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Given:

Radius of circular swimming pool = 15ft

Radius of the path around the pool = 3ft

radius of outer edge of the pool = 15 + 3 = 18ft

To find the circumference of the outer edge of the path around the pool, use the formula below:

where,

r = 18 ft

pi = 3.14

Thus, we have:

Therefore, the circumference of the outer edge of the path around the pool is 113.04 ft

ANSWER:

113.04 ft

The value of k is -1 of tangent over the parabola.

Equation of a line: y = (2 + x - k) ÷ 2, in line form of y = mx + c.

Equation of the parabola: x² = (y - 6x - 3) ÷ 2

Given,

y = (x ÷ 2) + (1) - (k ÷ 2)

where, m = 1 ÷ 2 and c = (1 - k) ÷ 2

For parabola equation in parabola form,

y = 2x² + 6x - 3

y = 2(x² + 3x - n) - 3

n = (b ÷ 2)²

n = (6 ÷ 2)²

n = 9

y = 2(x² + 3x - 9 + 9) - 3

y = 2(x² + 3x + 9) - 9 - 3

y = 2(x² + 3x + 9) - 12

y = 2(x + 3)² - 12, Hence the parabola equation is in vertex form.

Now, comparing the above vertex form with the parabola equation,

x² = 4ay

(x + 3)² = (y ÷ 2) + 6

where a = 1 ÷ 2

Now using the condition of tangency c = a ÷ m

c = (1 - k) ÷ 2

m = 1 ÷ 2

a = 1 ÷ 2

(1 - k) ÷ 2 = (1 ÷ 2) ÷ (1 ÷ 2)

1 - k = 2

k = -1

Therefore, the value of k is -1.

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Answer:

3

Step-by-step explanation:

Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once

The original price of the sweater is $48.

Given that, Kate used a 30% off coupon to purchase a sweater.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The cost of sweater is $33.60

Let the original price of the sweater be x

Now, x-30% of x=33.60

⇒ x-30x/100 = 33.60

⇒ x -3x/10 =33.60

⇒ 7x/10 =33.60

⇒ 7x=336.0

⇒ x=48

Therefore, the original price of the sweater is $48.

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Answer:

five blocks away

Step-by-step explanation:

because 4 +1 =5

please if it is wrong let me know so I can correct

The notebook's length in centimeters is 27.94 cm.

Since we are provided that

The  desk's width is 25 inches.

Convert into cm.

There is a stated measurement of 25 inches = 63.5 cm.

As previously stated, a measurement in inches differs directly from a measurement in centimeters.

As a result, we have said that

If the notebook's length is 11 inches

Let 'x' be the length of the notebook in cm.

As a result of the question,

[tex]\frac{25}{63.5} = \frac{11}{x}[/tex]

[tex]x=\frac{698.5}{25}[/tex]

x = 27.94 cm

Hence the length of note book is 27.84 cm.

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The answer to the given expression 2⁴· [(2²·2⁴)⁻³/2¹⁴] would be 2⁻²⁸ which is determined by the laws of the exponents.

The product rule is an exponent rule that states that when you multiply similar bases, the add exponents.

For example, (a²)·(a³) = a²⁺³ = a⁵

In the power rule, elevating one exponent to a second multiplies the exponents.

For example, (a²)³ = a²ˣ³ = a⁶

The given expression would be as

⇒ 2⁴· [(2²·2⁴)⁻³/2¹⁴]

As per the laws of the exponents, the solution would be as :

⇒ 2⁴· [(2²⁺⁴)⁻³/2¹⁴]

⇒ 2⁴· [(2⁶)⁻³/2¹⁴]

⇒ 2⁴· (2⁻¹⁸/2¹⁴)

⇒ 2⁴· (2⁻¹⁸⁻¹⁴)

⇒ 2⁴· (2⁻³²)

⇒ 2⁴⁻³²

⇒ 2⁻²⁸

Therefore, the answer would be 2⁻²⁸.

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The mistake is that, what we have to prove is taken as a known fact.

A theorem is a statement that can be proved or has already been proved true by a logical argument.

"there is no smallest negative integer" is taken as a fact

but it is the part of the theorem that we have to prove,

Therefore, we can conclude that the mistake in the given proof is what we have to prove is taken as a known fact.

