In this problem, we will look at properties of solids with base on the xy-plane given by the circle x2+y2=a2 and its interior, where a>0
is to be given in parts (i) and (ii) below.
(i). Let a=4, and assume that cross-sections of thesolid perpendicular to the x -axis are circular disks with diameters lying in the xy-plane. Find the area A(x) of the cross-section at location x.
(ii). Let a=9, and assume that cross-sections of the solid perpendicular to the x-axis are equilateral triangles with bases in the xy-plane. Find the area A(x) of the cross-section at location x.
(iii). Find the volume of the solid described in (i) above.

The volume of a rectangular prism is 8/15 in³ option - A is correct.

Therefore, the area of the base of a rectangular prism is multiplied by the height to determine its volume. The formula for calculating a rectangular prism's volume is Volume (V) = height of the prism base area. It is measured in cubic units like cm³, m³, and in³.

The Rectangular Prism's Volume Formula

The volume of a prism can be calculated by dividing the base area by the height. Consequently, a prism's volume is equal to its base area times its height.

The equation for calculating a rectangular prism's volume is

V = l × w × h

V = 1/2 in × 8/3 in ×2/5 in

V = 8/15 in³.

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It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.

No, a parallelogram is not always a rectangle. In a rectangle, all angles must be equal to 90°. But for a parallelogram, no angles need to be equal to 90°. In a rectangle the diagonals are equal but in a parallelogram, diagonals are not equal.

Parallelogram has opposite sides equal and parallel. Rectangle also has opposite sides equal and parallel. The difference between the two is that sides of rectangles form 90 degree while that of parallelogram don't.

A square is a parallelogram. This is always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides.

It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.

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The primitive data type number has the entry 1, or 1, in the database dictionary.

The database dictionary's entry for the number data type, which is a primitive data type, is 1, or 1. It is possible for a number to be a whole number, a positive or negative number, or a floating point number, and it can also denote an amount.

Numbers are stored as numeric data types in database columns. Exact numeric kinds, values where the precision and scale need to be retained, are normally the categories into which these data types are grouped. There are six distinct sorts of numbers: INTEGER, BIGINT, DECIMAL, NUMERIC, NUMBER, and MONEY.

Integral, Floating Point, Character, Character String, and Composite types are the five fundamental categories of data types recognized by the majority of current computer languages. Within each of these broad categories, numerous particular subtypes are established.

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Answer: [tex]m\angle YOZ, m\angle VOS, m\angle UOZ, m\angle XOS, m\angle TOZ[/tex]

Step-by-step explanation:

[tex]m\angle VOS=90^{\circ}\\\\m\angle UOZ=180^{\circ}-56^{\circ}=124^{\circ}\\\\m\angle YOZ=180^{\circ}-143^{\circ}=37^{\circ}\\\\m\angle XOS=126^{\circ}\\\\m\angle TOZ=180^{\circ}-33^{\circ}=147^{\circ}[/tex]

The probability of randomly selecting two women from 884 subjects is 1.

The probability of randomly selecting two women from 884 subjects can be calculated using the following formula: P(A and B) = P(A) x P(B). In this case, A is the event of randomly selecting a woman from 884 subjects and B is the event of randomly selecting a second woman from the remaining 883 subjects.

Therefore, P(A) = 884/884 = 1 and P(B) = 883/883 = 1. Thus, P(A and B) = 1 x 1 = 1. Then, the probability of randomly selecting two women from 884 subjects is 1. To round to four decimal places, the probability is 0.0000.

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Answer: -5

Step-by-step explanation:

The minimum value is -5 at x = 1. Coordinate (1,-5)

Answer:slow

Step-by-step explanation:

its slow

Answer:

Assuming it stays the same speed, 126km.

Step-by-step explanation:

By doing 84/2, I know it takes the car one hour to go 42km. For three hours, we must do 42x3, which is 126.

Answer:

-2.43, -2, 5/9, 2/3, 2, 2.045

Step-by-step explanation:

Negative numbers are less than positive numbers, and we can go in numerical order from 1, 2, 3 to find which number is greater than the other

They may bake 20 additional bags of cookies. The problem is represented by the inequality x < 80.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, A bakery wants to bag at most 100 cookies into cookie packs. Each cookie pack has 4 cookies. They have already bagged 20 cookies.

