Enter the number that belongs in the green box

Part A: The equation of the circle in standard form is x² + (y - 7)² = 2².

Part B: Center: (h, k) = (0, 7), Radius: 2

Part C: Please check the attachment.

In this problem we find the definition of the equation of a circle in general form, whose standard form must be found:

(x - h)² + (y - k)² = r²

Where:

This can be done by completing the square. First, write the equation of the circle:

x² + y² = 14 · y - 45

Second, complete the square by algebra properties:

x² + y² - 14 · y + 45 = 0

x² + (y² - 14 · y + 49) = 4

x² + (y - 7)² = 2² (PART A)

Third, write the coordinates of the center and the radius of the circle:

Center: (h, k) = (0, 7), Radius: 2 (PART B)

Finally, we proceed to graph the resulting expression.

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x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex], we can use the Factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).the remainder when we divide [tex]x^5+5x^4-2x^3+4x^2+8x+3976$[/tex] by x-7 is 4054.

To check if x-7 is a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$,[/tex] we can use the factor theorem which states that if f(a) = 0, then x-a is a factor of f(x).

To check if x-7 is a factor, we evaluate the polynomial at x=7:

[tex]f(7) = 7^5+5\cdot7^4-2\cdot7^3+4\cdot7^2+8\cdot7+3976 = 384004$.[/tex]

Since [tex]$f(7)\neq 0$[/tex], we can conclude that x-7 is not a factor of [tex]x^5+5x^4-2x^3+4x^2+8x+3976$.[/tex]

To find the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$[/tex]by x-7, we can use polynomial long division or synthetic division. Using polynomial long division, we get:

  [tex]x^4 + 12x^3 + 82x^2 + 578x + 4046\\x-7 | x^5 + 5x^4 - 2x^3 + 4x^2 + 8x + 3976\\- x^5 + 7x^4[/tex]

    ------------

      [tex]12x^4 - 2x^3 + 4x^2 + 8x\\ 12x^4 - 84x^3[/tex]

          -------------

                     [tex]82x^3 + 4x^2 + 8x\\ 82x^3 - 574x^2[/tex]

                      --------------

                                  [tex]578x^2 + 8x\\ 578x^2 - 4046[/tex]

                                    ------------

                                              4054

Therefore, the remainder when we divide [tex]$x^5+5x^4-2x^3+4x^2+8x+3976$ by $x-7$ is $4054$.[/tex]

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The required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

Given that the heights of adult parrots are normally distributed with a mean height of 34 cm and standard deviation of 8 cm.

The formula used to calculate the z-score for the height of 18 cm is

z = (x - mean) / standard deviation

By substituting the value of mean and standard deviation gives,

z = (18 - 34) / 8.

On simplification of numerator gives,

z= -16 / 8 = -2.

To find the proportion of parrots more than 18 cm tall by calculating the area under the standard normal curve to the right of z = -2 by the standard normal distribution table.

That implies, proportion = area to right of z = -2 is approximately equal to 0.9772.

The formula used to calculate the number of parrots that is more than 18 cm tall is  proportion × total number of parrots.

That implies, the number of parrots out of 400 birds which are more than 18 cm tall is 0.9772 × 400 = 390.88 ≈ 391.

Therefore, the required number of parrots out of 400 birds which are more than 18 cm tall is 391 parrots.

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The total area of the figure formed by the congruent triangles and the square is 60 sq in

For square

A = s²

where s is the side

Given:

s = 6 in

Area = 6 * 6

= 36 sq in

Area of triangle = 0.5bh

where b is the base

h is the height

Given:

b = 6 in

h = 4 in

A = 0.5 * 6 * 4

= 12 sq in

Total area of the figure = 2 * Area of triangle + area of square

= 2 * 12 + 36

= 24 + 36

= 60 sq in

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PART A: Linda has $4.41 more than Enrique after one year.

PART B: Enrique has $12.10 more than Linda after the second year.

PART A: After one year, we can calculate the amount of money each person has in their respective accounts.

For Linda's account:

Principal amount = $610

Interest rate = 1.2%

[tex]Interest $ earned = Principal $ amount \times (Interest rate/100) = $610 \times (1.2/100) = $7.32[/tex]

[tex]Total $ amount after one year = Principal amount + Interest earned = $610 + $7.32 = $617.32[/tex]

For Enrique's account:

Principal amount = $590

Interest rate = 3.9%

[tex]Interest $ earned = Principal amount \times (Interest rate/100) = $590 \times (3.9/100) = $22.91[/tex]

Total amount after one year = Principal amount + Interest earned = $590 + $22.91 = $612.91

Comparing the two amounts, after one year Linda has more money.

The difference in the amount is:

$617.32 - $612.91 = $4.41

Therefore, Linda has $4.41 more than Enrique after one year.

PART B: After a second year, we need to calculate the amounts again.

