Use quadratic regression and a graphing calculator to find the quadratic function that best fits the data set. Then use the model to forecast the value of the function at the indicated point.(Round your coeffiecients to two decimal places.) Years Abortions Since 1985(per 1000 live births) t3 10 15 16 17 422 389 350 324 325 319 What was the abortion rate in 2005? (Round your answer to the nearest whole number) abortions

The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

The lacking graph is included.

The student heights and arm spans in a classroom are depicted in the graph below.

For most people, their arm span is about equal to their height. Mathematicians say the arm span to height ratio is one to one: your arm span goes once into your height.

The x-axis represents the height in cm

The y-axis represents the arm span in cm

We must determine the height of a pupil whose arms are 143 cm long. The value of the specified arm span is not shown on the graph.

To get the best prediction of the height, we will select the line that best fits the data (the sold line in the graph shown).

Points (150, 150) and (160, 160) are on the line. The x-coordinates and y-coordinate are equivalent.

y = x is the line's equation.

A student's arm span is 143 cm,

Which is represented by the letter y. Replace the value of y in the equation for the line that best fits the data:

y = 143 = x,

Where x is a student's height.

The student stands 143 cm tall.

Therefore,

The height of a student with an arm span of 143 cm is most accurately predicted to be 143 cm.

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Answer:

angle A = 124 degrees, angle D = 124 degrees, angle C = 56 degrees

Step-by-step explanation:

1. apply that opposite angles in a parallelogram are congruent

measure of angle A = measure of angle C

measure of angle B = measure of angle D

2. given the measure of angle A = 56 degrees, angle C is also 56 degrees

angle A = angle C = 56 degrees

3. calculate the measure of angle A

measure of angle A + 56 degrees = 180 degrees

4. subtract 56 from both sides

measure of angle A = 124 degrees

5. measure of angle A = measure of angle D

angle A = angle D = 124 degrees

answer:

angle A = 124 degrees

angle D = 124 degrees

angle C = 56 degrees

5) The equation with a negative slope (- m) and a positive y - intercept (b) will be;

⇒ y = - mx + b

6) The value of slopes are,

a) Slope = 4

b) Slope = 3

c) Slope = 1

The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

In question 5;

The value of slope = - m

And, The y - intercept = b

In question 6;

The points are,

a) (3, 13) and (5, 21)

b) (- 2, - 7) and (1, 2)

c) (4, 9) and (10-, 15)

Now,

Since We know that;

The equation of line in slope - intercept form is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

Here, In question 5;

The value of slope = - m

And, The y - intercept = b

Hence, The equation of line is,

⇒ y = - mx + b

And, We know that;

The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Here, In question 6;

The points are,

a) (3, 13) and (5, 21)

b) (- 2, - 7) and (1, 2)

c) (4, 9) and (10, 15)

So, The slopes are find as;

a) (3, 13) and (5, 21)

⇒ m = (21 - 13) / (5 - 3)

⇒ m = 8/2

⇒ m = 4

b) (- 2, - 7) and (1, 2)

⇒ m = (2 - (-7)) / (1 - (-2))

⇒ m = 9/3

⇒ m = 3

c) (4, 9) and (10, 15)

⇒ m = (15 - 9) / (10 - 4)

⇒ m = 6/6

⇒ m = 1

Thus, We get;

5) The equation with a negative slope (- m) and a positive y - intercept (b) is,

⇒ y = - mx + b

6) The value of slopes are,

a) Slope = 4

b) Slope = 3

c) Slope = 1

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Answer:

C) y=1/2x-2

Step-by-step explanation:

In the graph we have to identify the slope and y-intercept.

Y-intercept = -2 (In the graph it goes down two units)

To find the slope I identified the next nearest point, which was (2,-1).

From my y-intercept, -2, I had to go up one unit and two units to the right.

That makes my slope = 1/2

You need to remember slope intercept form is: y=mx+b

When plugging in the numbers you get:

y=1/2x-2

Answer: A

Step-by-step explanation: when 18/20 is turned into a decimal it comes out as even and is the best one you can choose from

The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

Given that,

A circle has a circumference of 12 units and it has an arc of length 8/5 units.