Since each cookie pack can hold 4 cookies

Thus, 100 cookies will require = 100/4 packs

100 cookies will required = 25 packs

Since They have already bagged 20 cookies.

Thus,

The total pack they used = 20/4

The total pack they used = 5

Inequality:

let "x" be the number of cookies they can make

80 > x

Therefore, 20 more bags of cookies they could make. the inequality that represents the situation is x< 80.

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The nontrivial linear combination of vectors whose sum is equal to zero vector for the given set of linearly independent vectors is given by :

u = 2v  + (5/4)w .

As given in the question,

Given set of linearly independent vectors are:

S={(3,2),(−1,1),(4,0)}

Let us consider vectors u , v , and w represents the given set of linearly independent vectors which is given by :

u = ( 3, 2 )

v = ( -1 , 1 )

w = ( 4, 0 )

To get the nontrivial linear combination of vectors whose sum is equal to zero that is ( 0 ,0 ) is given by :

( 3, 2 ) - 2( -1 , 1 ) - (5 / 4)(4 ,0 ) = (0 , 0)

⇒ u -2v - ( 5 / 4 )w = 0

⇒ u = 2v + ( 5 / 4 )w

Therefore, the nontrivial linear combination of vectors whose sum is equal to zero is given by u = 2v + ( 5 / 4 )w.

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The estimation of the numbers given as 0.87 × 310 will give 270.

You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation. A figure is discovered through estimation.

A value, amount, or size that rounds off to the nearest whole number is said to be approximating.

The estimation of the numbers given as 0.87 × 310 will give:

= 0.9 × 300

= 270.

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Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Two friends, Caleb and Hassan, took summer jobs. The equation y = 21.5x represents Hassan's earnings in dollars and cents, y, for working x hours. Caleb earned $819.40 in 34 hours.

The rate of Caleb is given as,

Celeb's rate = $21.5 per hour

The rate of Hassan is given as,

Hassan's rate = $819.40 / 34

Hassan's rate = $24.1 per hour

The difference is given as,

⇒ $24.1 - $21.5

⇒ $2.6

Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.

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The lower limit that she traveled in three seconds is 33.45 feet and the upper limit that she traveled in three seconds is 43.45 feet

The first three seconds of a race saw a runner's pace rapidly grow.

The time is therefore 3 seconds.

The table provides her speed at half-second intervals.

We are aware,

Distance x Time Speed

Similarly

The distance equals speed x time.

t equals 0.5 seconds

Then, the minimum distance traveled overall is equal to 0.5(0 + 6.7 + 9.2 + 14.1 + 17.5 + 19.4).

Terms are multiplied and added.

= 0.5 × 66.9

= 33.45 feet

The maximum distance travelled is equal to 0.5 (6.7 + 9.2 + 14.1 + 17.5 + 19.4 + 20)

= 0.5 × 86.9

= 43.45 feet

Hence, the lower limit that she traveled in three seconds is 33.45 feet and the upper limit that she traveled in three seconds is 43.45 feet

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P(A) and P(B) are independent events.

Option (D) is correct.

What are events in probability?

In probability, an event is a set of outcomes of an experiment. For example, if you flip a coin, the possible outcomes are "heads" or "tails", and the event "getting heads" is the set of all outcomes where the coin lands on heads. Events can be mutually exclusive, meaning that they cannot happen at the same time, or they can be non-exclusive, meaning that they can happen at the same time.

The events A and B are independent. This means that the probability of event B happening (the second card selected is red) is not affected by whether or not event A has already happened (the first card selected is red).

In other words, the probability of selecting a red card on the second draw is still 1/2, regardless of whether a red card or a black card was selected on the first draw. This is because the cards are being drawn with replacement, meaning that the first card selected is returned to the stack before the second card is drawn, so the second draw is not affected by the first draw.

To calculate the probability of both events A and B happening, we can use the formula P(A and B) = P(A) x P(B|A) where P(B|A) is the conditional probability of event B given that event A has already happened. Since we know that the probability of event A is 1/2, and the probability of event B is also 1/2, we can calculate P(A and B) as: P(A and B) = (1/2) x (1/2) = 1/4

Therefore, P(A) and P(B) are independent events.

Option (D) is correct.

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For the complex number (13 - i)(13 + i), The real part is 170 and the imaginary part is 0.

