The value of John's baseball card collection decreases exponentially over time, and the value of his silver collection increases exponentially over time. If the value of John's two collections combined t years from now is given by the function V = 500(1.05)2t + 600(0.95)t, which statement must be true?

Answer:

1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.

2. The intrusion of the younger rock by the principle of cross-cutting relationship

3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.

Step-by-step explanation:

In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.

The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.

The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.

Answer:

3 [tex]\frac{9}{20}[/tex]

Step-by-step explanation:

3.45=3 45/100

reduce and divided by 5

3 45/100= 3  9/20

Answer:

Step-by-step explanation:

add me on fortnite

Answer:

a) Independent

b) Quantitative  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 517

Sample:

Married lawyers and their spouses.

Response variable:

Comparison of academic aptitudes of married lawyers and their spouses.

a) The given sampling is an example of independent sampling.

This is an independent sample because an individual of sample does not effect any other individual of the sample.

b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.

It is a quantitative measure because the scores can be expressed in numerical.

Answer:

The sampling is independent and the response variable is quantitative.

Explanation:

Given a random sample of [tex]517[/tex] couples

Learn more about Random sample, refer:

Answer:

I need help with this too

Step-by-step explanation:

Answer:

7920

Step-by-step explanation:

12C3 × 9C2

= 220×36

= 7920

The number of different ways the conference attendees be selected is 7920 ways

What are Combinations?

The number of ways of selecting r objects from n unlike objects is:

ⁿCₓ = n! / ( ( n - x )! x! )

Given data ,

The number of fresher men in sorority = 12 fresher men

The number of sophomores in sorority = 9 sophomores

In the conference ,

The number of fresher men from sorority =3 fresher men

The number of sophomores from sorority = 2 sophomores

To calculate the number of different ways the conference attendees be selected is by using combination

So , the combination will become

Selecting 3 fresher men from 12 and selecting 2 sophomores from 9

And , the equation for combination is

ⁿCₓ = n! / ( ( n - x )! x! )

The combination is ¹²C₃ x ⁹P₂

¹²C₃ x ⁹P₂ = 12! / ( 9! 3! )  x  9! / ( 7! 2! )

                = ( 12 x 11 x 10 ) / ( 3 x 2 )  x  ( 9 x 8 ) / 2

                = 1320 / 6  x  72 / 2

                = 220 x 36

                = 7920 ways

Hence , the number of different ways the conference attendees be selected is 7920 ways

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The solution is in the attachment

Answer:

Step-by-step explanation:

its just writing teh answwer out and then solving

Answer:

The surface area of a prism is the sum of the areas of the 6 faces. That will be

the 2 squares and the other 4 rectangles.

S=2*(b*h)+4(B*H)

b and h are base and height of the squares and B and H of the Rectangles.

b=2

h=2

B=5

H=2

so

S=2*(2*2)+4(2*5)=8+40=48

Answer:

[tex]\sqrt[4]{7^5}[/tex]

Step-by-step explanation:

I apologize, I do not know how to explain this.

Answer:    

7⁵/₄

Step-by-step explanation:

⁴√7⁵

The fourth root is equivalent to the power 1/4.

= 7^(1/4 * 5)

= 7^(5/4).

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]

Answer:

The answer to your question is 18 in²

Step-by-step explanation:

Data

Big rectangle                  Small rectangle

Area = 98 in²                   Area = ?

Height = 7 in                    Height = 3 in

Process

1.- Calculate the base of the big rectangle

         Area = base x height

solve for base

         base = Area / height

substitution

          base = 98 / 7

          base = 14 ni

2.- Use proportions to find the base of the small rectangle

           x / 3 = 14 / 7

Simplify

          x = (14)(3) / 7

result

          x = 6 in                    

3.- Calculate the area of the small rectangle

          Area = 6  x 3

                   = 18 in²

Answer:

The answer to the question is

The total cost C of the material as a function of the radius r of the cylinder is

0.6912·r² + 800/r Dollars.

