What is the area of a cylindrical ring where the diameter of the cross section is 6.3 in and the center line has a length of 48 in

Answer:

  120 units²

Step-by-step explanation:

Perimeter = PS + SQ + PQ

50 = SQ + SQ + (SQ -1)

51 = 3SQ

17 = SQ

17 -1 = 16 = PQ

The midpoint of the base is one leg of the right triangle whose other leg is the height of this isosceles triangle. That height is ...

  h = √(17² -(16/2)²) = √225 = 15

Then the area is ...

  A = (1/2)bh = (1/2)(16)(15) = 120 . . . . . square units

Answer:

  The first two tables show y as a function of x.

Step-by-step explanation:

A relation is not a function if the same x-value shows up more than once in the table. That will be the case for the last two tables, each of which has x=2 show up twice.

Answer:

3x⁴ + x³ + 3 x² - 18 x + 4  

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x^4+x^3+3x^2-18+4

The equation of a line is:

y = mx + c

The m is the gradient of the line, and the c is the y-intercept of the line

That means that the y-intercept of [y = -4x + 3]  is 3

and the y-intercept of [y = -4x + 4] is 4

So the distance between the two y-intercepts is:

4 - 3 = 1

Answer:

40

Step-by-step explanation:

The measure of the angle KJL is 40°.

Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices.

Given is a circle O where m arc IVK = 120° and m arc KP = 2 × m arc IP,

We need to find the measure of the angle KJL,

So,

According to the question,

m arc IVK + m arc KPI = 360° [whole circumference of a circle is 360°]

m arc IVK + m arc KP + m arc IP = 360°

120° + m arc IP + 2 × m arc IP = 360°

3 m arc IP = 240°

m arc IP = 80°

Therefore,

m arc KP = 160°

Now, according to the property of a circle,

m ∠KJL = 1/2 × [m arc KP - m arc IP]

m ∠KJL = 1/2 × [160° - 80°]

m ∠KJL = 80°/2

m ∠KJL = 40°

Hence the measure of the angle KJL is 40°.

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Answer:

Volume of the pyramid = 16m³ or 16 cubic meters.

Step-by-step explanation:

The equation for the volume of a pyramid is:

[tex]V=\frac{b*h}{3}[/tex]

where b = area of base and h = height.

In this case, the base is a square with a side length of 4m.

Area of the square base = (4m)² = b = 16m²

h = 3m

Insert b and a into the volume of a pyramid equation.

[tex]V=\frac{3m*16m}{3}[/tex]

= 16m³

Volume of the pyramid = 16m³ or 16 cubic meters.

Answer:

[tex](x-7)^2+(y-5)^2=16[/tex].

Step-by-step explanation:

The given circle has equation [tex]x^2+y^2=16[/tex].

This is the equation that has its center at the origin with radius 4 units.

When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).

The equation of a circle with center (h,k) and radius r units is [tex](x-h)^2+(y-k)^2=r^2[/tex].

This implies that, the translated circle will now have equation.

[tex](x-7)^2+(y-5)^2=4^2[/tex].

[tex](x-7)^2+(y-5)^2=16[/tex].

The correct equation for translating the circle x² + y² = 16 seven units to the right and five units up is (x - 7)² + (y - 5)² = 16. Therefore, option D is the correct answer.

The original equation for a circle with a radius of 4 units is x² + y² = 16. A translation of the circle seven units to the right and five units up would involve shifting the x-coordinate by +7 and the y-coordinate by +5. Therefore, the new equation would be (x - 7)² + (y - 5)² = 16.

This is due to the fact that a translation of a geometric figure does not alter its size, shape, or orientation; it simply shifts the figure in the plane. Keeping the radius the same, applying the translation to the circle's center (0,0) results in a new center at (7,5), which translates to the equation above.

The domain is the input values, which would also be X values.

{ x |x= -5, -3, 1, 2,6}

For this case we have by definition that the domain of a function y = f (x) is the set of all the values that the variable x takes, for which the function is defined. They are also represented by the starting set.

It is observed in the figure, that the domain is:

[tex]{x | x = -3,2, -5,1,6}\\{x | x = -5, -3,1,2,6}[/tex]

Answer:

Option A

Answer:

Slope = -1/2

Y-intercept is y = -1

Equation of the line: [tex]y=-\frac{1}{2}x-1[/tex]

Step-by-step explanation:

The slope intercept form is  y = mx + b

Where, m is slope, and

b is y-intercept

We need 2 points to find these. One point is  (-2,0) and second point is (2,-2).

