Using the description of the solid region, set up the triple integral for the mass, the center of mass, and the moment of inertia about the z-axis. Do not evaluate the integrals. the solid bounded by z = 16 - x2 - y2 and z = 0 with density function p(x, y, z) = kz (a) the mass m m = 1 (C ) cz ay ox dz dy dx √16x² To (b) the center of mass z z = (C ) dz dy dx -V16-2 Go (c) the moment of inertia about the z-axis I, (C 1- ) az dy dx dz dy dx

The future value of the annuity is $11,200. $30,000 was invested, and the interest earned is -$18,800.

To find the future value of an annuity using the simple interest formula, we can use the following formula:

FV = P × (1 + r × n)

where:

FV is the future value of the annuity,

P is the annual payment,

r is the annual interest rate, and

n is the number of years.

In this case, the annual payment (P) is $10,000, the annual interest rate (r) is 4%, and the number of years (n) is 3. Let's calculate the future value.

FV = $10,000 × (1 + 0.04 × 3)

FV = $10,000 × (1 + 0.12)

FV = $10,000 × 1.12

FV = $11,200

Therefore, the future value of the annuity is $11,200.

To determine the amount invested, we need to multiply the annual payment by the number of years.

Amount Invested = P × n

Amount Invested = $10,000 × 3

Amount Invested = $30,000

So, $30,000 was invested.

To calculate the interest earned, we subtract the amount invested from the future value.

Interest Earned = FV - Amount Invested

Interest Earned = $11,200 - $30,000

Interest Earned = -$18,800

The negative value indicates that the annuity has not earned interest but has incurred a loss. However, it's worth noting that the simple interest formula assumes that the interest earned is proportional to the initial investment and does not account for compounding. If you're looking for a more accurate calculation of interest earned, it's advisable to use a compound interest formula.

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Answer:

20

Step-by-step explanation:

90-50=40... therefor X must equal 20

a) Using the LCM of the sum of ratios of the number of games played by Team A and Team B, the smallest possible number of games that each team could have played is 30.

b) The smallest possible number of points that Team A could have had at the end of the season is 27.

The LCM refers to the lowest common multiple.

The lowest common multiple is the least or smallest number that two numbers can divide evenly.

Team A:

Win = \(\frac{1}{10}\)

Draw =   \(\frac{3}{5}\)

Loss =  \(\frac{3}{10}\) (1 - \(\frac{1}{10}\) - \(\frac{3}{5}\))

The ratio of Win, Draw, and Loss = 1:6:3

The sum of ratios = 10

Points

Team B:

The ratio of Win, Draw, and Loss = 1:4:1

The sum of ratios = 6

a) Least Possible Number of Games:

LCM of 10 and 6 = 30

b) Least Possible Number of Points for Team A:

The ratio of Win, Draw, and Loss = 1:6:3

Points for a win = 3

Points for a draw = 1

Points for a loss = 0

Total points = (\(\frac{1}{10}\) x 30 x 3 + \(\frac{6}{10}\) x 30 x 1 + \(\frac{3}{10}\) x 30 x 0)

= 27 (9 + 18 + 0)

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Two football teams were playing in a league last season. Team A won \(\frac{1}{10}\) of their games, drew \(\frac{3}{5}\) of their games, and lost the rest of their games.

The volume of the prim is 24 cubic cm and each cube represents  4/3 cm³

Volume is defined as the amount of substance that can be filled in the shape in such a way that the whole figure is complete filled with that substance. Vοlume is defined as the space οccupied within the bοundaries οf an οbject in three-dimensiοnal space. It is alsο knοwn as the capacity οf the οbject.

Here the measure the cube measure of a centimetre on one side

Length of the prim = \(1*4=4 cm\)

Breadth of the prism = \(1*2=2cm\)

Height of the prism = \(1*3=3 cm\)

So, the volume of the prism = l*b*h

Volume of the prism = \(\rm 4*3*2=24\ cm^3\)

Hence, the volume of the prism is 24 cubic cm.

There are total 18 cubes, so each cube represents= 24/18 = 4/3

Thus, each cube represents  4/3 cm³

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Answer:

A) 12 pins

B) 11 pins

Answer:

$3.85? 12/3.12 = $3.85

The answer would have came out of 3.84615384615

Then round up the answer to 3.85.  So the unit price is $3.85.

Leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

To calculate the cost, we need to determine the total energy consumed by the TV while you were on vacation and then convert it to dollars.

First, let's calculate the energy consumption in kilowatt-hours (kWh):

Power (in kilowatts) = Voltage (in volts) * Current (in amps) / 1000

Power = 120 V * 0.96 A / 1000 = 0.1152 kW

Now, we need to find the total energy consumed in kilowatt-hours (kWh) over the two-week period:

Energy (in kilowatt-hours) = Power (in kilowatts) * Time (in hours)

Energy = 0.1152 kW * 24 hours/day * 14 days = 38.4512 kWh

Next, let's calculate the cost of this energy consumption:

Cost = Energy (in kilowatt-hours) * Cost per kilowatt-hour

Cost = 38.4512 kWh * $0.116/kWh = $4.46 (rounded to two decimal places)

Therefore, leaving the TV on for two weeks while on vacation would cost you approximately $4.46.