Step-by-step explanation:

To solve the question, we note that

The area of the top and bottom combined  = 2·π·r²

The area of the sides = 2·π·r·h

and the volume = πr²h = 500 cm²

Therefore height = 500/(πr²)

Substituting the value of h into the area of the side we have

Area of the side = 2πr·500/(πr²) = 1000/r

Therefore total area of can = Area of top + Area of bottom + Area of side

Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side

Which is equal to

0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r

The cost of the can is $(0.6912·r² + 800/r)

To express the cost of the cylinder's material as a function of its radius, we first find the expression for the cylinder's height using the volume formula. The total cost C is computed by calculating the expenses for the top, bottom, and sides of the cylinder using their respective costs and surface areas. These give the final expression for the cost C(r)= 22πr^2 + 8000/r.

Given that the volume of the right circular cylinder is 500 cubic centimeters, we can first use the formula for the volume of a cylinder, which is V=πr2h, where r is the radius of the base and h is the height of the cylinder. This can be rearranged to solve for h, giving us h=V/(πr2).

Next, the total cost C is given by the cost of the materials for the top, bottom, and sides of the cylinder: C= 2(11πr2)+ (8 * 2π*r*h). Plugging the expression h= 500/(πr2) into the cost function gives us: C = 22πr2 + (16πr * 500/r2), which simplifies to: C = 22πr2 + 8000/r. So, the total cost of the material as a function of the radius r of the cylinder is C(r)= 22πr2 + 8000/r.

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Answer: There are 2 decorations that Eli makes.

Step-by-step explanation:

Since we have given that

Length of a meter of ribbon used = [tex]\dfrac{1}{10}=\dfrac{1}{10}\times 100=10[/tex]

Length of a meter cut into equal pieces = [tex]\dfrac{1}{5}=\dfrac{1}{5}\times 100=20[/tex]

So, Number of decorations that Eli make is given by

[tex]\dfrac{\text{Length of total ribbon}}{\text{Length of ribbon used}}\\\\=\dfrac{20}{10}\\\\=2[/tex]

Hence, there are 2 decorations that Eli makes.

Final answer:

Eli made 2 decorations from 1/5 meter of ribbon by using 1/10 meter of ribbon for each decoration.

Explanation:

Eli made fancy blue costume decorations for each dancer in his year-end dance performance.

Eli used 1/10 of a meter of ribbon for each decoration and initially cut a 1/5 meter ribbon into equal pieces.

To calculate the number of decorations Eli made, we need to divide the length of ribbon he cut (1/5 meter) by the length of ribbon used for each decoration (1/10 meter).

To solve this, we simply perform the division:

= 1/5 meter / 1/10 meter

= 2.
Therefore, Eli made 2 decorations from 1/5 meter of ribbon.

Solution set for given inequality  [tex]-18 < 5x - 3[/tex]  is  [tex]-3 < x[/tex].

" Solution set is defined as the such set of values which satisfies the given equation or any inequality."

According to the question,

Given inequality,

 [tex]-18 < 5x - 3[/tex]

Add 3 both the side of inequality we get,

[tex]-18 +3 < 5x - 3 +3[/tex]

[tex]= -15 < 5x[/tex]

Divide both the side by 5 to get the solution set ,

  [tex]-3 < x[/tex]

Hence, solution set for given inequality  [tex]-18 < 5x - 3[/tex]  is  [tex]-3 < x[/tex].

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Final answer:

The solution set for the inequality -18 < 5x - 3 is -3 < x, after adding 3 to both sides and then dividing by 5.

Explanation:

The student has asked to find the solution set for the inequality -18 < 5x - 3. To solve this, we first isolate the variable x by adding 3 to both sides of the inequality:

-18 + 3 < 5x - 3 + 3

-15 < 5x

Then, we divide both sides by 5 to solve for x:

-15 / 5 < 5x / 5

-3 < x

This simplifies to the inequality x > -3, which means that the correct answer is: -3 < x.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Factor                6n³  +  8n²  +  3 n +  4

- To factor this expression, factor the common terms of the first two factors

                        6n³ + 8n² = 2n²(3n + 4)

- Factor 1 in the second two terms    1(3n + 4)

- Factor all the expression by like terms      2n²(3n + 4) + 1(3n + 4)

                                                                     (3n + 4)(2n² + 1)

Answer:

Name the congruent triangles:

triangle RWS, triangle SWT, and triangle TSR

Answer:

10:10 AM

Step-by-step explanation:

The first thing is to use an identical time variable for both cases, we will do it as follows:

Let t = number of minutes of pumping time of the first fire engine

Therefore, for the second fire truck it would be:

(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.

