A spherical tank with radius 3 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 2 m spout at the top. Find the work W required to pump the liquid out of the spout. (Use 9.8 m/s2 for g.)

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)

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).

The height of the roller coaster is 200.11 feet

Method 1

Here, we make use of the cosine rule

So, we have

cos(45) = x/283

So, we have

x = 283 * cos(45)

Evaluate

x = 200.11

Method 2

Here, we make use of the sine rule

The sine can be calculated as

When x + y = 90;

sin(x) = cos(y)

This means that

sin(45) = cos(45)

So, we have

sin(45) = x/283

So, we have

x = 283 * sin(45)

Evaluate

x = 200.11

Hence, the height is 200.11 feet

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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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Answer: a type of equation

Step-by-step explanation:

Based on the information, the integer used will be (10 - 4). The difference is 6.

On a number line, there'll be 6 units between the numbers

To find the difference between two integers by adding the additive inverse, we can follow these steps:

Subtract the smaller integer from the larger one: (larger integer) - (smaller integer).

Take the absolute value of the result to get the distance between the two integers on a number line.

The distance between two integers is the absolute value of the difference, so we do not include the sign in our answer. The answer will always be a non-negative number.

By plotting the two integers on a number line and counting the units between them, we can visualize the distance between them.

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answer: 204!!!

tn = a + (n-1)d

a is the first value

n is the position

d is the difference

t(50) = 8+(50-1)(4)

t(50)= 204

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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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:

Answer:

The table represents a linear function because the rate of change is constant or all the points lie on a straight line.

Step-by-step explanation:

From the given table it is noticed that the line passing through the points (2,5), (4,10), (6,15) and (8,20).

The slope of the line is

The slope of line is . It means the value of y increased by 5 if the value of x increased by 2.

From the given points we can noticed that the value of y increased by 5 if the value of x increased by 2. So, the function has same slope for any two points.

Since the rate of change (slope) is same for all points, therefore the table represents a linear function.

If we plot these points on a coordinate plane and connect then we get a straight line. I means it is a  linear function.

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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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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Answer:

A. B is correct

B. A is correct

C. B is correct

Step-by-step explanation:

Area of triangle: A = 1/2bh

A. Area of each triangle: A = 1/2 x 11.5 x 12 = 69

Total surface areas = 4(area of triangle) + area of square = 4(69) + 12^2 = 420

So A is incorrect and B is correct

B. Area of triangle: A = 1/2 x 13.9 x 16 = 111.2

Surface area = 4(area of triangle) = 4(111.2) = 444.8

So A is correct and B is incorrect

C. Area of triangle with base of 10: A = 1/2 x 10 x 7 = 35

Area of triangle with base of 8.1: A = 1/2 x 8.1 x 16 = 64.8

Total surface areas = 2(area of triangle base of 10) + 2(area of triangle base of 8.1) + area of rectangle = 2(35) + 2(64.8) + (10x8.1) = 280.6

So A is incorrect and B is correct.

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

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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Based on the information, the equation can be simplified as follows: 7xy - 2x² - y

To simplify an equation we must carefully observe all the values that make up the equation. Once we identify the values with the same symbols, (x or y) we can group them. According to this procedure we can group the values of x as shown below:

In this case the 2x was added with the 5x to form the 7x. In the case of 2x², it cannot be added with the other values of x because it has an exponent of ².

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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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Mrs. Flips sold 240 large chocolate chips.

Mrs. Flips sold 60 small peanut butter cookies.

In order to write the required expressions that models the situation, we would assign variables to the number of large chocolate chips and the number of small peanut butter cookies, and then translate the word problem into algebraic equation as follows:

Since Mrs. Flips charged $1 for the chocolate chip and 50-cents for the peanut butter cookies and collected $270 total, an expression that models the situation is given by:

x + 0.5y = 270

Additionally, she sold a total of 300 cookies:

x + y = 300

270 - 0.5y + y = 300

0.5y = 30

y = 60 small peanut butter cookies.

x = 270 - 0.5(60)

x = 240 large chocolate chips.

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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

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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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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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:

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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Answer:

Step-by-step explanation:

divide the required value by the total value and multiply by 100.

a/bx100= y

2.2 - 2.1 =0.1 inches

percentage of error=

0.1 / 2.2 x100

4.54 %

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:

6

Step-by-step explanation:

F = 4 x 6 / 2^2

= 6

Answer:

-4

Step-by-step explanation:

I hate calc nevertheless, factor the top number, cancel out x+2 and then plug in -2. Its simple once you see the pattern

[tex]\frac{x^2 - 4}{x+2} \\\frac{(x+2)(x-2)}{x+2} \\(x-2)\\-2-2\\-4[/tex]

Answer:

B.y=(x+2)

Step-by-step explanation