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Answer:

Step-by-step explanation:

Two angles are called supplementary when their measures add up to 180 degrees.

Answer:

supplementary

Step-by-step explanation:

Two angles are called supplementary when their measures add up to 180 degrees.

The linear equation for the attendance in terms of the price, p is

2600= -150p + 3650

A =m*p + b

where A= attendance , m = slope , b = y-intercept and p = price

When p=11 then A=2000 , i  e , (11, 2000).

When p= 7 , then A=2600, i .e ,  (7 , 2600).

m= (b-d)/(a-c)

=> m = (2600-2000)/(7 - 11)

        = -150

Therefore , 2600= -150p + b

To get the value of b,

putting the value of p in the obtained equation,

we get,

2600= -150 * 7+ b

2600 = -1050 + b

b = 3650

Hence , our equation becomes

2600= -150p + 3650

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on

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An expression is defined as a set of numbers, variables, and mathematical operations. The sum of three and the square root of a number is expressed as 3 + √x.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let the unknown number be represented by x.

1.) The sum of three and the square root of a number.

3 + √x

2.) Nine less than a number cubed.

x³ - 9

3.) The quotient of a number and 7.

x ÷ 7

4.) Four times a quantity plus five.

4x + 5

Hence, The sum of three and the square root of a number is expressed as 3 + √x.

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Answer: used plot graph

Step-by-step explanation: sourced it with plot

The way to plot the graph is to find both x-intercept and y-intercept. (Unless if it's a polynomial function which you need to find vertexes. But this one is linear so no vertex.)

(1) - Find x-intercept, substitute y = 0

\(y=3x+1\\0=3x+1\\-1=3x\\3x=-1\\x=-\frac{1}{3}\)

Therefore, the graph intercepts x-axis at (-1/3, 0)

(2) - Find y-intercept, substitute x = 0

\(y=3x+1\\y=0+1\\y=1\)

Therefore, the graph intercepts y-axis at (0,1)

The graph's picture is below

The composition of similarity transformations that maps Triangle LMN to TriangleL'M'N is a dilation with a scale factor less than 1 and then a reflection. Opion A. This is further explained below.

Generally, In the case of a reflection across the y-axis, the y-coordinate of a point stays the same but the x-coordinate is changed into its inverse.

Triangle LMN has the coordinates (2, 1), (1, 1), and (1, 3).

(-4,-4) (-3,-4) (-3,-2).

In conclusion, Assuming that the coordinates (2, 1), (1, 1), and (1, 3) of Triangle LMN. This is the translation 5 units down (x,y-5): Two units to the right (x+2, y-5) of the coordinates (2,-4), (1,-4), and (1,-2): (4, -4), (3, -4), (3, -2)

It is a reflection along the y-axis, with coordinates of (-4,-4) and (-3,-4) (-3,-2)

Therefore, Triangle L'M'N' is the result of the transformation sequence in Option A.

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Answer: a

Step-by-step explanation:

i got it right on the test

Answer:CED

Step-by-step explanation:

Answer:

C, E, and D

Step-by-step explanation:

Given:

The different sets of ordered pairs in the options.

To find:

The sets of ordered pairs that show equivalent ratios

Solution:

The set of ordered pairs show equivalent ratios, if

\(\dfrac{y}{x}=k\)

Where, k is a constant.

For option 1,

(1, 2), (2, 3), (4, 7)

\(\dfrac{2}{1}\neq \dfrac{3}{2}\)

For option 2,

(2, 2), (4, 4), (6, 6)

\(\dfrac{2}{2}=\dfrac{4}{4}=\dfrac{6}{6}=1=k\)

The set of ordered pairs (2, 2), (4, 4), (6, 6) show equivalent ratios.

For option 3,

(3, 1), (4, 1), (5, 1)

\(\dfrac{1}{3}\neq \dfrac{1}{4}\)

For option 4,

(4, 1), (8, 2), (12, 3)

\(\dfrac{1}{4}=\dfrac{2}{8}=\dfrac{3}{12}=k\)

The set of ordered pairs (4, 1), (8, 2), (12, 3) show equivalent ratios.

For option 5,

(2, 1), (4, 3), (5, 4)

\(\dfrac{1}{2}\neq \dfrac{3}{4}\)

So, sets of ordered pairs in options 1, 3 and 5 does not show equivalent ratios.

Therefore, the correct options are 2 and 4.

Answer:

300%

Step-by-step explanation:

Let the production of rice in 1995 be x.