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

The standard form of a complex number is a + bi; where a is a real number and the real part while b is a real number and the imaginary part. Also, i = √(-1)

a) (13 - i)(13 + i)

= 169 + 13i - 13i - i² = 169 - i² = 169 - [√(-1)]²

= 169 + 1 = 170

The real part is 170 and the imaginary part is 0.

b) -9i - 2

The real part is -2 and the imaginary part is -9.

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The possible combinations of the number of each type of treat that Cindy can buy include:

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, 6 box of cookies and 4 box of brownies will be:

= 6($3) + 4($2)

= $26

8 box of cookies and 1 box of brownies also give $26.

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The slope through the line of (4, 7) and (6, 2) can be found by using the slope formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.

Substituting the values for (4, 7) and (6, 2) into the formula:

m = (2 - 7) / (6 - 4)

m = -5 / 2

m = -2.5

So, the slope of the line through (4, 7) and (6, 2) is -2.5.

Hello:

 --> find the slope between the points (4, 7) and (6, 2)

Let's consider our point given:

 --> (x1, y1): (4, 7)

 --> (x2, y2): (6, 2)

Let's consider what formula we need:

[tex]\text{Slope}=\dfrac{y2-y1}{x2-x1}=\dfrac{2-7}{6-4}=\dfrac{-5}{2}=-\dfrac{5}{2}[/tex]

Thus our slope is -5/2

Answer: -5/2

Answer:

To solve for g in the equation m + n^2 = g5M, we first need to isolate g on one side of the equation. We can do this by subtracting m and n^2 from both sides:

m + n^2 = g5M

m + n^2 - m - n^2 = g5M - m - n^2

0 = g5M - m - n^2

Now we can divide both sides by 5M:

0 = (g5M - m - n^2) / 5M

And we get the equation for g:

g = (m + n^2) / 5M

if i helped you, can you mark my answer as best?

PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.

The PPF is a boundary between the attainable and unattainable combinations of pizza and pasta.

Points inside the PPF and on the PPF are attainable and points outside the PPF are unattainable.

Unattainable points are outside the PPF.

Because the PPF shows the limits to production, it separates attainable combinations from unattainable ones.

PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.

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The probability that the next fruit out of the bag will be an apple is 2 / 3.

We're trying to figure out the probability of picking an apple at random from a bag of fruits, assuming that the odds are equal for each item.

Keep in mind that the chance is equal to the product of the quantity of apples and the quantity of all the other fruits in the bag.

The fruits taken out already include 2 plums and a peach which means 3 fruit have been taken out, leaving a total of:

= ( 4 + 3 + 2) - 3

= 6 fruits

The probability of the next fruit being an apple is:

= ( 4 apples + 2 peaches ) / 6 fruit

= 4 / 6

= 2 / 3

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The best way for the materials engineer to carry out the randomization for this study is by using a table of random digits to divide the 40 roadways into 20 pairs and then, for each pair, flipping a coin to decide which pavement to use on which member of the pair.

This can be represented by the formula P(A|B) = P(A) * P(B|A), where P(A|B) is the probability of pavement type A being used on a given roadway, P(A) is the probability of pavement type A being used on any given roadway, and P(B|A) is the probability of a given roadway being used for pavement type A.

The probability of pavement type A being chosen for any given roadway is 1/2 (since there are two pavement types). The probability of a given roadway being used for pavement type A is also 1/2 (since there are two members of each pair). This means that the probability of pavement type A being chosen for a given roadway is equal to P(A|B) = 1/2 * 1/2 = 1/4.

By randomly assigning pavement types to each pair of roadways, the materials engineer is ensuring that her experiment is as fair and unbiased as possible. This will allow her to accurately compare the durability of the two different types of paving material.

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Answer: They are like terms and terms

Hope this helps :)

Step-by-step explanation:

18p and 3p are terms that happen to have the same variable to be like terms.

No, you do not have to ratio test to find the radius of convergence if geometric test does into work,

when representing a function as a power series, it is not necessary to ratio test to find the radius of convergence if geometric test does into work. A geometric test does not always converge to the right value if it is used to find the radius of convergence of a function at a given point.

The radius of convergence is the distance between two points within a specified radius. If the geometry test fails, the convergence radius may not be found. To find the radius of convergence, use another test like a Venn diagram to see if there is a compatibility pattern.