THe formula for slope, m, is m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plugging the points, we get the slope to be:

[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{-2-0}{2--2}\\=\frac{-2}{4}\\=-\frac{1}{2}[/tex]

y-intercept is the point where the line crosses the y axis. Looking at the graph, y-intercept is y = -1.

Now we plug slope and y-intercept into the slope-intercept form to get:

[tex]y=mx+b\\y=-\frac{1}{2}x-1[/tex]

ANSWER

[tex]y = - \frac{1}{2} x - 1[/tex]

EXPLANATION

The graph passes through (-2,0) and (0,-1).

The slope can be calculated using the formula,

[tex]m= \frac{rise}{run} [/tex]

[tex]m = \frac{0 - - 1}{ - 2 - 0} [/tex]

[tex]m = - \frac{1}{2} [/tex]

The y-intercept is -1.

The equation in slope-intercept form is

y=mx + c

We substitute the slope and y-intercept to obtain

[tex]y = - \frac{1}{2} x - 1[/tex]

Answer:

  see below

Step-by-step explanation:

Of your remaining answer choices, the only one that shows a reflection (not a translation) is the one below. It has the orientation of the figure reversed (side lengths shortest-to-longest are CCW instead of CW).

The reflection over y=x reverses the coordinates: (x, y) ⇒ (y, x), so the vertices become ...

Answer:

  36, 32, 28, 24

Step-by-step explanation:

Fill in the values of n and do the arithmetic.

  a1 = 36 -4(1 -1) = 36

  a2 = 36 -4(2 -1) = 32

  a3 = 36 -4(3 -1) = 28

  a4 = 36 -4(4 -1) = 24

_____

You could recognize the formula as the specific case of the explicit formula for an arithmetic sequence with first term 36 and common difference -4. That tells you the second term is 36 -4 = 32, and each successive term is 4 less than the one before.

Answer: 144$

Step-by-step explanation: multiply 5 by 12 and then multiply that answer by 2.40

Notice you can factorize

[tex]x^5+5x^4-5x^3-25x^2+4x+20[/tex]

by grouping the terms as

[tex](x^5-5x^3+4x)+(5x^4-25x^2+20)=x(x^4-5x^2+4)+5(x^4-5x^2+4)[/tex]

[tex]\implies f(x)=(x+5)(x^4-5x^2+4)[/tex]

Then you know right away that [tex]x=-5[/tex] is a (real) root, so we eliminate C and D.

The remaining quartic can be factored easily:

[tex]x^4-5x^2+4=(x^2)^2-5x^2+4=(x^2-4)(x^2-1)=(x-2)(x+2)(x-1)(x+1)[/tex]

which admits four more (also real) roots, [tex]x=\pm2[/tex] and [tex]x=\pm1[/tex], so the answer is B.

Answer:

24 ˚

Step-by-step explanation:

Exterior angle of a regular    -sided polygon:

360 ˚/ n ⇒ 360 ˚/15 = 24 ˚

Answer:

A) 24

Step-by-step explanation:

Since the sum of the exterior angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equal exterior angles and therefore 15 vertices and sides to the polygon.

Answer:

  11.7%

Step-by-step explanation:

The account balance (A) for a principal amount P and monthly interest rate r will be ...

  A = P(1 +r)^8

Then we can divide by P and take the 8th root to find r:

  A/P = (1+r)^8

  (A/P)^(1/8) = 1 +r

  (A/P)^(1/8) - 1 = r

Since this is the monthly rate, we need to multiply this value by 12 to find the annual interest rate on the account:

  annual rate = 12((A/P)^(1/8) -1) = 12((9779/9047)^(1/8) -1) ≈ 0.11728 ≈ 11.7%

Answer:

Step-by-step explanation:

r = a5/a4 = (81/4)/(-27/4) = -3

an = a1·r^(n-1)

-27/4 = a1·(-3)^3 = -27·a1 . . . . fill in the known numbers for n=4

(-27/4)/(-27) = a1 = 1/4

First find the slope of the given line:

4x +2y = 1

Subtract 4x from each side:

2y = -4x + 1

Divide both sides by 2:

y = -2x +1/2

The slope is -2.

Now use the slope to find the y-intercept. Because  the line is perpendicular, you need to use the negative inverse of the slope.

