which statement is most strongly supported by the scatter plot?

The system of equations to solve for the unknowns is \(A= 2\), \(-6A + B = 0\) and \(9A- 3B + C = 1\)

The given parameters are:

\(\frac{2x^2 + 1}{(x - 3)^3} = \frac{A}{x - 3} + \frac{B}{(x - 3)^2} + \frac{C}{(x - 3)^3}\)

\(2x^2 + 1 =A(x -3)^2 + B(x -3) +C\)

Start by opening the brackets

\(2x^2 + 1 =A(x^2 -6x + 9) + Bx -3B +C\)

This gives

\(2x^2 + 1 =Ax^2 -6Ax + 9A + Bx -3B +C\)

Next, collect the like terms

\(2x^2 + 1 =Ax^2 -6Ax + Bx + 9A -3B +C\)

Next, compare both sides of the equation.

This gives

\(Ax^2 = 2x^2\)

\(-6Ax + Bx = 0\)

\(9A- 3B + C = 1\)

Lastly, cancel out the variable x

\(A= 2\)

\(-6A + B = 0\)

\(9A- 3B + C = 1\)

Hence, the system of equations to solve for the unknowns is \(A= 2\), \(-6A + B = 0\) and \(9A- 3B + C = 1\)

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Answer:

A and E

Step-by-step explanation:

Solution

- The range of the function is simply the y-values for which the function is defined.

- The y-values are given in the table.

- Thus, the Range is:

Answer:

8 millimeters 4x where x is 2 millimeters

Answer:

8/15

Step-by-step explanation:

1/5 + 1/3 = 3/15 + 5/15 = 8/15

There are 56 milligrams in 8 milliliters of the drug if the drug's label says each milliliter contains 7 milligrams of the substance.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Let x milligrams would in 8 ​milliliters.

We can write this as a ratio as

As per the given information,

1 milliliter  : 7 milligrams  = 8 milliliter   : x milligrams

⇒ 1 / 7 = 8 / x

⇒ x = 8 × 7

⇒ x = 56 milligrams

Hence, there are 56 milligrams in 8 ​milliliters of the drug.

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Answer:

The answer is 21

Step-by-step explanation:

The value of (p*q)(5) and (q*p)(5) is 288

The functions are given as:

p(x)=x+1

q(x)=2x^2-2

Calculate p(5) and q(5)

p(5)=5+1 = 6

q(5)=2(5)^2-2 = 48

The functions are then calculated as:

(p*q)(5) = p(5) * q(5)

(p*q)(5) = 6 * 48

(p*q)(5) = 288

Also, we have:

(q*p)(5) = (p*q)(5)

(q*p)(5) = 288

Hence, the value of (p*q)(5) and (q*p)(5) is 288

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Complete question

Suppose that the functions p and q are defined as follows. p(x)=-x-1 q(x)=-2x^2-2 Find the following. (p*q)(5) (q*p)(5)

Answer:

Step-by-step explanation:

Arithmetic sequence:

\(\boxed{a_n =a + (n-1)*d)}\)

a₅ = 10    a + 4d = 10

a₆ = 8     a + 5d = 8

Multiply the equation (I) by (-1) and then add. 'a' will be eliminated and we can find the value of 'd'

(I)*(-1)     -a - 4d = -10

(II)          a + 5d = 8     {Now add}

                     d = -2

Substitute d = -2 in equation (I)

 a + 4*(-2) = 10

 a -  8       = 10

           a   = 10 + 8

a =  18

a = 18 , d = -2

Sequence:  18 ,16 , 14 , 12 , 10 , ......

Answer:

7 cm is equal to 0.07 m.

To convert centimeters to meters, you need to divide the number of centimeters by 100, since there are 100 centimeters in a meter.

So, 7 cm / 100 = 0.07 m.

Answer:Case 1: Principal: 10,000; Period: 1 year Case 2: Principal: 1,000; Period: 10 years Case 3: Principal: 5,000; Period: 2 years Case 4: Principal: 2,500; Period: 4 years Simple Interest is a product of period, principal and interest rate, for a given interest rate, the interest earned would be equal if the product of principals and period is same for any number of cases. In our examples, we see that the product of principal and period comes out to be 10,000 in each case.