We have to find what is the central angle of the arc in degree.

We know that,

Circumference =12 units

Arc length =8/5= 1.6 units

If the central angle is "θ" then the length of the arc is given by

Arc length= θ/360°×circumference

Substituting values,

1.6=θ/360°×12

θ=48°

Therefore, The central angle of the arc in degree is 48° when a circle has a circumference of 12 units and it has an arc of length 8/5 units.

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Congruent triangles are triangles having corresponding sides and angles to be equal.

Congruent triangles are triangles that have both the same size and the same shape and they have the same perimeter and the same area. Congruence is denoted by “≅”.  For example, we can write ABC ≅ DEF. They have the same area and the same perimeter.

Congruent triangles have the same angle measures and the same side lengths.

On the other hand, the similar triangle is the term used for triangles that have the same shape, but not necessarily the same size.

Two triangles are considered to be congruent if they meet one of the following criteria.

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Answer:

  see attached

Step-by-step explanation:

You want the attached table of group size and number of groups filled in.

As you know from your early experience with multiplication and division relations, either factor of a product can be found by dividing the product by the other factor:

  P = a·b   ⇒   a = P/b, or b = P/a

Here, the total is equal to the product of the number of groups and the number in each group. That means the missing number on each line can be found by dividing the total by the known number on the line.

When the numbers are already in a spreadsheet, you can let the spreadsheet do the arithmetic.

Answer:

yes

Step-by-step explanation:

The entry to record this payment when the company’s estimated taxes for the first quarter total $50,000 will be:

Debit Income taxes payable $50000

Credit Cash $50000.

A journal is a book in which all of a company's transactions are recorded for the first time. Journaling is the process of recording transactions in a journal. Every transaction has two effects: one is debited and the other is credited.

The act of keeping or making records of any transaction, economic or non-economic, is referred to as journal entry. An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry may include multiple recordings, each of which is either a debit or a credit. A journal entry's purpose is to physically or digitally record every business transaction properly and accurately.

The journal entry based on the information is illustrated.

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Answer:

The equation of the line passing through the point (6,-2) that is parallel to the line y=4x-11 is y = 4x - 26

The equation of the linear passes through the point (6, -2) and is parallel to the line y = 4x - 11

Parallel lines have the same slope.

Therefore,

y = 4x - 11

using

y = mx + b

where

m = slope

b= y-intercept

Therefore, the slope of y = 4x - 11 is 4.

And the slope of the other line will be 4 because they are parallel.

Therefore,

y = mx + b

y = 4x + b

it passes through (6, -2)

-2 = 6(4) + b

-2 - 24 = b

b = -26

The equation will be y = 4x - 26

[tex](3x^2 y^5)^3\implies \left( 3^3 x^{2\cdot 3} y^{5\cdot 3} \right)\implies 27x^6 y^{15}[/tex]

Answer:

1

Step-by-step explanation:

The maximum number of automobile registrations that the police may have to check is 72 license.

Concept Introduction:-

Mathematics defines time as an ongoing and continuous series of events that take place in order, from the past to the present to the future.

Given Information:-

We have been given that a witness to a hit-and-run accident told the police that the license number contained the letters RLH followed by  3 digits, the first of which was a 5 . If the witness cannot recall the last  2 digits, but is certain that all 3 digits are different.

We have to find that the maximum number of automobile registrations that the police may have to check

According to the problem

Since digits are different, available digits are 0,1,2,3,4,6,7,8,9  ( as 5 is already used)

Number of available digits = 9

2nd digit can be any of the above 9 digits

3rd digit can be any of the remaining 8 digits

Police have to check 9*8 = 72 registrations.

Hence , The maximum number of automobile registrations that the police may have to check is 72 license.

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Answer:

Step-by-step explanation:

Amy’s monthly budget for textbooks in course supplies is $900.00

Amy's monthly budget for rent, utilities and food is $12,798.

Her monthly budget for a personal and miscellaneous cost is $2,259.

Her total monthly budget equals $15,957.

A budget is best defined as estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.

Budget for textbooks:

= $900.00

Budget for rent, utilities and food:

= $12,798.

Budget for personal and miscellaneous cost:

= $2,259.