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Answer: y =1x-5

Step-by-step explanation:

The question asks for the slope form y =mx+b, where m is the slope and b is the y-intercept. The y-intercept is the y value when x = 0, also known as when the line intercepts the verticle origin line. On your graph, this point is (0, -5). So, b = -5. Now, we need to pick two points to find the slope using the equation (y2-y1)/(x2-x1). Any two points on the line will work, so even if you do not pick the same points as me, you should still get the same answer.

point one: (0,-5)

point two: (4,-1)

m = (-1 - -5) / (4 - 0) = (-1+5)/(4) = 4/4 = 1

hope this helps!

Answer:

1/36, or approximately 0.028

Step-by-step explanation:

The probability of getting the same number on two six-sided dice is 1/6, or approximately 0.17.

This is because there are six possible outcomes for each dice, and only one of those outcomes results in the same number on both dice (for example, both dice showing a 6).

So, out of the 36 possible outcomes when rolling two dice, only one of them results in the same number on both dice. Therefore, the probability of this happening is 1/36, or approximately 0.028.

The value of m = 15 makes the equation a proportional relationship.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side

The given equation is y + m = 6x + 15.

If an equation has a proportional relationship, then the two variables will have a constant ratio.

General format of a proportional relationship is y = kx, where k is called the constant of proportionality.

We have to get the given equation in the form of y = kx.

It is possible only if m = 15.

y + 15 = 6x + 15

y = 6x + 15 - 15

y = 6x

Hence the value of m is 15, if the relationship is proportional.

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Glass A contains about twice as much as glass B.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Left Glass, height 10 cm , diameter 5.5 cm

And,  Right glass, height 3 cm , diameter 7 cm.

Now, We know that;

⇒ Volume of cylinder = πr²h

Where, 'r' is radius of the cylinder.

For left glass;

Height (h) = 10 cm ,

Diameter = 5.5 cm

⇒ Radius = 5.5 / 2

               = 2.75 cm

Hence, Volume = π × 2.75² × 10

                         = 3.14 × 2.75² × 10

                         = 237.46 cm³

For right glass;

Height (h) = 3 cm ,

Diameter = 7 cm

⇒ Radius = 7 / 2

               = 3.5 cm

Hence, Volume = π × 3.5² × 3

                         = 3.14 × 3.5² × 3

                         = 115.39 cm³

Thus, Glass A contains about twice as much as glass B.

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The complete question is this,

Which of these glasses contains more liquid?

Left Glass, height 10 cm , diameter 5.5 cm

And,  Right glass, height 3 cm , diameter 7 cm.

Glass A contains about twice as much as glass B

Glass A contains about 20% more than glass B

Glass A and B contain about the same amount

Glass B contains about 20% more than glass A

Glass B contains about twice as much as glass A

Submit QuestionQuestion 4

The landing space per step for the indoor staircase is solved to be

The vertical rise from first floor to second floor is 14 feet

The figure defined to be a right triangle and the dimensions are worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The right angle triangle comprises of

opposite = total vertical height

adjacent = total horizontal height = 13 feet

The total vertical height is calculated using tan, TOA

let the angle be x

tan x = opposite / adjacent

tan 47 = opposite / 13

opposite = (13 * tan 47) feet

opposite = 12 * (13 * tan 47) inch

opposite = 167.2895 inch

For a 14 inch vertical rise per step say number of step is y

14 y = total vertical height

14 y = 167.2895

y = 11.9493 steps ≈ 12 steps

The landing space for 12 steps is solved by

= horizontal space total in inch / number of steps

= 13 * 12 / 12

= 13 inches

vertical rise from the 1st floor to the 2nd floor

opposite = (13 * tan 47) feet

opposite = 13.94 feet

opposite = 14 feet (to the nearest foot)

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The minimum value for given linear equation 4x+3y will be 24.

What are linear equations?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

The minimum value for z=4x+3y will be at (6,0) i.e. 24

because this point follows the given linear inequalities too

as given in the graph provided in image.

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The correct option, C. The function is positive when x > 0, for the graph of cube root parent function.

The opposite of such cubic function is the cube root function.

Thus, using the domain and range we can see from the graph that, for the positive values of the function, the graph is increasing for positive values.

Therefore,  The function is positive when x > 0.

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