To find the value of t, we equalize the equations of the first engine and the second engine:

We know that the first one would be: 800 * t

And the second: 1000 * (t-10)

Thus

1000 * (t-10) = 800 * t

1000 * t - 10000 = 800t

1000 * t - 800 * t = 10000

200 * t = 10000

t = 10000/200

t = 50 minutes

In other words, 50 minutes after the first engine starts pumping, it equaled the second

To know the time they were matched it would be like this:

9:20 AM +: 50 = 10:10 AM

Therefore, at 10:10 AM both engines were matched.

To check the above we have to:

50 * 800 = 40000

40 * 1000 = 40000

Therefore, in that time, they were equalized.

Answer:

At 10:10 am

Step-by-step explanation:

Hi to answer this question we have to write a system of equations:

Where m: pumping time of the engine

Because it starts 10 minute later  

So, putting together both equations:

800m = 1000(m-10)

800m = 1000m - 10000

10000 = 1000m-800m

10000= 200m

10000/200=m

50 =m (50 minutes after the first engine starts)

So, 9:20 am + 50 minutes : 10:10 am .

Answer:

The smart-phone hit the ground when t = 7 s

Step-by-step explanation:

The height "h" is defined as:

h=16t^2 + 48t + 448

And, when the smart-phone hits the ground, h = 0 ft . Then,

16t^2 + 48t + 448 = 0

And this is a quadratic equation, and we can solve it using the formula for ax^2 + bx + c = 0, which is

x=[tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]

So,

t = [tex]\frac{-48±\sqrt{48^{2} -4(-16)(448)} }{2(16)}[/tex]

t = [tex]\frac{-48±\sqrt{2304+28672} }{-32}[/tex]

And, we have two responses,

t_1 = [tex]\frac{-48+\sqrt{30976} }{-32}[/tex]    and    t_2 = [tex]\frac{-48-\sqrt{30976} }{-32}[/tex]

t_1 = - 4 s              and    t_2 = 7 s

As we know, the time is a quantity that cannot have a negative value, so, we take the result 2.

Final answer:

The smart-phone will hit the ground after approximately 3 seconds.

Explanation:

To find when the smart-phone will hit the ground, we need to determine the value of t that makes h equal to zero in the quadratic equation h = -16t^2 + 48t + 448. This equation represents the height h of the smart-phone after t seconds. To solve the equation, we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = -16, b = 48, and c = 448, we can solve for t. The positive value of t will give us the time it takes for the smart-phone to hit the ground.

Step-by-step solution:

Substitute the values a = -16, b = 48, and c = 448 into the quadratic formula: t = (-48 ± sqrt(48^2 - 4*(-16)*448)) / (2*(-16))

Simplify the expression inside the square root: t = (-48 ± sqrt(2304 + 28672)) / (-32)

Simplify further: t = (-48 ± sqrt(30976)) / (-32)

Calculate the square root of 30976: t = (-48 ± 176) / (-32)

Determine the values of t: t = (-48 + 176) / (-32) = 3 or t = (-48 - 176) / (-32) = -5

Choose the positive value t = 3 since we are interested in the time it takes for the smart-phone to hit the ground

Therefore, the smart-phone will hit the ground after approximately 3 seconds.

Answer:

25/6

Step-by-step explanation:

Because the line in the middle is an angle bisector, 5*10 = 12*x.

This means that 50 =12x, so 25/6 = x

Answer: A $4000

Step-by-step explanation:

Let x represent the amount which he invested at 3% interest.

Let y represent the amount which he invested at 3.25% interest.

Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that

x + y = 7000

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 3% interest,

P = $x

T = 1 year

R = 3℅

I = (x × 3 × 1)/100 = 0.03x

Considering the account paying 3.25% interest,

P = $y

T = 1 year

R = 3.25℅

I = (y × 3.25 × 1)/100 = 0.0325y

He made a total of $220.00 in interest., it means that

0.03x + 0.0325y = 220 - - - - - - - -- -1

Substituting x = 7000 - y into equation 1, it becomes

0.03(7000- y) + 0.0325y = 220

210 - 0.03y + 0.0325y = 220

- 0.03y + 0.0325y = 220 - 210

0.0025y = 10

y = 10/0.0025

y = 4000

Answer:

8.899s

Solve: -5t^+40t+40

4-2√2 is the time taken by the ball to hit the ground.

