Surface area of a cylinder with a radius and height of 1.5 m

The prime factorization of a number is the set of prime numbers that can be multiplied together to give you that number. Therefore, two different numbers cannot have the same prime factorization, because if you multiply the same set of numbers together, you must get the same answer. For example, 2 × 3 × 5 will always give you 30.

Therefore, the answer will be no.

Answer:

Fourth answer choice:  y = x + 3

Step-by-step explanation:

Note that sides a and s are perpendicular to side r.  Both sides a and s have positive slopes, so we can immediately eliminate answer choices 1 and 2.

If we extend side s up and to the left, it intersects the y-axis at (0, 3).  Thus, the y-intercept is +3 and the desired equation is:

y = x + 3

Answer:

The answer is D

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Slopes of perpendicular lines are opposite reciprocal of one another i.e.

slope m1, of given line l1 = -1/slope m2, of its perpendicular line l2

slope m2, of its perpendicular line l2 = -1/slope m1, of given line l1

m2= -1/m1

Finding m1 from the given graph

m1= y2-y1/x2-x1

    = -2-1/2+1

    = -3/3

    = -1

m2= -1/-1

     = 1 !

Ok, so equation for this would be 2x-35=9, 2x because its twice a number, x. 35 because it is taking off of 35. 9 because the grand total is 9.

2x-35=9 First add 35 to 9

2x=44 Then divide 44 by 9

x= approximately 4.9 

Answer: She will be there 8 years.

Step-by-step explanation:

I assume the 38º measurement refers to the measure of arc BE. Then

[tex]37^\circ=\dfrac{m\widehat{AJ}-38^\circ}2\implies m\widehat{AJ}=112^\circ[/tex]

and so

[tex]32^\circ=\dfrac{112^\circ-m\widehat{FH}}2\implies m\widehat{FH}=\boxed{48^\circ}[/tex]

(I think the theorem I used here is called "angle of intersecting secants")

Answer:

I think that a pair could be the second choice. MTS and PWQ.  

Step-by-step explanation:

Answer:

the answer is anything less than 24

Step-by-step explanation:

[tex]x - 9 < 15 = x - 9 + 9 < 15 + 9[/tex]

[tex] \times < 24[/tex]

Answer:

x ≥ -2

Step-by-step explanation:

2x - 4 ≤ 4x

Subtract 2x from both sides:

-4 ≤ 2x

Divide by 2:

-2 ≤ x

So -2 ≤ x, or x ≥ -2.

You can check your answer by picking a number greater than -2 and see if it works.  For example, if x = 0:

0 - 4 ≤ 0

-4 ≤ 0

Answer:

y=8x-3

Step-by-step explanation:

Answer:

The ordered pair that represent the other zero is [tex](4,0)[/tex]

Step-by-step explanation:

we know that

The zeros or x-intercepts of the quadratic function, represent the value of x when the value of y is equal to zero

In this problem to find the other zero equate (x-4) to zero and solve for x

[tex](x-4)=0[/tex]

[tex]x=4[/tex]

therefore

The ordered pair that represent the other zero is [tex](4,0)[/tex]

Answer: The answer is y=3x-8

Step-by-step explanation: All you have to do is plug in the x values and see what you get for y. For example: when you plug in -3 for x.    y=3(-3)-8 than you multiply the -3 by 3 and that give you y=-9-8 which equals y=-17 so that shows you the equation works.

plugging in -2 for x

y=3(-2)-8

y=-6-8

y=-14

I hope this helps!!!

Answer:

y = 3x -8

Step-by-step explanation:

You can try a point in the function rules and see if it works. The first (x, y) pair is suitable for finding the right answer:

y = -3(-3) -8 = -1 ≠ -17 . . . . eliminates the first choice

y = 1/3(-3) -8 = -9 ≠ -17 . . . . eliminates the second choice

y = 3(-3) -8 = -17 . . . . . the third choice is viable

y = 1/3(-3) +8 = 7 ≠ -17 . . . . eliminates the last choice

__

Only the third choice is a possible solution. Checking other points from the table verifies this as the correct one.