For Linda's account:

Principal amount = $617.32

Interest rate = 1.2%

[tex]Interest earned = Principal amount \times (Interest rate/100) = $617.32 \times (1.2/100) = $7.41[/tex]

Total amount after the second year = Principal amount + Interest earned = $617.32 + $7.41 = $624.73

For Enrique's account:

Principal amount = $612.91

Interest rate = 3.9%

[tex]Interest earned = Principal amount \times (Interest rate/100) = $612.91 \times (3.9/100) = $23.92[/tex]

Total amount after the second year = Principal amount + Interest earned = $612.91 + $23.92 = $636.83

Comparing the two amounts, after the second year Enrique has more money.

The difference in the amount is:

$636.83 - $624.73 = $12.10

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An exponential function that best models the data include the following: A. [tex]r(x) = 223.06(1.09)^x[/tex]

In this scenario, the Company Time, x (months) would be plotted on the x-axis (x-coordinate) of the scatter plot while the Net Revenue, r(x (millions of dollars) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the Company Time, x (months) and the Net Revenue, r(x (millions of dollars), an exponential equation for the line of best fit is given by:

[tex]r(x) = 223.06(1.09)^x[/tex]

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Answer:

[-infinity, 4]

Step-by-step explanation:

-9x + 3 >= -33
-9x >= -36

x<=4 (sign switched because of dividing both sides by a negative integer in an inequality)
Therefore, x is less than or equal to 4

[ - infinity, 4]

After simplification,

(2x + 1)/2(x^2)

Given,

(x/4)+(1/8)/(x^2/4)

Simplifying,

Firstly take LCM of 4 and 8,

LCM of 4 and 8 will be 8.

Then,

(2x +1) /(8) / x^2 /4

Further,

Take reciprocal of the denominator,

(2x +1) /(8) (4/x^2)

(2x + 1)/2(x^2)

Hence after simplification the expression becomes (2x + 1)/2(x^2).

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Answer:

[tex] \frac{41}{3} \times 3 \times \frac{62}{3} = \frac{806}{3} = 268 [/tex]

The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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The value of c that makes z = 4 an extraneous solution is c = -1.

We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.

First, we substitute z = 4 into the equation:

√ (3/2 x + 10) = cz + 8

√ (3/2 x + 10) = c(4) + 8

√(16) = 4c + 8

4 = 4c + 8

4c = -4

c = -1

Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.

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Answer:

the answer is 10.63km/L.

The area of the triangular figure is 16 m²

The area of a triangle is given by A = 1/2bh where

Given the figure below, we see that it is two triangles with height, h = 2 m and base, b = 8 m.

Since the area of each triangle is A = 1/2bh, and the area of both triangles are the same, then the area of both triangles is A" = A + A

= 2A

= 2(1/2bh)

= bh

Substituting the values of the variables into the equation, we have that

A" = bh

= 8 m × 2 m

= 16 m²

The area is 16 m²

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Answer:

p(3) = 16

Step-by-step explanation:

to evaluate p(3) substitute x = 3 into p(x)

p(3) = 0.5(3 - 5)² + 14

      = 0.5(- 2)² + 14

      = 0.5(4) + 14

      = 2 + 14

      = 16

The cost of the fondue pot after the 45% discount and 6% sales tax is calculated using the following equations:

In this example, the original price of the fondue pot is $92 and the discount is 45%, which would make the discount amount $41.40. The sales tax is 6%, which would be $2.48

Therefore, the final price of the fondue pot would be $43.88

Stem-leaf plot for the given data:

1 | 2 3 4 5

2 | 1 2 2

3 | 3 3

4 | 1

The stem represents the tens digit and the leaf represents the ones digit of the data points. For example, the number 18 is represented as 1|8 in the plot.

A stem-and-leaf plot for the given data:

1 | 2 3 4

---+-------

1 | 2 2

2 | 2 2 3 8

3 | 3 3

4 | 1

5 |

6 | 6

7 | 7

8 |

In this plot, the tens digit is used as the stem, and the ones digit is used as the leaf. For example, the first two numbers in the data set are 18 and 17, which have stems of 1 and leaves of 8 and 7, respectively. These are shown in the first row of the plot as "1 | 8 7". Similarly, the number 23 has a stem of 2 and a leaf of 3, so it is shown in the second row as "2 | 3". The remaining numbers are arranged in the same way.

The numbers are arranged in ascending order within each row, and there are blank spaces for stems that do not appear in the data.

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Answer:

LN and NK

Step-by-step explanation:

A perpendicular bisector of a line segment divides the line segment into 2 equal halves.

Here, line JM is a perpendicular bisector of line segment LK at point N. So, line JM divides the line segment LK into 2 equal halves.

The two equal halves are segment LN and segment NK.

Therefore, segment LN is congruent to segment NK.

The rate of change of the number of oil changes with respect to the number of hours will be 3.

The table is given below.

Number of hours              Number of oil changes

            1.5                                          4.5

             3                                             9

           5.5                                         16.5

             8                                            24

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the line gradient linking the interval's ends on the graph depicting the function.

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The rate of change is calculated as,

Average rate = (24 - 9) / (8 - 3)

Average rate = 15 / 5

Average rate = 3

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Answer:

The rectangle is 7.9 meters by 2.9 meters.

Step-by-step explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

[tex]w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9[/tex]

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m

The horizontal transformations are defined as follows:

cos(ax).

They are classified as follows:

The vertical transformations are defined as follows:

acos(x).

