which is equivalent to "12 chars for every 3 tables"?

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:

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:

Step-by-step explanation:

[tex]\text{The formula of a discriminant of}\ ax^2+bx+c=0:\\\\b^2-4ac\\\\================================\\\\\text{We have the equation:}\\\\3x^2-4x+2=0\to a=3,\ b=-4,\ c=2\\\\\text{Substitute:}\\\\b^2-4ac=(-4)^2-4(3)(2)=16-24=-8[/tex]

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: 144$

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

Answer:

10.153 years

Step-by-step explanation:

The future value of such an investment is given by ...

FV = P·(1 +r/12)^(12t)

where P is the principal invested, FV is the future value of it, r is the annual interest rate, and t is the number of years.

Dividing by P and taking the log, we have ...

FV/P = (1 +r/12)^(12t)

log(FV/P) = 12t·log(1 +r/12)

Dividing by the coefficient of t gives ...

t = log(FV/P)/log(1 +r/12)/12 = log(3000/2000)/log(1 +.003333...)/12 ≈ 121.842/12

t ≈ 10.153 . . . years

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:

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:

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:

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.

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

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:

  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:

  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:

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

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:

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:

h = 7 + 6x

Step-by-step explanation:

Since we are trying to find the height of the tree, we put h on the left side of the equation. Since the tree is 7ft tall at the moment, we write 7ft on the right side of the equation. Knowing that the tree grows 6 inches each year (x) we write 6x on the right side of the equation.

Answer:

H=7+6x

Hope this helps

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

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

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:

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:

b= -1

Step-by-step explanation:

y=3x+b

8=3(3)+b

8=9+b

b= -1

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:

[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.

Answer:

• c = √89 ≈ 9.434

• A = arcsin(8/√89) ≈ 57.995°

• B = arcsin(5/√89) ≈ 32.005°

Step-by-step explanation:

By the law of cosines, ...

c² = a² + b² -2ab·cos(C)

Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.

c = √(8² +5²) = √89 ≈ 9.434

Then by the law of sines (or the definition of the sine of an angle), ...

sin(A) = a/c·sin(C) = a/c = 8/√89

A = arcsin(8/√89) ≈ 57.995°

sin(B) = b/c·sin(C) = b/c = 5/√89

B = arcsin(5/√89) ≈ 32.005°

Answer:

i think it is the last one

Step-by-step explanation:

-2/25^3x^3

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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