Answer:

Step-by-step explanation:

If it's less than or greater than (<, >), then the circle is hollow.

If it's less than or equal to, or greater than or equal to (≤, ≥), then the circle is solid.

Less than points to the left, greater than points to the right.

Here we have less than (not equal to).  So the circle is hollow, and the arrow points left.  So the correct answer is the first one.

We can check our answer by picking a point and seeing if it's true.  If we pick c=-6, is it true that -6 < -1?  Yes.

Answer:

option D

4998 J

Step-by-step explanation:

Given in the question that,

mass of the diver = 68 kg

distance of the diver from the surface of a pool = 7.5 m

The gravitational potential energy of an object is given by

GPE = m(g)(h)

here,

m is the mass of the diver

g is the acceleration due to gravity = 9.81m/s²

h is the height from the surface

Plug values in the formula to calculate GPE

GPE = 68(9.8)(7.5)

        = 4998 J

Therefore, the gravitational potential energy of the diver with respect to the surface of the pool is 4998 J

Final answer:

The diver has 4986 Joules of gravitational potential energy in relation to the pool's surface, with the closest answer choice being 4998 J, assuming rounding differences. Hence, the answer is D.

Explanation:

To calculate the gravitational potential energy (GPE) of the diver in relation to the pool's surface, we can use the formula GPE = mgh, where m is the mass of the diver, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the diving platform above the pool's surface.

Substituting the diver's mass (68 kg) and the height of the diving platform (7.5 m) into the equation, we get:

GPE = (68 kg) times (9.8 m/s2) times (7.5 m)

GPE = 4986 Joules

Therefore, the diver has 4986 Joules of gravitational potential energy in relation to the pool's surface. Since this value isn't exactly one of the choices, it's likely due to rounding differences, and the closest provided option is 4998 J, which we could assume is the intended answer.

Answer:

22.5 lbs

Step-by-step explanation:

First you find the cubic feet. That is the volume of the object which is length*width*height.

In your example, they are using inches. So you have to convert all units to feet. That would be 0.5 inches, 0.5 inches, and 5/3 inches. The volume would be 0.5*0.5*5/3 which is about 5/12 cubic feet

You then take that 5/12 cubic feet and multiply it by the 54 lbs/cubic foot. The answer would be 22.5 lbs

Answer:

18.=400%

Step-by-step explanation:

80/20 we get 4 then we multiple 4 ×100 we get 400 and we check the answer 400% ×20 =80

Answer:

see explanation

Step-by-step explanation:

The vertex form of f(x) is

f(x) = (x - h)² + k

where (h, k) are the coordinates of the vertex

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 14x

f(x) = x² + 2(7)x + 49 - 49 + 36

     = (x + 7)² - 13

The minimum value of f(x) is the y- coordinate of the vertex

vertex = (- 7, - 13), that is minimum value = - 13

The vertex form of the function f(x)=x²+14x+36 is (x + 7)² - 13, with the vertex at (-7, -13). The minimum value of f(x) is -13.

To convert the function f(x) = x²+ 14x + 36 into vertex form, we need to complete the square. First, factor out the coefficient of the x² term if it is not 1 (in this case it is 1, so no factoring is necessary), and then group the x terms.

f(x) = (x²+ 14x) + 36

Add and subtract the square of half of the coefficient in front of x within the parenthesis to complete the square:

f(x) = (x² + 14x + 49) - 49 + 36

Simplify:

f(x) = (x + 7)² - 13

Now the function is in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex. Here, the vertex is at (-7, -13).

The minimum value of the function f(x) occurs at the vertex since the coefficient of the x² term is positive, indicating a parabolic shape opening upwards. Therefore, the minimum value of f(x) is -13.

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Answer:

The experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).

