 0.03) = P(0 < z < 2).

We can use a standard normal table or a calculator to find the area under the standard normal curve between 0 and 2. This area represents the required probability. For example, using a standard normal table, we can find that P(0 < Z < 2) = 0.9772.

Therefore, the probability that a randomly selected lid will fit on a randomly selected cup is 0.9772, or 97.72%.

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The statements that are not characteristics of a normal curve are III, IV, and VI. The answer is B.

A normal curve is a bell-shaped probability distribution that is commonly used in statistics. It has several key characteristics that make it useful in modeling real-world data. These include the fact that the mode and median occur at the mean, the curve is symmetric about the mean, and the total area under the curve and above the horizontal axis is equal to 1.

In addition, the normal curve is asymptotic to the horizontal axis on both sides. However, not all normal curves are asymptotic to the horizontal axis on both sides, as this is only true for curves with a finite standard deviation.

Finally, the probability that a normal random variable is equal to a specific discrete value is always zero, since the normal variable is continuous, and the probability that the variable is between two values is given by the area under the curve between those values and the horizontal axis.

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The possible value of n in the triangle given is, n < 3x+5

The triangle is a polygon with three side, vertex, and angles.

Given that, a triangle has side lengths measuring 2x + 2 ft, x + 3 ft,

and n ft.

We asked to find the expression that represents the possible values of n.

We know that,

The sides of a triangle rule assert that the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side.

Therefore,

2x+2+x+3 = 3x+5

Thus, the possible value of n is,

n < 3x+5

Hence, the possible value of n in the triangle given is, n < 3x+5

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Answer:

10y - 3

Step-by-step explanation:

(y + 9y) + (-10 - 3)

(1 + 9) x y + (-10 - 3)

10y - 13

The Probability that all four of the light bulbs work is 0.004 approx.

The probability that all four light bulbs work can be calculated by taking the product of the probability that each individual light bulb works. If each light bulb works independently of the other light bulbs, then the probability that all four light bulbs work is:

P(all 4 bulbs) = P(bulb 1) * P(bulb 2) * P(bulb 3) * P(bulb 4)

P(all 4 bulbs) = 0.25 * 0.25 * 0.25 * 0.25

P(all 4 bulbs) = 0.25^4

P(all 4 bulbs) = 0.00390625

So, the probability that all four light bulbs work is 0.00390625 or approximately 0.004.

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Answer:

B.y=(x+2)

Step-by-step explanation

Based on theoretical probabilities, the best estimate of the total number of times Jon tossed the cube would be 60 times. The probability of rolling a "4" on a standard die is 1/6. If Jon got "4" on 5 of the tosses, then the total number of tosses would be 5/ (1/6) = 30 tosses. To find the best estimate of the total number of tosses, it is common to round up to the nearest multiple of 10, which in this case would be 60. Therefore, the best estimate would be 60 times (Option B).

Answer: 15/7

Step-by-step explanation:

9/16 / 7/10 = 9/6 * 10/7 multiply by recipricol to find answer

90/42

15/7 simplify

The circumcenter of the triangle is (-3, -4), units.

The circumcenter is the intersection point of the perpendicular bisectors of sides of a triangle. It is the Centre of a triangle's circumcircle.

For a right-angled triangle, the circumcenter lies on the hypotenuse.

The middle of the horizontal length of the triangle = - 3

The  middle of the vertical length of the triangle = - 4

The circumcenter of the triangle is located at (x, y ) = ( -3, -4 )

Thus, the circumcenter of the triangle is determined from the interception point of the horizontal length and vertical length.

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164 pounds is equal to 74.389 kilograms (kg). To convert pounds to kilograms, you can use the conversion factor of 0.45359237, which is the number of kilograms in one pound.

To convert 164 pounds to kilograms, you can use the conversion factor of 0.45359237, which represents the number of kilograms in one pound. Multiplying 164 pounds by this conversion factor gives the result in kilograms. Using this method, 164 pounds is equivalent to 74.389 kilograms. This conversion is useful in many situations, such as when traveling to countries that use the metric system, or when working with scientific measurements that use metric units. Understanding the relationship between pounds and kilograms can help to make conversions easier, and allow for more accurate and consistent measurements across different systems of measurement.

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The difference between a right circular cylinder and a cylinder is that a right circular cylinder has a circular base and is perpendicular to the base, whereas a cylinder can have any shaped base and the sides do not have to be perpendicular to the base.

A right circular cylinder has a circular base and its sides are perpendicular to the base, forming a right angle. This means that the axis of the cylinder is at a right angle to the base.

On the other hand, a cylinder can have any shaped base, such as a rectangle or an ellipse, and the sides do not have to be perpendicular to the base. This means that the axis of the cylinder can be at any angle to the base.

In summary, the main difference between a right circular cylinder and a cylinder is the shape of the base and the angle of the sides to the base. A right circular cylinder has a circular base and perpendicular sides, while a cylinder can have any shaped base and the sides can be at any angle to the base.

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