A certain circle can be represented by the following equation.
x^2+y^2+8x-16y+31=0
What is the center of this circle?
What is the radius of this circle?

There are 15 spiders in the backyard. The correct option is D

Let's begin by resolving the issue using algebra. Let's use "s" for the quantity of spiders and "d" for the quantity of dogs in the backyard.

As a result of the difficulty, we know that there are 3 times as many animals as there are spiders.

s + d = 3s

Simplifying this equation, we get:

d = 2s

We also know that there are 240 legs in the backyard, with each dog having 4  legs and each spider having 8. Thus, we can create the following equation:

8s + 4d = 240

Substituting d = 2s, we get:

8s + 4(2s) = 240

Simplifying and solving for s, we get:

16s = 240

s = 15

Therefore, there are 15 spiders in the backyard.

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Answer:

30508

Step-by-step explanation:

5800(1+0.052)^5

according to the question the balance in the account earning compound interest after 6 years is $4,156.22.

Multiply the principal with the rate of interest, the time period, and various other factors to determine simple interest. Simple returns = money + interests + hours is the marketing formula. This approach makes calculating interest the simplest. The approach to calculating interest that is most usually employed is as a percentage over the principal sum. For instance, he will just pay his share of the interest at 100% when he borrows $100 with a friend and agrees to shell out it back with 5% interest. $100 has been reduced to $5 (0.05). Every time you borrow money, you must pay interest, which is applied to whatever loans you make. On the loan balance, interest is typically calculated using an annual percentage.

given,

To calculate the balance in the account earning compound interest after 6 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the sum of money at the end of the period of time

P stands for the principle (beginning sum).

the decimal representation of the annual interest rate (r).

n represents how many times the interest rate is compounded annually.

t is the duration (in years).

In this case, we have:

P = $3500 (the principal)

r = 2.16% = 0.0216 (the annual interest rate)

Since interest is compounded four times a year (quarterly), n is equal to four.

t = 6 (the time period is 6 years)

With these values entered into the equation, we obtain:

A = 3500(1 + 0.0216/4)^(4*6)

A = $4,156.22

Therefore, the balance in the account earning compound interest after 6 years is $4,156.22.

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The balance in the account earning compound interest after 6 years when the principal is $3500 at an annual interest rate of 2.16% compounded quarterly is approximately $4,029.53.

Compound interest is the term used to describe the interest that is calculated on both the initial investment and any accumulated interest. It is interest on top of interest, to put it another way.

We can use the formula for compound interest to find the balance in the account after 6 years:

A = P(1 + r/n)^(nt)

where:

A = balance after 6 years

P = principal = $3500

r = annual interest rate = 2.16%

n = number of compounded times  per year = 4 (quarterly)

t = time in years = 6

Plugging in the values, we get:

A = 3500(1 + 0.0216/4)^(4×6)

A ≈ $4,029.53

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the correct response to the question is: Yes, No, Yes, No and Yes.

We can determine if each set of numbers can be the lengths of the sides of a right triangle by evaluating each set.

Evaluating each set :

#1 :

5, 12, 13

5² + 12² = 13²

25 + 144 = 169

169 = 169

It is a Yes

#2 :

12, 35, 20

12² + 35² = (20√3)²

144 + 1225 = 400*3

1369 ≠ 1200

It is a No

#3 :

5, 10, 5√5

5² + 10² = (5√5)²

25 + 100 = 25(5)

125 = 125

It is a Yes

#4 :

8, 12, 15

8² + 12² = 15²

64 + 144 = 225

208 ≠ 225

It is a No

#5 :

20, 99, 101

20² + 99² = 101²

400 + 9801 = 10201

10201 = 10201

It is a Yes

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The question lacks some details, see complete question in the attached image.

The equation for the orange graph is the one in the last option:

f(x) = -3x³

We can see that the orange graph seems to be:

From the given options, the only one that matches all these options is the last one:

f(x) = -3x³

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The method you would use to prove the two triangles are congruent include the following: B. ASA.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides are proportional to the  lengths of corresponding altitudes when two (2) triangles are similar.

In Mathematics and Geometry, ASA is an abbreviation for Angle-Side- Angle and it states that when two (2) angles and their included side in two (2) triangles are congruent, then the triangles are said to be congruent.