Step-by-step explanation:

Theoretical probability of number 3 on a die:

Total no. of possibilities = 6

Probability of getting a 3 on a die each time it is rolled = 1/6

= 0.16667

= 17%

Experimental probability of number 3 on a die:

Total no. of rounds = 4

Rolls each round = 20

no. of 3s in round 1 = 6

no. of 3s in round 2 = 6

no. of 3s in round 3 = 5

no. of 3s in round 4 = 7

Total rolls = 20*4 = 80

no. of times 3 comes up = 6+6+5+7 = 24

Experimental probability of getting a 3 on a die

each time it is rolled = no. of 3s/total rolls

= 24/80

= 0.3

= 30%

Difference = 30% - 17% = 13%

Experimental probability of getting a 3 on a die is 30% which is approximately 13% more than its theoretical probability (17%).

Answer:

The experimental probability of rolling a 3 is  30 %, which is approximately  13 % more than its theoretical probability.

Step-by-step explanation:

PLATO

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{\textit{Lyle's cabin}}{(\stackrel{x_1}{-27}~,~\stackrel{y_1}{23})}\qquad \stackrel{\textit{dining hall}}{(\stackrel{x_2}{-6}~,~\stackrel{y_2}{3})}\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-6-(-27)]^2+[3-23]^2}\implies d=\sqrt{(-6+27)^2+(3-23)^2} \\\\\\ d=\sqrt{21^2+(-20)^2}\implies d=\sqrt{841}\implies d=29[/tex]

The shortest distance from Lyle's cabin to the dining hall is 29 meters.

To calculate the shortest distance between Lyle's cabin and the dining hall, we can use the distance formula for two points in a coordinate plane. The distance formula is:

d = √[(x2 - x1)² + (y2 - y1)²]

Given:

Lyle's cabin coordinates: (-27, 23)

Dining hall coordinates: (-6, 3)

We use the following steps:

Calculate the difference in the x-coordinates: -6 - (-27) = -6 + 27 = 21

Calculate the difference in the y-coordinates: 3 - 23 = -20

Square these differences: 21² = 441 and (-20)² = 400

Add the squares: 441 + 400 = 841

Take the square root of the sum: √841 = 29

Thus, the shortest distance from Lyle's cabin to the dining hall is 29 meters.

972pi mm^3 as height is 12 mm radius is half of 18 mm ie 9mm

therefore volume=pi(r^2)h

ie 972pi mm ^3

Answer: [tex]972\pi\text{ mm}^3[/tex]

Step-by-step explanation:

We know that the volume of a cylinder is given by :-

[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.

Given: Diameter of cylinder = 18 mm

Then , radius of cylinder = [tex]\dfrac{18}{2}=9\ mm[/tex]

Height of cylinder = 12 mm

Then the volume of cylinder will be :-

[tex]\text{Volume}=\pi (9)^2 (12)\\\\\Rightarrow\text{Volume}=972\pi\text{ mm}^3[/tex]

Hence, the volume of the given cylinder = [tex]972\pi\text{ mm}^3[/tex]

Answer:

y = x - 4

Step-by-step explanation:

Rewrite y – 4 = (x – 8) in slope-intercept form.  To do this, solve the given equation for y:

y - 4 = x - 8  →  y = 4 + x - 8, or y = x - 4

As the point-slope form is given, we will simplify it;

                                [tex]y-4=x-8[/tex]

By adding +4 on both the sides, we get:

                            ⇒[tex]y=x-8+4[/tex]

                           ⇒[tex]y=x-4[/tex]

The slope-intercept form of the equation for this line is y=x-4.

Hence, the correct answer is option (b).

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

Examples. y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3. y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.

Learn more about slope-intercept, refer to:

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Answer:

6x - 11

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

f(x) - g(x) = 2x - 3 - (- 4x + 8) = 2x - 3 + 4x - 8 = 6x - 11

Answer:

6x -11

Step-by-step explanation:

f(x) = 2x-3 and g(x) = -4x+8

f-g (x) =2x-3 - (-4x+8)

Distribute the minus sign

       = 2x - 3 +4x -8

Combine like terms

       = 6x -11

Answer:

The discriminant is 0

Step-by-step explanation:

Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.

