Consider a cone with a height of 9 in and a base diameter of
6 in.
Using a calculator, approximate the volume of the cone.
To do the approximation, do not round any intermediate
steps, and use the button on the calculator. Round your
answer to the nearest hundredth.
Make sure that you use the correct units in your answer.

The given system of equations can be represented in matrix form as:

| 10 13 15 | | x | | 4 |

| 12 -2 5 | x | y | = |-8 |

| 2 2 -6 | | z | | 4 |

Therefore, the matrix A is:

| 10 13 15 |

| 12 -2 5 |

| 2 2 -6 |

And the vector ⇾b is:

| 4 |

|-8 |

| 4 |

Answer:

3

Step-by-step explanation:

(15×1)÷5=

Answer:  

Distant with current is 30, distance against current is 24.

Rate with current is 6, rate against current is 4.

Time with current is 8 hours, time against current is 14

Step-by-step explanation:  

2nd question answer: 24 - 6x = 8.

According to the nearest hundredth, the length of the wire in the photograph is 200 cm.

What in mathematics is a semicircle?

By dividing a circle into two halves along a diameter line, a semicircle is created, which is a half-circle.

The wire will be cut into four semicircles, each of which will have a circumference equal to its length.

Therefore, if one semicircle has a diameter of 32 cm, its radius is 32/2 cm, or 16 cm.

Right now, a circle's circumference equals 2*(pi)*(radius).

Since this is a semicircle, its circumference is equal to (pi)*(radius), or one-half of a circle.

The circumference of four semicircles is then equal to four * pi * radius.

Pi has a value of 22/7.

Thus, the length of the wire is 4*(22/7)*16 cm, which, when rounded to the nearest hundredth, is 200 cm.

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Hence, 201 [tex]cm^{2}[/tex] long is the wire to the nearest hundredth.

In mathematics, a semicircle is a  one-dimensional locus of points that forms  half of a circle. It is a circular arc that  measures 180°.  It has only one line of symmetry.

In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure .

In other words ,The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.

According to figure

diameter of  all semi circle (d) = 32 cm.

so radius of  all semi circle r = [tex]\frac{32}{2}[/tex] = 16 cm.

length of wire = circumference of semicircle =

⇒ total length length of wire = 4 * circumference of semicircle

                                                                                 {∵ no. of semicircle=4

∴ total length length of wire = 4 * [tex]\pi*r[/tex]      

∴ total length length of wire = 4 *3.14*16              {we know that , [tex]\pi=3.14[/tex]

∴ total length length of wire =200.96[tex]cm^{2}[/tex] ≅ 201[tex]cm^{2}[/tex]

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The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).

To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.

The gradient vector of T(x,y) is given by:

∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of T(x,y) with respect to x and y, we get:

∂T/∂x = (x² - y²)/(x² + y²)²

∂T/∂y = -2xy/(x² + y²)²

Substituting x = 2 and y = 5, we get:

∂T/∂x = (4 - 25)/(29)² = -21/1681

∂T/∂y = -20/1681

Therefore, the gradient vector of T(x,y) at the point (2, 5) is:

∇T(2,5) = (-21/1681)i - (20/1681)j

The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:

u = (∇T(2,5))/|∇T(2,5)|

where |∇T(2,5)| is the magnitude of the gradient vector, given by:

|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41

Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:

u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j

Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).

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Work Shown:

[tex]\displaystyle \int \sin(x) dx = -\cos(x)+C\\\\\displaystyle \int f(x)dx = g(x)+C\\\\\displaystyle \int_{a}^{b} f(x)dx = g(b)-g(a)\\\\\displaystyle \int_{0}^{\pi} f(x)dx = g(\pi)-g(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)-(-\cos(0))\\\\[/tex]

[tex]\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)+\cos(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -(-1)+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 1+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 2\\\\[/tex]

The area is 2 square units. You can use WolframAlpha or GeoGebra to confirm.

Using multiplication we know that after 141 min there will be 400,000 bacteria present.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

When you take a single number and multiply it by several, you are multiplying.

A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).

We multiplied the number five by four times.

Multiplication is commonly referred to as "times" because of this.