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The time that both gongs will strike together again after striking simultaneously at 12 noon is 2 : 34 pm.

The time the gongs will strike together again can be determined by calculating the least common multiple of 22 and 77. The multiple of a number is the product of a number and another number. For example, a multiple of 2 is 10. The least common multiple is the smallest multiple that is common to two or more numbers.

The least common multiple would be determined using the prime factorisation method.

Prime factors of 22 = 2 x 11

Prime factors of 77 = 7 x 11

The least common multiple = 2 x 7 x 11 = 154

The next time both gongs would strike at the same time is 154 minutes or 2 hours 34 minutes

12 noon + 2 hours + 34 minutes = 2 : 34 pm

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Answer: You can only bring 5 people maximum.

Step-by-step explanation:

1) Set up the equation

(>= greater than or equal to)

134.50 >= 24x +14.5

We set up the equation here with 24x as x is the amount of people. 14.5 is the starting value as it never changes. 134.50 is the amount that they can't overspend.

2) Solve the equation

134.50 >= 24x +14.5

120>= 24x

5>= x

3) Solve

You can only bring 5 people maximum.

Answer: 0.01 more

Step-by-step explanation:

60% sure!

Answer:

$43071

Step-by-step explanation:

Commission = 5.6%

So $2,412 represents 5.6% of total value of sold vacation packages

Image the numbers as ratios:

$2,412 : 5.6%

X : 100%

To get from 5.6% to 100% you can divide by 5.6 and then multiply by 100

So to find X you do:

(2,412 / 5.6)*100 = 43071.428…

Now round the answer to nearest dollar:

43071.428… = $43071 (to nearest dollar)

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on then the 7th term of the series 6, 12, 24, ........... is 384

Let the first term (a) be 6.

The given series is in geometric progression,

we know that, 7th term = a × [tex]$$r^{7-1}[/tex] = a[tex]$ r^6[/tex]= [tex]6 \times(2)^{6}[/tex] = 384

The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on.

Here, a is the first term and r is the common ratio.

The nth term of a Geometric Progression Formulas is [tex]$T_n=a r^{n-1}$[/tex]

Common ratio [tex]$=\mathrm{r}=T_n / T_{n-1}$[/tex]

Therefore, the correct answer is 384.

The complete question is:

Find the 7th term of the series 6,12,24,....?

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Answer:

Step-by-step explanation:

u will have 1 niche of water in 2 hours

You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

C = 2πr

If we substitute 125ft for r and use 3.14 to approximate π

we get a circumference of:

C = 2 * 3.14 * 125

C = 6.28 *125

C = 785ft

We can now convert the circumference in feet to inches as follow;

As we know that 1ft = 12inches

∴ 785ft = 12(785) inches = 9,420 inches.

To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:

=[tex] 9,420in\ X \ \frac{1\ flower}{6 in} [/tex]

=[tex] \frac{9,420}{6 } \ flower [/tex]

=1,570 flowers

Hence You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.

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Answer:

Let b represent the number of hours babysitting, and let l be the number of hours landscaping. We have this system of equations:

[tex]7b + 8l = 134[/tex]

[tex]b = l + 2[/tex]

Answer: Following the pattern, the prediction for the next numbers is as follows:

Confirmation by calculator use:

Therefore the predicted numbers are the correct one.

the product of negative 1/3 ⁵⁰

The expression is :

Since the product of negative to negative is positive

and negative x negative x negative = negative

Thus, if we multiply the negative upto odd number times the resultant will be negative

if we multiply the negative upto even number times the resultant will be positive

In the given expression we multiply (-1/3) upto 50 times

50 is the even number so the the resultant value will be positive

Answer : Positive

becasue if we multiply the negative upto odd number times the resultant will be negative & if we multiply the negative upto even number times the resultant will be positive

Answer:

Step-by-step explanationFrom your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.:

Answer: 4x+6/x^2

Step-by-step explanation:

If you use excel solver for this analysis, the number of different variable cells should you use are 12

Option- C

The right answer is 12.

Given that,

There are four buses that transport children to the district's three main schools. You are aware of the price of transporting each student to each school.