If a quadratic equation has only one real root, then the discriminant is 0

If x = -3 is the only x-intercept of the graph of a quadratic equation then the discriminant is 0

[tex]\bf (\stackrel{x_1}{t}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{-10}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-7}{-10-t}=\stackrel{\stackrel{slope}{\downarrow }}{9}\implies \cfrac{-9}{-10-t}=9 \\\\\\ -9=-90-9t\implies 81=-9t\implies \cfrac{81}{-9}=t\implies -9=t[/tex]

T=-9 and the work is there

If you have any questions about what I did

Hope this helps.if it does please mark brainliest

Answer:

[tex]A=376.99\ units^2[/tex]

Step-by-step explanation:

By definition, the surface area of a cylinder is given by the following formula:

[tex]A = 2\pi r h + 2\pi r ^ 2[/tex]

Where r is the radius and h is the height.

In this case, we have to:

[tex]r = 4\\\\h = 11[/tex]

then the surface area is:

[tex]A = 2\pi(4)(11) + 2\pi(4) ^ 2[/tex]

[tex]A=120\pi[/tex]

[tex]A=376.99\ units^2[/tex]

120pi units^2

Step-by-step explanation:

For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.

So:

We look for the factors of 18 and 36:

18: 1,2,3,6,9,18

36: 1, 2,3,4, 6,9,18 ...

Thus, the GFC of both numbers is 18.

Then, the GFC of[tex]18x ^ 2[/tex] and [tex]36x[/tex] is:

[tex]18x[/tex]

Answer:

[tex]18x[/tex]

Final answer:

The Greatest Common Factor of 18x² and 36x is 18x, which is the product of shared prime factors to the lowest powers and includes the variable x.

Explanation:

Finding the Greatest Common Factor (GCF)

To find the Greatest Common Factor of 18x² and 36x, we need to break down each term into its prime factors and include the variable parts:

The GCF is the product of the lowest powers of common factors in both terms. Hence, the GCF of 18x² and 36x is 18x, which consists of 2 × 3 × 3 × x (or 2 × 3² × x).

Step-by-step explanation:

Volume of a cylinder is the area of the circular cross section times the height:

V = πr²h

Answer:

V=(3.14)r^2×h

Step-by-step explanation:

(3.14)= pie

r^2= radius to the second power

h=height of cylinder

By arranging the numbers in ascending order we get,

2, 2, 6, 9, 9, 11, 11, 12, 32, 43, 46, 54, 54, 59

The 2 middle numbers are:

11, 12

To find the median we have to add them and divide them by 2

So, (11+12)÷2

23÷2

11.5

For this case we have by definition that the median of a set of numbers is the average number in the set, after the numbers have been arranged from the lowest to the highest. If there is an even number of data, the median is the average of the two average numbers. So:

We order the numbers from least to greatest:

2,2,6,9,9,11,11,12,32,43,46,54,54,59

We have 14 numbers:

[tex]\frac {11 + 12} {2} = \frac {23} {2} = 11.5[/tex]

Answer:

11.5

Answer:

Step-by-step explanation: if she runs 1 lap in 6 minutes, divide 66 by 6 to find how many laps she runs. this is 11. 11 is the minimum amount of laps that she runs.

n≥11

Answer:

11 ≤ n

Explanation:

[tex] \frac{66}{6} = 11[/tex]

More than indicates the minimum value, so you use the greater than or equal to.

The above answer is written in reverse, which the exact same result.

I am joyous to assist you anytime.

Answer:

9 months

Step-by-step explanation:

Answer: 6 months

Step-by-step explanation: you take the initial membership fee of $49.50 and add it to the monthly for the first fee so it would be $67 and subtract that from the $172 he has. then divide the left over which is 105 and 17.50 you get 6