So, in the given situation:

At the initial stage, the number of bacteria is: 50,000

Then, after 47 min: 50,000 * 2 = 100,000

Then, after 47 min which is after 94 min: 100,000 * 2 = 200,000

Then, after 47 min which is after 141 min: 200,000 * 2 = 400,000

Therefore, using multiplication we know that after 141 min there will be 400,000 bacteria present.

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Answer:

for the following question the answer will be

1/5=0.2 given as example

60%=0.6

50%=1/2

3/4=0.75

for 1/6 there os no answer for it the answer is 0.166

So Wanda will make more money from the second deal than the first deal if she sells more than 20,000 books.

In mathematics, an inequality is a statement that two values or expressions are not equal. It describes a relationship that is either greater than, less than, or not equal to another value or expression. Inequalities are often represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Here,

To determine the range of sales for which Wanda would make more from the second deal than the first deal, we need to set up an inequality that compares the total earnings for each deal. Let's let x be the number of books sold.

For the first deal, Wanda will earn:

Total earnings = $70,000 + $2x

For the second deal, Wanda will earn:

Total earnings = $40,000 + $3.50x

We want to find the range of x values for which the second deal earns more than the first deal. Mathematically, we can express this as:

$40,000 + $3.50x > $70,000 + $2x

Subtracting $2x from both sides gives:

$40,000 + $1.50x > $70,000

Subtracting $40,000 from both sides gives:

$1.50x > $30,000

Dividing both sides by $1.50 gives:

x > 20,000

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Answer: The given equation is 11 = -2z + 8, which can be rearranged into the form of ax + b = c by moving the terms containing z to one side:

-2z + 8 = 11

-2z = 11 - 8

-2z = 3

z = -3/2

Comparing this with the standard form ax + b = c, we see that:

a = -2

b = 8

c = 11

Therefore, the correct answer is option B: a = -2, b = 8, c = 11.

Step-by-step explanation:

The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

An example of a graph that employs Cartesian coordinates to show values for two categories for a collection of data is a scatter plot, sometimes referred to as a scatter diagram. Each pixel in the data's representations is a point with a horizontal position (indicating the value of one variable) and a vertical displacement (representing the value of the other variable). In order to observe correlations among variables and spot patterns in the data, scatter plots is utilised. They are frequently employed in data processing, statistics, and academic studies.

given

The scatter plot reveals a positive connection since the y-values grow as the x-values grow.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the formula:

distance = rate x time

Since Tina bicycles at a constant speed, we can simplify the formula to:

distance = speed x time

For the first 2 hours, Tina bicycles at a constant speed, so the distance she travels is:

distance = speed x time = s x 2

After taking a 1-hour break, Tina continues to bicycle at the same speed for another 2 hours, so the distance she travels is:

distance = speed x time = s x 2

Therefore, the total distance Tina travels over the 5-hour period is:

total distance = 2s + 2s = 4s

This means that the total distance Tina bicycles is directly proportional to the speed at which she travels. In other words, if Tina travels twice as fast, she will cover twice the distance in the same amount of time.

With this in mind, we can eliminate choices (A) and (B), which show linear relationships between distance and time. Since Tina is traveling at a constant speed, the graph of her distance should be a straight line with a positive slope.

Choice (C) shows a straight line with a positive slope, but the slope is too steep. This graph would indicate that Tina is traveling at a much faster speed than she actually is.

Choice (D) shows a straight line with a positive slope that is not as steep as (C). This graph accurately represents Tina's constant speed and shows the increase in distance after the break. Therefore, the correct graph is (D).

Example

It took Markus half an hour to drive home from work.  He averaged 34 miles per hour.  How far does Markus live from his work?

Solution

We are given that it takes 1/2 an hour for the trip.  This is a time:

       t  =  1/2

We are given that he averages 34 miles per hour.  This is a rate:

       r  =  34

We are asked how few he has traveled.  This is a distance.  We use the d=rt equation:

       d  =  rt

           =  (34)(1/2)

           =  17

Markus lives 17 miles from work.

The solution in natural numbers for the equation is x = 100 and y = 1.