The negative inverse of -2 is 1/2

Now using the point-slope form y - y1 = m(x-x1)

Use the inverse slope for m, and the given point(-4,3) to get:

y - 3 = 1/2(x+4)

Simplify:

y - 3 = x/2 +2

Add 3 to each side:

y = x/2 + 5

Reorder the terms to get y = 1/2x +5

The answer is D.

Answer:

a. 0.169x+69.11 > 0.126x+76.74

Step-by-step explanation:

So, there's a lot of talk in the question statement.  Of course, it presents some important data... but it's also meant to confuse you.

We can boil it down to the following life expectancies :

Men =  0.169x+69.11

Women = 0.126x+76.74

Then they ask you to write with that men have a greater life expectancy than woman using the models above.

Start by writing the goal:

men > women

Then replace "men" by the model and "women" by the model:

0.169x+69.11 > 0.126x+76.74

And you have your answer.

Answer:

A

Step-by-step explanation:

maybe, maybe not

Answer:

Step-by-step explanation:

3(4x+2)-6x=5x-5(2+x)

12x +6 -6x = 5x -10 -5x . . . . . eliminate parentheses using the distributive property

6x +6 = -10 . . . . . . . . . . . . . . . collect terms

x +1 = -10/6 . . . . . . . . . . . . . . . divide by 6

x = -1 - 5/3 . . . . . . . . . . . . . . . add -1

x = -8/3 . . . . . . . . . . . . . . . . . simplify

Answer: 9\20 or 45% hope this helps

The "odds" of picking a green are 9 to 11 .

The "probability" of picking a green is 9/20 or 45% .

Answer:

The measure of the angle is [tex]68.79\°[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=78.5\ cm^{2}[/tex]

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]78.5=(3.14)r^{2}[/tex]

[tex]r^{2}=78.5/(3.14)[/tex]

[tex]r=5\ cm[/tex]

step 2

Find the circumference of the circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ cm[/tex]

[tex]\pi =3.14[/tex]

Substitute

[tex]C=2(3.14)(5)[/tex]

[tex]C=31.4\ cm[/tex]

step 3

Find the measure of the angle by an arc length of 6 cm

we know that

The circumference of a circle subtends a central angle of 360 degrees

So

by proportion

[tex]\frac{31.4}{360}=\frac{6}{x}\\ \\x=360*6/31.4\\ \\x=68.79\°[/tex]

Answer:

The measure of the angle subtended by the arc is 68.8°

Step-by-step explanation:

Formula for calculating length of an arc is expressed as:

Length of an arc = theta/360×2πr

Where theta is the angle subtended by the arc

r is the radius of the circle

To get the radius r;

Given Area of the circle to be 78.5cm²

Since area = πr²

78.5 = πr²

78.5 = 3.14r²

r² = 78.5/3.14

r² = 25

r =√25

r = 5cm

This radius of the circle is 5cm

Remember that

Length of an arc = theta/360° × 2πr

6 = theta/360 × 2(3.14)(5)

6 = 31.4theta/360

2160 = 31.4theta

theta = 2160/31.4

theta = 68.8°

Answer:

$25.20

Step-by-step explanation:

Cost of the meal = $21

Total cost

= c + 0.20c

= 21 + 0.20(21)

= $25.20

For this case we have the following function, to calculate the total cost of the meal, including 20% of the tip:

[tex]f (c) = c + 0.20c[/tex]

They tell us that a meal costs $ 21.00. That is,[tex]c = 21[/tex]

[tex]f (21) = 21 + 0.20 (21)\\f (21) = 21 + 4.2\\f (21) = 25.2[/tex]

Thus, the total cost of the meal is 25.2

Answer:

$ 25.2

Answer:

B. Events H and C are dependent and P(H|C) < P(C|H)

Step-by-step explanation:

The ratios of groups with children to hiking groups on the trail are different for the two trails.

P(H|C) = 15/45 = 1/3

P(C|H) = 15/40 = 3/8

1/3 < 3/8 so the comparison of choice B is appropriate.

Answer:

1/4

Step-by-step explanation:

The are 8 different sections that the spinner can land on

2 of them are labeled blue

P(blue) = spots labeled blue/ total spots

            = 2/8

            = 1/4

Answer:

y = -x+7

Step-by-step explanation:

We need to get x+y=4 in slope intercept from to determine the slope

x+t=4

Subtract x from each side

x-xy = -x+4

y= -x+4

The slope is -1

Parallel lines have the same slope

We have the slope and a point of the new line.