They are classified as follows:

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The minimum number of times Johnny needs to use to the wheelbarrow until the delivery truck is filled up to 70%, whereby the shape of the truck is a rectangular prism is about 41 times

A rectangular prism is a three dimensional geometric figure with three pairs of parallel facing sides, and perpendicular adjacent faces.

Whereby the wheelbarrow and the truck are rectangular prisms, we get;

The dimensions of the wheel barrow are;

2 feet by 3 feet by 1.5 feet

The dimensions of the truck are;

11 feet by 8 feet by 6 feet

The amount of soil John puts in the truck = 70% of the volume of the truck

Therefore;

The amount of soil John puts in the truck = 11 feet × 8 feet × 6 feet × 70%

11 feet × 8 feet × 6 feet × 70% = 528 ft³ × 70% = 369.6 ft³

The number of times to use the wheelbarrow, n, is therefore;

n = 369.6 ft³ ÷ (2 ft × 3 ft × 1.5 ft) ≈ 41.0

The minimum number of times Johnny needs to use the wheelbarrow until the delivery truck is 70% filled is therefore 41  = 41 times

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The measure of <BED = 135 degrees

To determine the value, we need to know the following;

From the information given, we have that;

Angle AED + Angle ACD are on a straight line

Now, susbtitute the values, we have that;

135 + ACD = 180

collect like terms

ACD = 180 - 135

subtract the values

ACD = 45

Then, we have that;

<BED = <ACD + <BEC

Substitute the values

<BED = 45 + 90

<BED = 135 degrees

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The domain of the exponential function is all real numbers.

The domain of a function refers to the set of all possible input values (also known as the independent variable) for which the function is defined.

For the exponential function y = 2ˣ + 6, the domain includes all real numbers.

This is because there are no restrictions on the input values that can be plugged into the function.

We can take any real number x, substitute it into the expression 2ˣ, and then add 6 to get a corresponding output value y.

Hence,  the domain of the exponential function is all real numbers.

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Answer:

Median, because Sunny Town is symmetric.

Answer:

The Answer to This question Is x + 5 So Basically 5

Answer:

-6

Step-by-step explanation:

[tex]\frac{x}{-3} = 2\\x = 2 * (-3)\\x = -6[/tex]

The answer is x equals negative 6

09. The total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals.

10. The total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

In order to find the marginal frequencies, we need to calculate the totals for each category separately.

For question 9:

The marginal frequency for "Set Academic Goals - yes" is 64 + 54 = 118. This represents the total number of individuals who answered "yes" to setting academic goals.

The marginal frequency for "Set Academic Goals - no" is 168 + 142 = 310. This represents the total number of individuals who answered "no" to setting academic goals.

The marginal frequency for "Male" is 64 + 168 = 232. This represents the total number of males.

The marginal frequency for "Female" is 54 + 142 = 196. This represents the total number of females.

Interpretation:

The marginal frequencies provide us with the total counts for each category in a contingency table. In this case, we can see that out of the total sample, 118 individuals set academic goals (regardless of gender), while 310 individuals did not set academic goals. Additionally, there were 232 males and 196 females in the sample.

For question 10:

The marginal frequency for "Cat - yes" is 104 + 186 = 290. This represents the total number of individuals who have cats.

The marginal frequency for "Cat - no" is 208 + 98 = 306. This represents the total number of individuals who do not have cats.

The marginal frequency for "Dog - yes" is 104 + 208 = 312. This represents the total number of individuals who have dogs.

The marginal frequency for "Dog - no" is 186 + 98 = 284. This represents the total number of individuals who do not have dogs.

Interpretation:

The marginal frequencies reveal the total counts for each category in the contingency table. In this case, we can observe that out of the total sample, 290 individuals have cats, while 306 individuals do not have cats. Furthermore, 312 individuals have dogs, while 284 individuals do not have dogs.

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Since the difference between the areas of the two rectangles is 64 cm², it has been proven that it is equal to x² - 2x - 35 = 0.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

Area of rectangle M = L × B

Area of rectangle M = (x - 3) × (3x + 4)

Area of rectangle M = 3x² - 5x - 12

Area of rectangle N = L × B

Area of rectangle N = (x + 2) × (x - 3)

Area of rectangle N = x² - x - 6

Difference = Area of rectangle M - Area of rectangle N

Difference = 3x² - 5x - 12 - (x² - x - 6)

Difference = 3x² - 5x - 12 - x² + x + 6

64 = 2x² - 4x - 6

0 = 2x² - 4x - 6 - 64

0 = 2x² - 4x - 70

By dividing all through by 2, we have:

0 = x² - 2x - 35

x² - 2x - 35 = 0 (Proven).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The graph of the modulus function is plotted

Given data ,

Let the modulus function be represented as A

Now , the value of A is

| x | + 1 < 3

On simplifying the inequality , we get

Subtracting 1 on both sides , we get

| x | < 2

When x is positive or zero: In this case, the absolute value of x is equal to x itself. Therefore, we have x < 2

When x is negative: In this case, the absolute value of x is equal to -x. Therefore, we have -x < 2

Hence , the graph of function is plotted

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