Directions: Please choose ONE (you may answer all if you would like) question. Make sure to EXPLAIN your work. NO EXPLANATION=NO FULL CREDIT



Is the table proportional? Explain why or why
not.
If it is proportional, what is the constant of
proportionality?
What is the equation?

Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

ŷ= 6.45x + 31.5 is the equation of the regression line for the given data

Construct the table of the data as follows:

x    >>>>     y  >>>>  x²  >>>>  y²  >>>>   xy

1                39            1            1521         39

2               45            4           2025       90

3               52             9          2704       156

4               49            16          2401        196

5               61             25         4096       305

5               72            25          5184        360

................................................................................................

20             318           80          17931       1146

.................................................................................................

∑x = 20,  ∑y = 318, ∑x²= 80, ∑xy = 1146,  n = 6 (number data points)

The linear regression equation is of the form:

ŷ = ax + b

where a and b are the slope and y-intercept respectively

a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )

a = (6×1146 - 20×318) / ( 6×80-20² )

a = 6876-6360 / 480-400

a = 516 / 80

a = 6.45

x' =  ∑x/n

x' = 20/6 = 10/3

y' = ∑y/n

y' = 318/6 = 53

b = y' - ax'

b = 53 - 6.45×(10/3)

b = 53 - 21.5

b = 31.5

ŷ = ax + b

ŷ= 6.45x + 31.5

Thus,  the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)

(a) x=3 hours

ŷ= 6.45(3) + 31.5 = 50.85

(b) x=4.5 hours

ŷ= 6.45(4.5) + 31.5 = 60.525

(c) x=13 hours

ŷ= 6.45(13) + 31.5 = 115.35

(d) x=1.5 hours

ŷ= 6.45(1.5) + 31.5 = 41.175

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Given two points coordinate

The equation of the line in slope-intercept form can be obtained using

Define the x and y values, then substitute in the above formula

Hence, Option C is the correct answer

The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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Answer: See Below

Step-by-step explanation:

Concept:

Here, we need to know the idea of alternative interior angle, alternative exterior angle, and corresponding angles.

Alternative interior angle: a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

Alternative exterior angle: a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Corresponding angle: A pair of angles that occupy the same relative position at each intersection where a straight line crosses two others.

All three kinds of angles above occur to be congruent (equal) when the lines are parallel to each other.

If you are still confused, please refer to the attachment below for a graphical explanation

Solve:

PART ONE

a) Name two pairs of alternative exterior angles: ∠1 and ∠7 / ∠2 and ∠8

b) Name two pairs of corresponding angles: ∠1 and ∠5 / ∠2 and ∠6

c) Name two pairs of alternative interior angles: ∠4 and ∠6 / ∠3 and ∠5

PART TWO

a) If the measure of angle 7 is 52°, what is the measure of angle 1?

b) If the measure of angle 8 is 112°, then what is the measure of angle 3?

Hope this helps!! :)

Please let me know if you have any questions

Answer:

4in

Step-by-step explanation:

Given

Amount of rain that fell in October = 14in

If this value is 3 1/2times amount of rain that fell in September, we can express it mathematically as;

3 1/2 of September = 14

7/2 of x = 14

x is the amount of rain that fell in September

From the expression

7x/2 = 14

Cross multiply

7x = 14×2

7x = 28

Divide both sides by 7

7x/7 = 28/7

x = 4in

Hence the amount of rain that fell in September is 4in

Greece is different from most other countries in southern Europe because its most popular religion is not Catholicism. Option B

Catholicism refers to the traditions, beliefs, and behaviors of the Catholic Church

Greece is predominantly an Orthodox Christian country, whereas most other countries in southern Europe, such as Italy, Spain, and Portugal, are predominantly Catholic.

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Answer:

Working out 20% of 30

If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is 20% of 30? how would you calculate it?

30 : 100 * 20 = 6

or

30 * 0.20 = 6

Answer:

y- (0,2.5) x-(3.5,0)

Step-by-step explanation:

This is because the intercepts of a graph are the points at which a line intersects with a desired axis. So for the Y axis the inercept would be at 2.5 making the y intercept (0,2.5). The same concept is used on the X axis.

The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

c) $450,000

Step-by-step explanation:

The calculation of the cost of the walk-in program is shown below:-

Cost of the walk-in program = 1 ÷ 4 × Salaries + 1 ÷ 2 × (Rent + Depreciation) + 1 ÷ 5 × (Utilities)

= 1 ÷ 4 × $1,000,000 + 1 ÷ 2 × ($300,000 + $80000) + 1 ÷ 5 × $50,000

= $250,000 + $190,000 + $10,000

= $450,000

Therefore for computing the cost of the walk-in program we simply applied the above formula.