The positive integers 1, 2, 3, 4, 5,... are known as "natural numbers." N stands for the set of natural numbers. Natural numbers are the building blocks of mathematical operations including addition, subtraction, multiplication, and division. They are also used to count objects. They make up a portion of the set of whole numbers, which also contains the natural numbers and 0 as well. There is no biggest natural number since the collection of natural numbers is endless and unbounded.

To determine the solution of the equation we use the difference of square identity given as:

(x + y)(x - y).

Now, for the given function we have:

(x - y)(x + y = 303

The two factors of 303 are 101 and 99.

Thus,

x + y = 101

x - y = 99

Adding the two equations we have:

2x = 200

x = 100

Now, for x = 100 the value of y is:

100 - y = 99

y = 1

Hence, the solution in natural numbers is x = 100 and y = 1.

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Answer:

input output

3 7

8 16

n blank

Step-by-step explanation:

we can see that the function's output is twice the input plus one. Therefore, when the input is 6, the output will be 2 * 6 + 1 = 13. When the input is 14, the output will be 2 * 14 + 1 = 29. However, since the output for the input value "n" is not given in the table, we cannot determine the output for that input.

I hope it helps you

Using the laws of outside angle, we can find the value of the angle x° to be = 77°.

The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.

Here in the question,

The measure of the 2 arcs is given as 85° and 172°.

The measure of the 3rd arc that is subtended by the tangents is:

360° - 85° - 172°

= 103°

As per the outside angle theorem,

x° = 180° - 103°

= 77°

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Answer:

Let's use a system of equations to solve the problem.

Let x be the number of regular admission tickets sold, and y be the number of fast pass tickets sold.

From the problem, we know that:

x + y = 104 (equation 1)

and

8x + 22y = 1280 (equation 2)

We can use equation 1 to solve for x in terms of y:

x = 104 - y

Substituting this expression for x into equation 2, we get:

8(104 - y) + 22y = 1280

Simplifying and solving for y, we get:

832 - 8y + 22y = 1280

14y = 448

y = 32

So the student sold 32 fast pass tickets.

To find the number of regular admission tickets sold, we can substitute y = 32 into equation 1 and solve for x:

x + 32 = 104

x = 72

So the student sold 72 regular admission tickets.

Therefore, the student sold 72 regular admission tickets and 32 fast pass tickets.

The correct options for the given rational numbers are (a) ii and iv.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. The natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers.

To compare the rational numbers, we need to perform the given operations and determine their relative magnitudes:

i. -2.3 - 1.3 = -3.6

ii. -2.3 -1.3 = -3.6

iii. -2.3 > -3.3

iv. -2.3 -3.3 = -5.6

Comparing i and ii, we see that they are equal. Therefore, both options i and ii are true.

Comparing iii, we see that -2.3 is greater than -3.3. Therefore, option iii is true.

Comparing iv, we see that -5.6 is less than both -2.3 and -3.3. Therefore, option iv is false.

So, the correct options are (a) ii and iv.

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Answer:

its taking the immage on the right and moving it ounter clockwise 90°

The side lengths of the triangle are CA = 42.0 and BC = 36.4

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the tangent rratio, we have

tan(60) = BC/21

So, we have

BC = 21 * tan(60)

Evaluate

BC = 36.4

Next, we have

CA = √[36.4^2 + 21^2] -- pythagoras theorem

Evaluate

CA = 42.0

Hence, the side lengths are CA = 42.0 and BC = 36.4

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Answer:

  8%

Step-by-step explanation:

You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.

The fraction of the total number that had whipped cream is ...

  2/(2+23) = 2/25

The percentage is found by multiplying the fraction by 100%:

  2/25 × 100% = 8%

8% of the milkshakes had whipped cream.

So, the area of the shape is 164.4 square meters.

In geometry, area is the measure of the size of a two-dimensional surface or region. It is the amount of space inside the boundaries of a flat object such as a polygon, circle, or rectangle. Area is measured in square units, such as square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and so on. To calculate the area of a shape, you typically need to use a specific formula depending on the type of shape, such as base times height for a triangle, or length times width for a rectangle.

Here,

The area of the shape is equal to the sum of the areas of these smaller pieces. We can calculate each area as follows:

The area of the rectangle on the left is 4m x 8.4m = 33.6 square meters.