Step-by-step explanation:

Answer:

Step-by-step explanation:

​(a) What proportion of​ 18- to​ 34-year-old respondents are more likely to buy when made in their​ country? What proportion of​ 35- to​ 44-year-old respondents are more likely to buy when made in their​ country?

The proportion of​ 18- to​ 34-year-old respondents is

0.66

The proportion of​ 35- to​ 44-year-old respondents is

0.56

(b) What age group has the greatest proportion who are more likely to buy when made in their country?

18-34 yrs

(c) Which age group has a majority of respondents who are less likely to buy when made in their country?

55+

(d) What is the apparent association between age and likelihood to buy when made in their country?

As age decreases, the likelihood to buy homegrown increases

Answer:

24

Step-by-step explanation:

Answer:

\(37.7in.\)

Step-by-step explanation:

The circumference of a circle is: \(C=2\pi r\)

However, the question wants us to use 3.14 instead of \(\pi\).

We are given 12 inches as the diameter of the circle.

We want the radius, which is half of the diameter.

The radius of the circle is 6 inches.

Now that we have the radius, we plug and chug.

\(C=2*3.14*6in.\\C=6.28*6in.\\C=37.68in.\\\)

However, the question wants us to round the answer to the nearest tenth.

Therefore, the new answer is: \(37.7in.\)

Answer:

B

Step-by-step explanation:

Reflects over x axis then translates down and left.

Step-by-step explanation:

-181+485=304

-146-(-181)=35

Answer:

To find the number of square yards equivalent to the total area, we can simply divide the total area in square feet by the number of square feet in a square yard.

1 square yard = 9 square feet

So, total area in square yards = (4500 square feet) / (9 square feet/square yard)

= 500 square yards

Therefore, the total area is equivalent to 500 square yards.

Step-by-step explanation:

Answer:

Therefore, the total area is equivalent to 500 square yards.

Step-by-step explanation:

To find the number of square yards equivalent to the total area, we can simply divide the total area in square feet by the number of square feet in a square yard.

1 square yard = 9 square feet

So, total area in square yards =( 4500 square feet) / (9 square feet/square yard)

= 500 square yards

Answer:

there are no outlier in this data set beacuse

1.  Put the data in numerical order.

2.  Find the median.

3.  Find the medians for the top and bottom parts of the data.  This divides the data into 4 equal parts.

The median with the smallest value is called Q1.  The median for all the values - usually just called the median is also called Q2.  The median with the largest value is Q3.

4.  Subtract...Q3 - Q1.  This value is the InterQuartileRange or IQR.  Remember that the range means taking the largest minus the smallest.  This is a special range having to do with the quartiles.

5.  Multiply...1.5 * IQR

6.  Take your answer from #5 and do 2 things with it.  A). Subtract it from Q1 and B)  Additional to Q3.

7.  Look at all your data points.  If any are SMALLER than Q1 - 1.5 *IQR, they are outliers.  If any are LARGER than Q3 + 1.5 *IQR, they are also outliers.

For your data....the median, Q2 is

(43+38)/2 = 40.5.

Q1 = (30+26)/2 = 28.

Q3 = (54+52)/2 = 53

The IQR is 53 - 28 = 25

1.5 * IQR = 37.5

Q1 - 37.5 = 28 - 37.5 = -9.5. There is no data value less than -9.5.

Q3 + 37.5 = 53 + 37.5 = 90.5.  there is no data value greater than 90.5.

My conclusion is that there are no outliers in this data.

I hope this helps!