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Missing information:

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

you did not provide enough information to answer the question

The ceiling function, denoted by ⌈x⌉, gives the smallest integer that is greater than or equal to x. Therefore, ⌈-0.75⌉ is the smallest integer that is greater than or equal to -0.75.

Since -1 is the smallest integer that is greater than or equal to -0.75, we have:

⌈-0.75⌉ = -1

Therefore, the functional value for the ceiling function at -0.75 is -1.

The answer is option A.

Therefore , the solution of the given problem of expression comes out to be 6.5 is the abbreviated numerical expression.

Shifting numbers, which can be expanding, variable diminishing, or blocking, should be used instead of random estimations. Only through exchanging goods like tools, expertise, or answers to problems could they assist one another. The explanation on the reality equation may include the justifications, elements, or mathematical claims for tactics like increased argumentation, falsification, and blending.

Here,

The mathematical expression is expressed as follows:

=> 42 / 7 + (3 / 6)

We can use the division operations to make the expression simpler:

=> 7 /42 = 6

=> 6 / 3 = 0.5.

The statement is thus more easily expressed as follows:

=> 6 + 0.5

When we add the two numbers, we get:

=> 6.5

Therefore, 6.5 is the abbreviated numerical expression.

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The complete question is " Write and simplify this numerical expression. Forty-two divided by seven plus the quantity three divided by six"

None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

what is rounding ?

Rounding is a mathematical process of approximating a number to a specified degree of accuracy. It involves replacing a number with a simpler, but close value that is easier to work with or understand.

In the given question,

The question asks us to find the annual premium for a $75,000 10-year term policy for a 25-year-old male, using the table of annual life insurance premiums per $1,000 of face value.

First, we need to find the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. Looking at the table, we can see that the premium for a 10-year term policy for a 25-year-old male is $4.79 per $1,000 face value.

To find the annual premium for a $75,000 policy, we need to multiply the premium per $1,000 face value by 75. So:

Annual premium = $4.79 per $1,000 x 75 = $359.25

Rounding this answer to the nearest cent gives us:

$359.25 ≈ $359.26

Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male is $359.26.

None of the answer choices match this result exactly, but the closest option is (a) $363.75, which is only off by a small amount due to rounding.

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Answer:

1,607 plus the amount of people multipled by 1.15

Step-by-step explanation:

2 fog machines = $80

1 sound equipment = $165

1 disco ball = $45

80+165+45+855+462= $1,607

The angles of △ABC are approximately:

A ≈ 36.1 degrees

B ≈ 55.9 degrees

C ≈ 101.3 degrees

To find the angles of △ABC, we can use the Law of Cosines, which states that:

c^2 = a^2 + b^2 - 2ab*cos(C)

where C is the angle opposite the side c.

Using the given values, we can substitute and solve for cos(C):

18^2 = 11^2 + 20^2 - 2(11)(20)cos(C)

324 = 441 + 400 - 440cos(C)

cos(C) = -17/440

C ≈ 101.3 degrees

We can now use the Law of Sines to find the other angles:

sin(A)/a = sin(C)/c

sin(A)/11 = sin(101.3)/18

sin(A) ≈ 0.593

A ≈ 36.1 degrees

sin(B)/b = sin(C)/c

sin(B)/20 = sin(101.3)/18

sin(B) ≈ 0.820

B ≈ 55.9 degrees

Therefore, the angles of △ABC are approximately:

A ≈ 36.1 degrees

B ≈ 55.9 degrees

C ≈ 101.3 degrees

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Answer: should be 24?

Step-by-step explanation:

im not sure

Therefore , the solution of the given problem of percentage comes out to be  14 gallons of the first brand and 56 gallons of the second brand must be utilised.

In statistics, a figure or metric than may be presented as a percentage or 100 is denoted by the abbreviation "a%". Another unusual spelling is "pct," "pct," and "pc." The percent symbol ("%") is the method that is most usually used for this. Additionally, there are no indications or predetermined ratios of any component to the whole. Numbers are effectively integers since they frequently add up to 100.

Here,

Let's write "x" for the first brand's (35% pure antifreeze) number of gallons and "y" for the second brand's (60% pure antifreeze) number of gallons.