The area of the rectangle on the right is 8m x 11.4m = 91.2 square meters.

The area of the triangle on the top is (8.4m x 4m) / 2 = 16.8 square meters.

The area of the triangle on the bottom is (11.4m x 4m) / 2 = 22.8 square meters.

Therefore, the total area of the shape is:

33.6 + 91.2 + 16.8 + 22.8 = 164.4 square meters

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(1) The right solution of given equation is  8.(2)The equation 8x = 64 has only one solution

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Part A: Masha's solution is incorrect.

In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8

So, the correct step to solving this equation is

8x = 64

x = 64/8

x=8

Hence the right solution of given equation is  8

Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.

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(1) The right solution of given equation is 8.

(2)The equation 8x = 64 has only one solution

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Part A: Masha's solution is incorrect.

In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8

So, the correct step to solving this equation is

8x = 64

x = 64/8

x=8

Hence the right solution of given equation is 8

Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.

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If a random sample of 20 gas stations was selected to estimate the gas prices. The type of error that could have occurred is a type I error, which is the rejection of a true null hypothesis. The probability of making a type I error is equal to the level of significance (α), which is 10% in this case. So, there is a 10% chance of making a type I error in this test.

To test if the true average gas price is under $3.50, we can use a one-tailed t-test with a null hypothesis of:

H0: μ >= $3.50

And an alternative hypothesis of:

Ha: μ < $3.50

where μ is the true population mean gas price.

Using a t-test with a sample size of 20, we can calculate the t-value as:

t = (x -bar - μ) / (s / sqrt(n))

where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (3.40 - 3.50) / (0.22 / sqrt(20))

t = -2.03

Looking up the t-distribution table with degrees of freedom (df) = 19 and a 10% alpha level (α = 0.10), we find the critical t-value as -1.325.

Since our calculated t-value (-2.03) is less than the critical t-value (-1.325), we reject the null hypothesis in favor of the alternative hypothesis. Therefore, we can conclude that there is sufficient evidence to suggest that the true average gas price is under $3.50.

The type of error that could have occurred is a Type I error, which is rejecting a true null hypothesis. In this case, it means that we conclude that the true average gas price is under $3.50 when it's actually not. The probability of making a Type I error is equal to the alpha level, which is 10% in this case. So there's a 10% chance that we falsely reject the null hypothesis.

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Answer: A.

Step-by-step explanation: It is parallel because of the angles that are the same and if u fill all the angles up angles 2 and 6 will be congruent there fore its parallel

Answer:

A. Yes, because angles 2 and 6 are congruent.

Step-by-step explanation:

The lines arent touching, parallel. Angles 2 and 6 share the same angle, congruent.

Answer:

a = -2 b = -3

Step-by-step explanation:

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He needs to make 15 throws if the ratio is the same as the first game

From the question, we have the following parameters that can be used in our computation:

Player was successful on 18 out of his 24 last free throws attempts

Using the above as a guide, we have the following:

Proportion = 18/24

For the number of games, we have

Throws made = Proportion  * Number of throws

Substitute the known values in the above equation, so, we have the following representation

Throws made = 18/24 * 20

Evaluate

Throws made = 15

Hence, the number of throws made is 15

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Answer:

The surface area (SA) formula for a rectangular prism is:

SA = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

For the cereal box object given, we have:

l = 12 inches

w = 8 inches

h = 1.75 inches

So, substituting these values into the formula, we get:

SA = 2(12)(8) + 2(12)(1.75) + 2(8)(1.75)

SA = 192 + 42 + 28

SA = 262 square inches

Therefore, the surface area of the rectangular prism cereal box is 262 square inches.

Step-by-step explanation:

The SURFACE AREA OF THE RECTANGULAR PRISM is 262 in²

SURFACE AREA (S.A) OF RECTANGULAR PRISM= 2lw+2lh+2wh

LENGTH=12 inches

WIDTH= 8 inches

HEIGHT=1.75 inches



Applying the formula

We get

S.A=2*(12*8)+2*(12*1.75)+2*9(8*1.75)

S.A = 192+42+28 sq inches

S.A= 262 sq inches