Answer:

B C E

Step-by-step explanation:

trust me... its too hard to explain

Answer:

114.29

Step-by-step explanation:

Answer: Length = 7 and Width = 2

Step-by-step explanation:

Perimeter = 2(length + width)  
18 = 2(L+W)
\(\frac{18}{2}\) = (L+W)  
9 = L+W  
Make width the subject.
w = 9-L ------Equation 1

  Area = Length × Width
⇒14 = L×(9-L)   | Substitute Eq.1 in place of Width
⇒14 = 9L - L²
⇒L² - 9L + 14 = 0
⇒L² -7L - 2L + 14 = 0
⇒L×(L-7) -2×(L-7) = 0
⇒(L-7)(L-2) = 0
∴ L=7(Answer) or L=2(Not Applicable since length can't be larger than width)

Substitute the value into eq.1
when L=7
W=9-7      
  =2      

Lenth=7
Width=2

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Answer:

Step-by-step explanation:

Let the length of the plank be "l" and the width be "w".

The perimeter of the plank is the sum of the lengths of all four sides, which is:

2(l + w) = 18

Simplifying the equation, we get:

l + w = 9

The area of the plank is given by:

lw = 14

We can solve for one of the variables in terms of the other by rearranging the equation:

l = 14/w

Substituting this expression for "l" into the equation for the perimeter, we get:

(14/w) + w = 9

Multiplying both sides by "w", we get:

14 + w^2 = 9w

Rearranging the terms, we get:

w^2 - 9w + 14 = 0

This is a quadratic equation that can be factored as:

(w - 7)(w - 2) = 0

Therefore, the possible values of "w" are 7 and 2.

If we take "w = 7", then using the equation l = 14/w, we get:

l = 14/7 = 2

Therefore, the length and width of the plank are 2 feet and 7 feet, respectively.

If we take "w = 2", then using the equation l = 14/w, we get:

l = 14/2 = 7

Therefore, the length and width of the plank are 7 feet and 2 feet, respectively.

In summary, the plank could have a length of 2 feet and a width of 7 feet, or a length of 7 feet and a width of 2 feet, given its perimeter of 18 feet and area of 14 square feet.

Answer:

The next two numbers following:

431

141311

1114111321

311431131211

are:

132114132113111221

AND

11131221141113122113312211

Step-by-step explanation:

I shall explain the pattern below:

431 (just the digits 4, 3, and 1)

141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)

1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)

311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)

NEXT TWO NUMBERS:

one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)

that makes: 132114132113111221

one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)

that makes: 11131221141113122113312211

The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.

The surface area of the sphere is 1810 cm²

A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of sphere is expressed as;

A = 4πr². where r is the radius.

A = 4 × 3.14 × 12²

A = 1809.7 cm²

approximately to the nearest whole number

A = 1810 cm²

Therefore the surface area of the sphere to the nearest whole number is 1810 cm².

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Answer:

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In this case, the ladder forms the hypotenuse, the distance from the wall to the base of the ladder forms one leg, and the height of the ladder forms the other leg. Let's call the length of the ladder "L".

Using the Pythagorean theorem, we can write:

L^2 = (distance from the wall)^2 + (height of the ladder)^2

Substituting the given values, we get:

L^2 = 10^2 + 24^2

L^2 = 100 + 576

L^2 = 676

Taking the square root of both sides, we get:

L = sqrt(676)

L = 26

Therefore, the length of the ladder is 26 feet.

Answer:

it can be 100 because percentages are out of 100

Answer:

x = 10

Step-by-step explanation:

\(5x + 19 = 7x - 1 \\ (corresponding \: \angle s) \\ \\ 5x - 7x = - 1 - 19 \\ \\ - 2x = - 20 \\ \\x = \frac{ - 20}{ - 2} \\ \\ x = 10\)

Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

Answer:

C. 36 degrees

Step-by-step explanation:

Exterior angles sum = 360 degrees

72+144=216

360-216=144

Supplementary angles(Angles on opposite sides of the transversal) sum = 180

180-144= 36

Therefore, x=36 degrees

Answer:

The number of observations is 3

Step-by-step explanation:

According to the given situation, The computation of the number of observations in each cell treatment via intersecting row-column is shown below

Here

N represents the number of observations

So from the given data, the number of observations is 3

i.e.

N = 3

The same is to be considered and relevant too

Answer:

4

Step-by-step explanation:

12 divided by 3 sides of triangle