Distance is the total movement of an object without any regard to direction

Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.

The given function is

h(t)=40t-5t²

Let h(t)=40

We get,

40t-5t²=40

5t²-40t+40=0

t²-8t+8=0

(t-4)²=8

t-4=±√8

t=±√8+4

t=√8+4; t=4-√8

By considering the reality we know t>0

t=4-2√2

Hence  t=4-2√2 is the time taken by the ball to hit the ground.

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Answer:

(32.2,34.7)  

Step-by-step explanation:

Solution :

Given that,

\bar x = 33.4 ​hg

s = 6.4 hg

n = 177​

Degrees of freedom = df = n - 1 = 177 - 1 = 176

At 99% confidence level the t is ,

α = 1 - 99% = 1 - 0.99 = 0.01

α / 2 = 0.01 / 2 = 0.005

tα /2,df = t0.005,176 = 2.604

Margin of error = E = tα/2,df * (s /√n)

= 2.604* ( 6.4/ √177)

= 1.25

The 95% confidence interval estimate of the population mean is,

\bar x - E < \mu < \bar x + E   =   33.4 - 1.25 < \mu < 33.4 + 1.25

32.15 < \mu < 34.65

32.2 < \mu < 34.7  

(32.2,34.7)  

Question:

Here are summary statistics for randomly selected weights of newborn​ girls: n = 177​, x = 28.9 ​hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 98​% confidence level. Are these results very different from the confidence interval 28.1 hg < μ < 30.7 hg with only 20 sample​ values, x' =29.4 ​hg, and s = 2.3 ​hg? What is the confidence interval for the population mean μ​?

Answer:

The confidence interval for the population mean μ is 27.73  ≤ μ ≤ 30.0714

Step-by-step explanation:

The equation to identify the confidence interval for the mean is given by

[tex]x'-z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} } \leq \mu\leq x'+z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} }[/tex]

Where

x' = Sample mean = 28.9

s = Standard deviation = 6.7

n = Sample size = 177

[tex]z_{\frac{\alpha }{2}}[/tex] = Critical value =  2.326

Therefore we have

[tex]28.9-2.326\frac{6.7}{\sqrt{177} } \leq \mu\leq 28.9+2.326 \frac{6.7}{\sqrt{177} }[/tex]

27.73  ≤ μ ≤ 30.0714

  T test we have

t = [tex]\frac{x'-\mu}{\frac{s}{\sqrt{n} } }[/tex]  

=[tex]\frac{29.4-28.9}{\frac{2.3}{\sqrt{16} } }[/tex] = 0.8696      which is < 1      

df = 15 as sample size = 15

Upper tail statistics lies between 0.3 and 0.1

Answer with Step-by-step explanation:

We are given that

LHS

[tex]\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)[/tex]

Using distribution property

[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]

[tex]\frac{1}{5}(5x)-\frac{1}{5}(20)-\frac{1}{2}(4x)+\frac{1}{2}(8)[/tex]

After multiplication we get

[tex]x-4-2x+4[/tex]

Combine like terms

[tex](x-2x)+(4-4)[/tex]

Then, we get

[tex]-x+0=-x[/tex]

Hence,verified.

Answer:D

Step-by-step explanation: I took the unit test

Answer:

9

Step-by-step explanation:

We want to evaluate

[tex]A^2[/tex]

for A=-3.

This means, we need to substitute A=-2, into the given equation and simplify.

We substitute to get:

[tex] A^2 = {( - 3)}^{2} [/tex]

In this case the base is -3, so it multiplies itself twice.

[tex]A^2 = {( - 3)} \times - 3[/tex]

This gives us:

[tex]A^2 = 9[/tex]

The standard deviation is his IQ score above the mean is found by the Z score whose value is 4.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

It is given that,

Sample average, x = 160

mean, [tex]\mu[/tex] = 100

Standard deviation, [tex]\sigma =[/tex] 15

The Z-test value is found as,

[tex]\rm Z = \frac{x- \mu}{\sigma} \\\\ Z = \frac{160-100}{15} \\\\ Z = 4[/tex]

Thus, the standard deviation is his IQ score above the mean is found by the Z score whose value is 4.