We can use the point slope form

y-y1 = m(x-x1)

y-8 = -1(x--1)

y-8 = -1(x+1)

Distribute the negative sign

y-8 = -x-1

Add 8 to each side

y-8+8 = -x-1+8

y = -x+7

Answer:

-4x=-3

3= 4x

Step-by-step explanation:

The equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct

Given that,
To determine the expression consist of the isolation of the variable and constant.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
-6 + 2x = 6x - 9
-4x = -3 or 4x = 3

Thus, the equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct.

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Answer:

Sadly, it is still high in debate. Scientists are still in doubt of the Hypothesis, so no. Some may claim there is a solution, though.

Step-by-step explanation:

Final answer:

The Riemann Hypothesis is an unsolved mathematical problem, with no validated solution as of yet, and remains one of the Millennium Prize Problems in mathematics.

Explanation:

The Riemann Hypothesis is one of the most famous and long-standing unsolved problems in mathematics, specifically in the area of number theory. It postulates that all non-trivial zeros of the Riemann zeta function, a complex function important for understanding the distribution of prime numbers, have their real parts equal to 0.5. Despite significant efforts by mathematicians over the years, the solution to the Riemann Hypothesis remains elusive, and no proof or disproof has been universally accepted by the mathematics community.

As of my knowledge cutoff in 2023, researchers continue to explore various mathematical approaches and even computational methods to tackle this problem. However, no experiment or scientific test can validate the hypothesis since it is a purely mathematical conjecture. A resolution of the Riemann Hypothesis would have profound implications for number theory and related fields, yet it remains one of the seven Millennium Prize Problems, with a reward of one million dollars offered for a solution.

Answer:

1. Yes

2. No

3. Yes

4. No

Step-by-step explanation:

When you say a random sample, this means that every member of the population will have a chance to be part of the sample. If you consider the scenarios, only the 1st and 3rd option will come up with a random sample because the respondents of the sample is not predetermined. If you take the other options into consideration, you can see that not everyone would have had a chance to be part of the sample.

Answer:

1. all the right angles are congruent

2. opposite sides of a parallelogram are congruent

3. SAS congruent postulate

4. corresponding parts of a congruent triangle are congruent

Step-by-step explanation:

1. As all the right angles are congruent

          ∠JML≅∠KLM≅ ∠90°

2. As per the properties of a parallelogram, the opposite sides are congruent.

                  Hence the sides JM≅KL

3. SAS postulate is defined as Side-Angle-Side postulate. When the side, adjacent angle and the other other adjacent side of two triangle are congruent then the two triangles are said to be congruent. In the given case both the sides JM and ML of ΔJML are congruent to both the sides KL and ML of ΔKLM.

                            Hence ΔJML≅ΔKLM

4. As proven in part 3, ΔJML≅ΔKLM so the congruent parts of two congruent triangle are congruent.

                In given case the side JL(of ΔJML)≅MK(ΔKLM)

!

The completed proof is presented as follows;

Parallelogram JKLM is a rectangle and by definition of a rectangle, ∠JML

and ∠KLM are right angles, ∠JML ≅ ∠KLM because, all right angles are

congruent, [tex]\overline{JM}[/tex] ≅ [tex]\overline{KL}[/tex] because opposite sides of a parallelogram are

congruent, and [tex]\overline{ML}[/tex] ≅ [tex]\overline{ML}[/tex] by reflective property of congruence. By the SAS

congruence postulate, ΔJML ≅ ΔKLM. Because, congruent parts of

congruent triangles are congruent, [tex]\overline{JL}[/tex] ≅ [tex]\overline{MK}[/tex]

Reasons:

The given quadrilateral is a parallelogram, that have interior angles that are right angles, therefore, the figure has the properties of a rectangle, and

parallelogram including;

All right angles are congruent and equal to 90°

The length of a side is equal to itself by reflexive property, therefore,  [tex]\overline{ML}[/tex]

≅ [tex]\overline{ML}[/tex]

The Side-Angle-Side SAS postulate states that if two sides and an included

angle of one triangle are congruent to the corresponding two of sides and

included angle of another triangle, the two triangles are congruent.

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Answer:

x = ±(√2)/3

Step-by-step explanation:

For the quadratic ...

ax^2 +bx +c = 0

the quadratic formula gives solutions as ...

x = (-b ±√(b^2-4ac))/(2a)

Comparing your quadratic to the general form above, we find ...

a = 9; b = 0, c = -2

Filling these values into the formula gives ...

x = (-0 ±√(0^2 -4(9)(-2)))/(2·9)

x = ±(√72)/18 = ±(6√2)/18

x = ±(√2)/3