Total monthly budget:

= $900 + $12,798 + $2,259

= $15,957.

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As per the given matrix, the stable age distribution vector is 25 and 25

Matrix:

In algebra, matrix means a set of numbers arranged in rows and columns so as to form a rectangular array.

Given,

Here we have the age transition matrix L and the age distribution vector x1 to find the age distribution vectors x2 and X3.

In order to find a stable age distribution vector we need to find an eigenvalue λ and a corresponding eigenvector x such that 

=> Lx=λx.

Here the characteristics polynomial of L is x2−41​ which implies the eigenvalues are 21​ and −21​.

Now, we have to choose the +ve eigenvalue, λ=21​, we need to find the corresponding eigenvector i.e. to find a basis of the solution space (L−21​I2​)x=0.

Then the augmented matrix is

[tex]\begin{bmatrix}200 & 0 \\ 0& 200\end{bmatrix}[/tex]

Then the age transmission is written as 25 and 25.

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Midpoint formula is used to find the centre point of a straight line.

Given :

Let ( x1 , y1 ) and ( x2 , y2) are two points on the straight line.

Midpoint :

The center point of the straight lines with two points is called as midpoint.

Midpoint formula :

( x , y ) = ( x1 + x2 / 2 , y1 + y2 / 2 )

Example :

( x1 , x2 ) = ( 1 , 5 ) and ( y1 , y2 ) = ( 2 , 4 )

( x , y ) = ( 1 + 2 / 2 , 5 + 4 /2 )

= ( 3/2 , 9/2).

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The given trigonometric equations have the value tan x, -cot x.

Since the given trigonometric equations  are: cos2x-cos4x/sin2x+sin4x   and  cos2x+cos4x/sin2x-sin4x. The problem is related to trigonometric Ratios, which are the ratios of the side of a right-angled triangle.Now for the equation (cos 2x - cos 4x )/(sin2x +sin4x)

since we know the formulas  :

cos A + cos B = - sin (A+B)/2 sin(A-B)/2

sin A - sin B = sin( A+B)/2 cos (A-B)/2

so for the equation, we can

= (-sin 3x) sin ( -2x)/2)/( cos 3x cos x)

= sin 3x sin x/ (sin 3x) cos x

= tan x

for the second equation    cos2x+cos4x/sin2x-sin4x

= cos 3x cosx/ cos3x sin(- x)

= - cot x

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The sections of the function that are decreasing, defined by the ordered pairs are;

Section 2; (-1, 4) to (1, 0)

Section 4; (3, 2), to (5, -2)

The part of the second function that is decreasing is; (2, -2) to (3, -5)

A function is a definition of the mapping of the set of input variables unto the set of the output variables.

The points in the specified functions are;

Section 1 line ; (-3, 4) to (-1, 4)

Section 2 line ; (-1, 4) to (1, 0)

Section 3 line ; (1, 0) to (3, 2)

Section 4 line ; (3, 2) to (5, -2)

The points through which the function goes through are; (-4, -2.5), (3, -5), (-2, -2), (0, 5), (2, -2), (3, -5), (4, 2.5) and (5, -2)

A function is decreasing when the positive increase in the x-value of the function is accompanied by a decrease in the y-value.

The sections of the functions that are decreasing are;

Section 2 line ; (-1, 4) to (1, 0),

Section 4; (3, 2) to (5, -2)

Parts of the function that is decreasing is; (2, -2), (3, -5)

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Answer:

The function is going up

Step-by-step explanation:

the arrow is going up

Answer: y=2^{x}

Step-by-step explanation:

As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

In the given question, Decker scientific is considering an investment of $850,000 in a new product line.

The company will make the investment only if it will result in a rate of return of 20% per year or higher.

If the revenue is expected to be between $290,000 and $325,000 per year for each of 5 years, we have to determine if the decision to invest is sensitive to the projected range of income using an annual worth analysis.

AW of investment when expected revenue is

290000 = -1080000*(A/P,20%,4) + 290000

A/P = -1080000*0.386289 + 290000

A/P = -127192.12

A/P = -127192

AW of investment when expected revenue is

369000 = -1080000*(A/P,20%,4) + 369000

A/P = -1080000*0.386289 + 369000

A/P = -48192.12

A/P = -48192

As Company will not invest in both cases, decision to invest is not sensitive over this annual revenue range.