Since there are four buses and three schools according to the supplied description, each bus has three school alternatives, thus 4*3=12, bearing in mind that there must be the least expensive route to transport all of the students to their schools.

There must therefore be 12 separate variable cells employed.

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The dimensions of this cuboid are 2 cm, 11 cm, and 17 cm respectively.

Mathematically, the volume of a cuboid can be calculated by using this following formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula, we have;

Volume = 2 × (x + 3) × (x + 9)

374 = 2 × (x² + 9x + 3x + 27)

374 = 2 × (x² + 12x + 27)

Dividing both sides by 2, we have:

187 = x² + 12x + 27

Rearranging the equation, we have:

x² + 12x + 27 - 187 = 0

x² + 12x - 160 = 0

Next, we would solve the quadratic equation by using the factorization method as follows:

x² + 12x - 160 = 0

x² + 20x - 8x - 160 = 0

x(x + 20) - 8(x + 20) = 0

(x - 8)(x + 20) = 0

x = 8 or x = -20

Since the dimensions cannot be negative, the value of x is equal to 8.

Check:

x² + 12x - 160 = 0

8² + 12(8) - 160 = 0

64 + 96 - 160 = 0

160 - 160 = 0 (True).

For the dimensions, we have:

Width = x + 3 = 8 + 3 = 11 cm.

Height = x + 9 = 8 + 9 = 17 cm.

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When the radius of a cylinder is 6 ft. and it is increasing at the rate of 2 feet per minute, its volume will change at rate of 509.14 ft³/minute.

Given a cylinder with:

r = radius

h = height = 3/2 . r

The volume of the cylinder is:

V = πr².h

Substitute h = 3/2 . r,

V = πr².(3/2 r)

V = 3/2 . πr³

Take the derivative with respect to t:

dV/dt = 9/2 . πr²  . dr/dt

Substitute dr/dt = 2 ft./minute and r = 6 ft.,

dV/dt = 9/2 . π.6²  

dV/dt = 9/2 . π.6²  = 509.14 ft³/minute.

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Answer:

A

Step-by-step explanation:

When distributing, you multiply the outside number to each number in the inside as well as looking at the operation inside the parenthesis. Hope this helps!

The total number of pages in the book is 180.

Total number of pages:

It refers the number of pages in the prescribed book.

And if we want to find the total number of pages, then we have to add the read pages and the remaining pages.

Given,

Jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday.

Here we need to find the total number of pages in the book.

Let us consider x be the number of pages in the book.

The portion of book read by Jimmy on Monday is 2/15

The portion of book read by Jimmy on Tuesday is 1/3

The portion of book read by Jimmy on Wednesday is 2/9

The portion of book read by Jimmy on Thursday is 3/4

And the remaining pages to read on Friday is 14

So, the total of all is:

=> x (2/15 + 1/3 + 2/9)

=> x (6 + 15 + 10)/45

=> 31x/45

So, for Thursdays, he reads 3/4 of the remainder of the book.

He has (1 - 31/45)x left that is 14x/45.

So, he reads 3/4 of this; which is

=> 3/4(14x/45) = 42/180x.

Therefore, until Thursday he has read

=> 31/45x + 42/180x.

We know that here 180 would be a common denominator;

Now we have to convert these fractions,

Then we have,

124/180x + 42/180x = 166/180x

Up to this point, he has 14 pages left;

Therefore, this means he has read 14 pages less than x, the total number of pages.

Then the given equation is written as,

166/180x = x-14

0 = 14/180x - 14

Adding 14 to each side gives us, then we get,

14 = 14/180x

14(180)/14 = x

180 = x

Therefore, there are 180 pages in the book.

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For a random sample of 130 mortgages with 20 delinquents on their current payment, the mean of the sampling distribution of the proportion of delinquent payments is not possible to say because population proportion is not known.

A random sample refers to a randomly selected subset of the population. In random sampling, each member of the population has an equal chance of selection, reducing the risk of selection bias. Random sampling ensures that the conclusion drawn from the sample should approximate the results obtained if entire population had been measured. The mean of the sampling distribution is the mean of the population from which results were sampled. As the population proportion (fraction of  the population with certain characteristic) is unknown, the mean cannot be determined.

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Answer: y = -3x - 2

Step-by-step explanation:

slope intercept form: y=mx+b