Answer:

i-

ok

Step-by-step explanation:

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer:

180%

Step-by-step explanation:

The radius of the gear should be approximately 2.8644 inches.It is important to note that when making calculations involving units, we need to make sure that all units are consistent and convert them when necessary. In this case, we converted the answer from feet to inches to match the given unit.

To find the radius of the gear that will pull a chain at 60 ft/min when rotating at 40 rev/min, we can use the formula:

chain speed = 2 x pi x radius x rotational speed

where pi is a mathematical constant approximately equal to 3.14.

We know that the chain speed is 60 ft/min and the rotational speed is 40 rev/min, so we can substitute those values into the formula:

60 = 2 x 3.14 x radius x 40

Simplifying the equation, we get:

radius = 60 / (2 x 3.14 x 40)

radius = 0.2387 ft

To convert feet to inches, we can multiply the answer by 12:

radius = 0.2387 x 12 = 2.8644 inches.

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Answer:

153.86

Step-by-step explanation:

The area of a circle is \(\pi r^2\). So, \(\pi (7)^2 = (3.14)(49) = 153.86\)

Answer:

1

Step-by-step explanation:

The graph is shifted up one unit

Answer:

Step-by-step explanation:

Given function:

Since the value of the  |x - 2| can be zero or positive only, the graph has its maximum at x = 2:

The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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x-intercept(s): (2, 0)

y-intercept(s): (0, -5)

M= \(\frac{5}{2}\)

Answer:

(a)

Step-by-step explanation

(b) is not a binary operation, because sqrt(a) is not a monomial

By answering the presented question, we may conclude that so by SAS congruency property we have said that all these triangles are similar.

A triangle is a closed, a double geometric shape made up of three line segments known as sides that connect at three parameters known as vertices.

Triangles are differentiated by their angles and their sides. Triangles can be collinear (all sides equal), angles, or scalene dependent on their sides.

Triangles are classed as acute (all angles just under 90 degrees), right (one angle of approximately to 90 degrees), or ambiguous (all angles greater than 90 degrees).

The area of a triangle may be determined with the formula A = (1/2)bh, where A is the surface, b is really the right triangle base, and h is the triangle's height

here, from the figure, we have

Two sides of the triangle are equal.

And also all angles are also same.

Therefore, so by SAS congruency property we have say that all these triangles are similar.

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A tessellation is a pattern made by repeating geometric shapes without any gaps or overlaps. These shapes, called tiles or polygons, fit together perfectly to cover a plane or a surface. Tessellations can be found in various forms of art, architecture, and design. They are used to create visually appealing patterns and decorations, as well as to explore mathematical concepts.

Tessellations are utilized in various practical applications, such as tiling floors, walls, and pavements, designing mosaics and quilts, and creating computer graphics and textile patterns. They are also studied in mathematics to understand concepts like symmetry, geometry, and transformations.

For polygons to tessellate, certain conditions must be met at their vertices. At each vertex, the angles formed by the polygons must add up to a whole number of degrees, typically 360 degrees. In other words, the sum of the interior angles of each polygon meeting at a vertex must be a multiple of 360 degrees.

This ensures that the polygons can fit together seamlessly without leaving any gaps or overlaps. Examples of polygons that tessellate include equilateral triangles, squares, and hexagons, as their angles add up to 360 degrees at each vertex.

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The area of the triangle is 48 square units.

To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.

Length of side BC = 9+3 = 12 units

Length of side CA = 3+5 = 8 units

Length of side BA = 9+5 = 14 units

Area of triangle = (1/2 × Base × Height) square units

Area of triangle ACB = 1/2 × CA× BC sq units

                          Area = 1/2 × 8 × 12 = 48 sq units

Hence, the area of triangle ACB is 48 square units.

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Answer:

47.91 units²

Step-by-step explanation:

The radius of each circle is:

Therefore, the side lengths of the triangle are:

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

\(\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}\)

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:

\(\implies s=\dfrac{14+12+8}{2}=17\)

To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:

\(\implies A=\sqrt{17(17-14)(17-12)(17-8)}\)

\(\implies A=\sqrt{17(3)(5)(9)}\)

\(\implies A=\sqrt{2295}\)

\(\implies A=47.906158268...\)

\(\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)\)

Answer:  the answer is number four.

Step-by-step explanation:

the answer is 4/5 this is know to be hard

Answer:

It means Progressing

In Progress

Step-by-step explanation:

For one to isolate the variable by using equation rules. Inverse inequality sign if multiplying/dividing by negative. Steps to isolate variable in inequality: Simplify, move constants with inverse operations. Divide coefficient to isolate variable. Reverse direction if using negative number.

Inequalities require you to apply the same principles as those used in equations when isolating a variable. For example, if there is an inequality 3x - 5 < 7. one can isolate the variable, by first:

Add 5 to both sides to be: 3x < 12.

Then divide both sides by 3: x < 4.

So, the variable x is one that is isolated, and the solution to the inequality is one where x < 4.

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