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Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

There are numerous ways to define an equation in mathematics. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. In the equation 2x + 4 = 14, for example, the two expressions 2x + 4 and 14 are separated by the symbol "equal." Mathematical variables are used in even the simplest and most basic mathematical equations.

Here,

the ferris wheel  radius = 10 meters

and he is 14 meters above the ground.

So we can build an equation with given data to find the time todd needed to complete one full rotation around the Ferris wheel

thus time is represented as t

Therefore ,the Ferris wheel rotates at a constant rate so that the angle sweeps out & radians per minute

so speed =8 rad/min

t=distance/speed

t=2[tex]\pi[/tex]/8 min

t=0.785min

Therefore the  the time todd needed to complete one full rotation around the Ferris wheel is 0.785min

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Answer:

94%

Step-by-step explanation:

The real zeros of the quadratic function  f(x) = 2x² - 5x + 1 is between

The given quadratic function is  f(x) = 2x² - 5x + 1

Using a calculator the zeros of the function  f(x) = 2x² - 5x + 1 is solved to be

x = 2.28 OR 0.22

The value 0.22 falls between 0 and 1 = 0 < x < 1

this means greater than 0 and less than 1

The value 2.28 falls between 2 and 3 = 2 < x < 3

this means greater than 2 and less than 3

Therefore the second option is the right choice

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The distance the car was driven for if the total cost of the rental was $151.55 is 259 miles

From the question, we are to determine how far the car was driven in one day

From the given information,

The formula that represent the cost of renting the car for one day is

C= 0.45m + 35

We are to determine how far the car was driven if the total cost of the car rental was $151.55

That is,

We are to determine m when C is $151.55

Substitute C = 151.55 in the formula

151.55 = 0.45m + 35

Calculate the value of m

151.55 = 0.45m + 35

151.55 - 35 = 0.45m

116.55 = 0.45m

Therefore,

0.45m = 116.55

m = 116.55/0.45

m = 259

Hence, the car was driven for 259 miles

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The volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

In the given question, the radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week.

The thickness of the rind is always one tenth of the radius.

We have to find the volume of the rind is growing at the rate cubic centimeters per week at the end of the fifth week.

Assume that the radius is initially zero.

Let r be the radius of watermelon.

dr/dt = 2 cm/week

Radius after 5 week = 10 cm

Thickness of the rind = r/10 cm = 0.1r cm

Now the volume of rind

V = 4/3 π[r^3-(0.9r)^3]

dV/dt = 4/3 π[3r^2-3r^2(0.9)^3]dr/dt

dV/dt = 4/3 π[1-(0.9)^3](3r^3)(2)

dV/dt = 8(3.14)(0.271)(10)^3

dV/dt = 8(3.14)(0.271)(1000)

dV/dt = 681.097 cm^3/ week.

Hence, the volume of the rind is growing at the rate 681.097 cubic centimeters per week at the end of the fifth week.

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The missing part of the triangle are x = 7.5 units, y = (7.5√3)/2 units, y = (7.5√3)/2 units, z = (15√3)/2 units, a = 3.75 units and b = 11.25 units

Given: c = a+b = 15, X = 30°, Z = 60°, C = 90° for the triangles

Using the sine rule

x/sin X = z/sin Z = c/sin C

x/sin X =  c/sin C

x/sin30 = 15/sin90

x/0.5 = 15/1

x = 0.5 × 15 = 7.5 units

Using trigonometrical ratio:

sin 60 = y/x

(√3)/2 = y/7.5

y = (7.5√3)/2 units

sin 30 = y/z

1/2 = (7.5√3)/2/z

z = [(7.5√3)/2] / (1/2)

z = (15√3)/2 units

cos 30 =  b/z

(√3)/2 = b/(15√3)/2

b = [(√3)/2] × [(15√3)/2]

b = 45/4 = 11.25 units

a+b = 15

11.25 + b = 15

a = 15 - 11.25

a = 3.75 units

b = 45/4 = 11.25 units

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