Given:

70 gallons of mixture are required in total.

Desired antifreeze content in the combination is 55%

Based on the information provided, we can construct the following system of equations:

=> Equation 1: x + y = 70

=> Equation 2: 0.5*70 = 0.55x + 0.60y

=> x = 70 - y

=> 0.35(70 - y) + 0.60y = 0.55 * 70

=> 24.5 - 0.35y + 0.60y = 38.5

=> 0.25y = 14

=> y = 56

=> x = 70 - 56

=> x = 14

In order to get 70 gallons of a mixture that contains 55% pure antifreeze, 14 gallons of the first brand and 56 gallons of the second brand must be utilised.

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the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

How to solve the question?

To find the mean absolute deviation (MAD) for the high temperatures in Julia's town, we first need to find the mean temperature for the week.

To do this, we add up all the temperatures and divide by the number of temperatures:

(49 + 55 + 42 + 46 + 47 + 42 + 38) ÷ 7 = 43.3

The mean temperature for the week is 43.3 degrees.

Next, we need to find the distance of each temperature from the mean. To do this, we subtract the mean from each temperature:

|49 - 43.3| = 5.7

|55 - 43.3| = 11.7

|42 - 43.3| = 1.3

|46 - 43.3| = 2.7

|47 - 43.3| = 3.7

|42 - 43.3| = 1.3

|38 - 43.3| = 5.3

We take the absolute value of each difference to ensure that the distances are positive.

Now, we find the mean of the distances by adding up all the distances and dividing by the number of temperatures:

(5.7 + 11.7 + 1.3 + 2.7 + 3.7 + 1.3 + 5.3) ÷ 7 = 4.9

Therefore, the mean absolute deviation for the high temperatures in Julia's town for the week is 4.9 degrees.

In conclusion, the mean absolute deviation is a measure of the variability of a set of data. It is calculated by finding the mean of the absolute distances of each data point from the mean. In this case, the MAD is 4.9 degrees, indicating that the temperatures for the week were relatively close to the mean.

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Answer:

no

Step-by-step explanation:

-5/3x+10=5

-5/3x=5-10=-5

3x=-5/-5=1

=>x=1/3

Answer:

the required answer are -8,0,4

The surface area of the pyramid is 64 square feet.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To find the surface area of the pyramid, we need to find the area of each face and add them together.

First, let's find the area of the base, which is a square with side length 4 feet:

Area of base = 4 feet x 4 feet = 16 square feet

Next, we need to find the area of each triangular face. We know that the height of each triangular face is 6 feet, and the base of each triangular face is one of the sides of the square base, which is 4 feet. To find the area of a triangle, we use the formula:

Area of triangle = 1/2 x base x height

Area of each triangular face = 1/2 x 4 feet x 6 feet = 12 square feet

There are 4 triangular faces, so the total area of all the triangular faces is:

Total area of triangular faces = 4 x 12 square feet = 48 square feet

Now we can find the total surface area by adding the area of the base and the area of the triangular faces:

Total surface area = area of base + area of triangular faces

Total surface area = 16 square feet + 48 square feet

Total surface area = 64 square feet

Therefore, the surface area of the pyramid is 64 square feet.

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Step-by-step explanation:

Look at the points  (0,-3)  and  ( 3,0)

slope,  m = rise / run =   3 / 3 =  1  

Answer:

1

Step-by-step explanation:

y=x+3

The average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.

Based on the survey results of 1500 adults, we can be 95% confident that the true mean number of hours worked in the previous week for the entire population of the country lies between 38.4 hours and 43.5 hours.

This means that if we were to repeat this survey multiple times, 95% of the time the sample mean would fall within this range. Therefore, we can conclude that the average number of hours worked in the previous week for adults in the country is likely to be between 38.4 and 43.5 hours.

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The expressions are solved to give;

1.n = 1

2. h = 1

3. x = -5

4. n = 1/4

5. x = 7/2

6. p = 2/3

7. x = -12

8. n = 3

9. c = -1

10. x = 6

These are expressions that are made up of term, variables, constants, factors and coefficients.

They are also made up of mathematical operations.