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A student with an IQ score of 160 is 4 standard deviations above the mean IQ of 100 according to the given normal distribution, where one standard deviation equals 15 points.

To calculate how many standard deviations a score is above or below the mean, you can use the formula:

Z = (X - x) / SD

Where:

Applying this to the student's IQ score:

Z = (160 - 100) / 15

Z = 60 / 15

Z = 4

Therefore, a student with an IQ score of 160 is 4 standard deviations above the mean IQ, which is considered exceptionally high.

Answer: The test statistic is t= -0.90.

Step-by-step explanation:

Since we have given that

n₁ = 50

n₂ = 25

[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]

So, s would be

[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]

So, the value of test statistic would be

[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]

Hence, the test statistic is t= -0.90.

5  √ 3  c m

A t = √ 34  *  s 2  =  25  √ 3

this makes the sides 10cm

At= 1/2 b * h

25 √ 3  =  12  ⋅ 10  ⋅  h  = 5 √ 3 c m

Answer:

Height = 8.66 cm

Step-by-step explanation:

The formula for the area of an equilateral triangle is expressed as

A = S²√3/4,

where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore

25 √3 = S²√3/4

Dividing both sides of the equation by √3, it becomes

25 √3/√3 = S²√3/4√3

25 = S²/4

Cross multiplying, it becomes

S² = 25 × 4 = 100

Taking square root of both sides of the equation, it becomes

√S² = √ 100

S = 10 cm

In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

10² = h² + 5²

100 = h² + 25

h² = 100 - 25 = 75

h = √75

h = 8.66 cm

Answer:

65

62

Step-by-step explanation:

In inscribed quadrilaterals, opposite angles are supplementary.

First problem:

x + 148 = 180

x = 32

2x + 1 = 65

Second problem:

x + 20 + 3x = 180

x = 40

180 − (2x + 38) = 62

Answer:

b. Steve's Scratch and Dent.

Step-by-step explanation:

Tom should purchase his washing machine from Steve's Scratch and Dent.

Answer:

The change in the value of Dave's shares = $ 105

Step-by-step explanation:

Total number of shares = 15

Let initial value of a share = x

On Monday, the value of each share rose = $ 2

Now the value of each share = x + 2

Total value of 15 shares on Monday = 15 (x + 2) -------- (1)

On Tuesday the value of each share fell = $ 5

Now the value of each share = x - 5

Total value of 15 shares on Tuesday = 15 (x - 5) --------- (2)

The change in the value of Dave's shares = 15 (x + 2) - 15 (x - 5)

⇒ 15 x + 30 - 15 x + 75 = 105

⇒ Thus the change in the value of Dave's shares = $ 105

Answer:

Step-by-step explanation:

given that Joan is building a sandbox in the shape of a regular pentagon.

The perimeter of the pentagon is

[tex]35y^4 - 65x^3[/tex]inches.

Since regular pentagon we know that all sides are equal and there are totally five sides.

Perimeter of regular pentagon = 5*side

= 5a where a = length of side

Equate 5a to given perimeter to get

[tex]5a=35y^4 - 65x^3\\[/tex]

divide by 5

[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]

Answer:

D. 7y^4 - 13x^3 inches

Answer:

r=17.0

Step-by-step explanation:

In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:

[tex](x -h)^2 + (y - k)^2 =r^2[/tex]

Center (h,k)=(-6,1)

(x,y)=(7,12)

[tex]r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03[/tex]

radius, r=17.0 (to the nearest tenth)

The radius of the circle with center (-6,1) and passing through the point (7,12) can be found using the distance formula. The radius, or distance between these two points, calculates to approximately 17.0 units when rounded to the nearest tenth.

In Mathematics, you can determine the radius of a circle if you have the coordinates of the center and a point on the circle. Here, we have the center of the circle at (-6,1) and a point (7,12) lying on the circle. We will use the distance formula to find the radius, r, which is essentially the distance between these two points.

Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

By substituting the given points into the distance formula, we get

Radius (r) = sqrt((7 - (-6))^2 + (12 - 1)^2)

Sample calculation: r = sqrt((7 - (-6))^2 + (12 - 1)^2) = sqrt(169 + 121) = sqrt(290). Therefore, the radius of the circle, rounded to the nearest tenth, is approximately 17.0 units.

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