From 1995 to 1996, the production increased by 50%

This implies that the production of rice is now:

(100 + 50) / 100 * x = 150/100 * x = 1.5x

It means the production is now 1.5 that of 1995.

We want the production in 1997 to be 6 times that in 1995, that is 6x, this implies that we have to find the percentage increase from 1996 to 1997:

(100 + P) / 100 * 1.5x = 6x

By cross-multiplying:

100 + P = 6x * 100 / 1.5x

100 + P = 400

P = 400 - 100

P = 300%

Therefore, the production must be increased by 300%.

The probability of choosing a red marble is given as 7/12. This probability is the ratio of the number of red marbles to the total number of marbles.

Let's denote the number of red marbles as \(\( R \)\).

So, we have the equation:

\(\( R / 84 = 7 / 12 \)\)

We can solve this equation to find the value of \(\( R \)\).

The solution to the equation is \(\( R = 49 \)\). Therefore, there must be 49 red marbles in the bag.

The smaller zero of the given quadratic equation as required in the task content is; -12.

As evident in the task content; the smaller zero of the zeroes of the given equation as required can be determined as follows;

To determine the zeroes;

x² - 144 = 0

x² = 144

x = 12 Or x = -12.

Ultimately, since -12 < 12; it follows that the smaller zero as required is; -12.

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The equation of the tangent line to the curve y = 5x^2 − x^3 at the point (1, 4) is y = 7x - 3.

For the equation of the tangent line to the curve at the point (1, 4), we need to find the slope of the tangent line and the point-slope form of the equation.

First, we find the derivative of y with respect to x:

y' = 10x - 3x^2

Next, we plug in x = 1 to find the slope of the tangent line at the point (1, 4):

y'(1) = 10(1) - 3(1)^2 = 7

So the slope of the tangent line at the point (1, 4) is 7.

Now we use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point.

Plugging in m = 7, x1 = 1, and y1 = 4, we get:

y - 4 = 7(x - 1)

Simplifying, we get:

y = 7x - 3

So the equation of the tangent line to the curve y = 5x^2 − x^3 at the point (1, 4) is y = 7x - 3.

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Answer:

Step-by-step explanation:

-1/3 on my diagnostic test

Solution:

The sequence is given below as

Concept:

To figure out the common ratio, we will use the relation below

By substituting the values, we will have

Hence,

The common ratio of the sequence is

Therefore, the solution to the given differential equation that passes through the origin is \(z = -1/4 ln(-12t^2)\).

To find the solution to the given differential equation \(dz/dt = 6te^(4z)\)that passes through the origin, we can separate the variables and integrate.

Starting with the differential equation:

\(dz/dt = 6te^(4z)\)

We can separate the variables by moving all terms involving z to one side and terms involving t to the other side:

\(e^(-4z) dz = 6t dt\)

Now, we can integrate both sides:

∫\(e^(-4z) dz = ∫6t dt\)

To integrate the left side, we can use the substitution u = -4z, du = -4dz:

\(-1/4 ∫e^u du = ∫6t dt\\-1/4 e^u + C1 = 3t^2 + C2\)

Simplifying and using the initial condition that the solution passes through the origin (z = 0 when t = 0), we have:

\(-1/4 e^(-4z) + C1 = 3t^2 + C2\)

Since the solution passes through the origin, when t = 0, z = 0. Substituting these values into the equation:

\(-1/4 e^(-4(0)) + C1 = 3(0)^2 + C2\)

-1/4 + C1 = 0 + C2

C1 = C2

Now, substituting C1 = C2 back into the equation:

\(-1/4 e^(-4z) + C1 = 3t^2 + C1\\-1/4 e^(-4z) = 3t^2\)

To solve for z, we isolate \(e^(-4z):\)

\(e^(-4z) = -12t^2\)

Taking the natural logarithm of both sides:

\(-4z = ln(-12t^2)\\z = -1/4 ln(-12t^2)\)

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By inspection, the cost appears to be $380

\( \sf \: = \sqrt[3]{50} \: \:cm \\ \sf \: = 3.68 \: cm\)

Answer:

3.68 cm

Hope you could get an idea from here.

Doubt clarification - use comment section.

There are 66,960 number of ways to set up a batting order of 9 players from among the 12 players on the baseball team.

To determine the number of ways to set up a batting order of 9 players from among the 12 players on a baseball team, we can use the concept of permutations.

Since the order matters in a batting order, we can use the formula for permutations.

The number of permutations of selecting 9 players from a pool of 12 players is given by:

P(12, 9) = 12! / (12 - 9)!

Calculating this, we have:

P(12, 9) = 12! / 3!

= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4) / (3 * 2 * 1)

= 12 * 11 * 10 * 3 * 7 * 2

= 66,960

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Answer:

transitive property of equality

Step-by-step explanation:

if a=b and b=c then a=c

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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