From the information given, we have;

1. 5n + n = 2n + 4

collect and add the like terms

4n = 4

Make n subject

n = 1

2. 5h + 2 = h - 2

collect and add the like terms

4h = 4

h = 1

3. 2x - 1 = 3x + 4

collect and add or subtract the like terms

-x = 5

x = -5

4. n = n + 1/5

cross multiply

4n = 1, n = 1/4

5. x + 5 = 3x - 2

collect like terms

-2x = -7

x = 7/2

6. p = p + 2/4

cross multiply

3p = 2

p = 2/3

7. 4(2 + x) = 3x - 4

expand the bracket

8 + 4x = 3x - 4

collect like term

x = -12

8. 5n + 2 = 3n + 4

collect like terms

n = 3

9. 3c - 2 = -3c - 8

collect like terms

6c = - 6

c = -1

10. 3x + 1 = 2x - 5

collect the like terms

x = 6

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Answer:

1,200

Step-by-step explanation:

The formula is Length x Width x Height so it will be 20 x 5 x 12 and you get 1,200.

Hope this helps!

It would take about 402.985 gallons of water to fill the fish tank completely.

To calculate the number of gallons of water it would take to fill the fish tank completely, we need to multiply the dimensions of the fish tank in cubic feet by the conversion factor to convert cubic feet to gallons.

Given:

Length = 9 ft

Width = 2 ft

Height = 3 ft

Conversion factor: 1 gallon = 0.134 ft³

Step 1: Calculate the volume of the fish tank in cubic feet

Volume = Length × Width × Height = 9 ft × 2 ft × 3 ft = 54 ft³

Step 2: Convert cubic feet to gallons

54 ft³ × (1 gallon / 0.134 ft³) ≈ 402.985 gallons

So, it would take approximately 402.985 gallons of water to fill the fish tank completely.

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Answer: i think its 366

Step-by-step explanation:

i just did 61X6

Answer:

[tex]\frac{8}{10}[/tex]

Step-by-step explanation:

[tex]cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}[/tex]

Answer:

Answer:

\frac{8}{10}

10

8

Step-by-step explanation:

\begin{gathered}cos(A) = \frac{adjacent}{hypotenuse} \\= \frac{AB}{AC}\\= \frac{8}{10}\end{gathered}

cos(A)=

hypotenuse

adjacent

=

AC

AB

=

10

8

Given:

[tex]\sqrt{z+5}+4\leq 13[/tex]

Move 4 to the right side:

[tex]\sqrt{z+5}\leq 9[/tex]

Simplify

[tex]z+5 \leq 81[/tex]

Move 5 to the right side:

[tex]z\leq 76[/tex]

Find singularity points

Find non-negative values for radicals:  [tex]z\geq -5[/tex]

Combine the intervals

[tex]z\leq 76 \ \text{and} \ z\geq -5[/tex]

Merge overlapping intervals

[tex]-5\leq z\leq 76[/tex]

Answer:

Answer:

It Does. Cool

Answer:

c.) silver bikes

Step-by-step explanation:

Given the bike shop has 11 red bikes, 3 blue bikes, 12 silver bikes

here, the number orange bikes = 4

Given for every 1 orange bike there 3 __ bikes

Divide each number of bikes by the number of orange bikes  

For 11 red bikes

= 11/4 = 2.75    [which means for 1 orange bike 2.75 red bikes ]

For 3 blue bikes

= 3/4 = 0.75    [ which means for 1 orange bike 0.75 blue bikes ]

For 12 silver bikes

= 12/4 = 3        [ which means for 1 orange bike 3 silver bikes ]

For every 1 orange bike, there are 3  silver bikes.

The possible values of a are 3 and -3.

We know that the coefficient of x⁷ in the given expression is 1215, the expression is:

[tex]x^3(ax + 3)^5[/tex]

The term with x⁷ will be:

[tex]5*(3x^7*a^4) = (15a^4)*x^7[/tex]

Then we need to solve the equation:

15a⁴ = 1215

a⁴ = 1215/15

a⁴ = 81

a = ⁴√81 = ± 3

These are the possible values of a.

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Answer: median

Step-by-step explanation:

A is not a center of measure and nethier ia mode and since the data is skewd it is the median and if it is not skewd it is the mean