A circular swimming pool has a radius of 15 ft. There is a path all around that pool that is three feet wide.

What is the circumference of the outer edge of the path around the pool? Use 3.14 for pi
56.52 ft
94.20 ft
113.04 ft
114.04 ft

The sum of the first four terms of the arithmetic series 4+8+12+... is calculated using the sum formula for arithmetic series, resulting in a sum of 40.

The question seeks the expression for the sum of the first four terms of the arithmetic series 4+8+12+... To solve this, we utilize the formula for the sum of the first n terms of an arithmetic series, which is Sn = n/2 [2a + (n-1)d], where Sn is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

For the series 4+8+12+..., the first term a = 4, the common difference d = 4, and the number of terms n = 4. Plugging these values into the formula gives us:

S4 = 4/2 [2(4) + (4-1)4] = 2 [8 + 12] = 2 × 20 = 40.

Therefore, the sum of the first four terms of the arithmetic series 4+8+12+... is 40.

This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly.

An arithmetic series is a sequence of numbers in which the difference between any two consecutive terms is constant. In this case, the series given is:

[tex]\[ 4 + 8 + 12 + ... \][/tex]

The common difference between consecutive terms is (8 - 4 = 4).

The general formula for the sum of an arithmetic series is:

[tex]\[ S_n = \frac{n}{2}(a_1 + a_n) \][/tex]

Where:

[tex]- \( S_n \)[/tex] is the sum of the first ( n ) terms,

[tex]- \( a_1 \)[/tex]is the first term,

[tex]- \( a_n \) is the \( n \)[/tex]-th term.

To find the sum of the first four terms, we can use this formula.

Now, let's look at each option:

[tex]a. \( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

[tex]b. \( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

[tex]c. \( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

[tex]d. \( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

We need to choose the expression that correctly represents the sum of the arithmetic series.

Using the formula for the sum of an arithmetic series, we have:

[tex]\[ a_1 = 4 \][/tex]

[tex]\[ a_n = 4 + (4 \times (n-1)) \][/tex](since the common difference is 4)

Now, let's plug these values into the formula:

[tex]\[ S_4 = \frac{4}{2}(4 + (4 + 4 \times (4-1))) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(4 + 4 + 16) \][/tex]

[tex]\[ S_4 = \frac{4}{2}(24) \][/tex]

[tex]\[ S_4 = 2 \times 24 \][/tex]

[tex]\[ S_4 = 48 \][/tex]

So, the sum of the first four terms of the series is 48.

Now, let's see which expression correctly represents this sum.

a. [tex]\( \sum\limits_{(a-1)^4}^{(2n+4)} \)[/tex]

  - This expression doesn't seem to represent an arithmetic series.

b. [tex]\( \sum\limits_{(s=1)}^{4} (1+4n) \)[/tex]

  - This expression doesn't seem to represent an arithmetic series either.

c.[tex]\( \sum\limits_{(k=1)}^{4} (n+4) \)[/tex]

  - This expression sums[tex]\( n+4 \) for \( k = 1 \) to \( k = 4 \)[/tex], but it doesn't seem to correctly represent the arithmetic series.

d. [tex]\( \sum\limits_{(k-1)^4}^{4n} \)[/tex]

  - This expression sums from [tex]\( (k-1)^4 \) to \( 4n \),[/tex] which doesn't represent the arithmetic series either.

None of the given expressions seem to represent the arithmetic series [tex]\(4 + 8 + 12 + ... \)[/tex] for four terms correctly. If none of the options are correct, it's possible that there might be a typo or a mistake in the options provided.

2. Which expression defines the arithmetic series 4+8+12+.. for four terms? a.sumlimits _(a-1)^4(2n+4)

b.sumlimits _(s=1)^4(1+4n)

c.sumlimits _(k=1)^4(n+4)

d.sumlimits _(k-1)^44n

B. 900 inches squared

Work is shown in IMG

ANSWER

D.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

EXPLANATION

We want to find the expression which is a square of a binomial.

In other words, we want to identify the expression which is a perfect square trinomial.

[tex]16 {x}^{2} + 24xy + 9 {y}^{2} [/tex]

This expression can be rewritten as,

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} [/tex]

This is a perfect square trinomial that can be factored as:

[tex] {(4x)}^{2} + 2(4 \times 3)xy + {(3y)}^{2} = (4x + 3y) ^{2} [/tex]

This is the square of a binomial.

The correct answer is D

The answer is:

D) [tex]16x^{2} +24xy+9y^{2}[/tex]

We are looking for an expression that satisfies the perfect square trinomial form, which can be defined by the following notable product:

[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]

From the given options, we can see that the only option that matches with the perfect square trinomial form is:

[tex]16x^{2} +24xy+9y^{2}[/tex]

We can rewrite the expression by the following way:

[tex](4x+3y)^{2}[/tex]

If we square the binomial, we will have the perfect square binomial expression given from the options.

So, squaring, we have:

[tex](4x+3y)^{2}=(4x)^{2}+2*(4x*3y)+(3y)^{2}\\\\(4x+3y)^{2}=16x^{2} +24xy+9y^{2}[/tex]

Hence, the answer is:

D) [tex]16x^{2} +24xy+9y^{2}[/tex]

Have a nice day!

Answer: 4/13 or 0.308

Step-by-step explanation: Let event A be selecting a face card and event B be selecting a 3. A has 12 outcomes and B  has 4 outcomes. Because A & B are disjoint events the probability is:

P( A or B)= P(A) + P(B)= 12/52 + 4/52 = 16/52 simplified to 4/13

5 gallons, 24 quarts (6 gallons), 10.6 gallons

To arrange 5 gallons, 10.6 gallons, and 24 quarts from smallest to largest, first convert all measurements into the same unit (quarts). The arrangement from smallest to largest is 5 gallons, 24 quarts, and 10.6 gallons.

To arrange the given measurements of 10.6 gallons, 5 gallons, and 24 quarts from smallest to largest, we first need to convert them into the same unit for an accurate comparison. Given the conversion factor of 1 gallon equals 4 quarts, we can start the comparison process.

In quarts, the order from smallest to largest is as follows: 20 quarts (5 gallons), 24 quarts, and 42.4 quarts (10.6 gallons). Therefore, when we arrange the original units from smallest to largest, it will be 5 gallons, 24 quarts, and then 10.6 gallons.

Answer:

it is the surface of the 3d shape spread out like an blue print

Step-by-step explanation:

Answer:

A pattern which you can cut and fold to make a model of a solid shape.

Answer:

The volume ratio of Prism A to Prism B is [tex]\frac{729}{8}[/tex]

Step-by-step explanation:

Step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> scale factor

x/y----> ratio of the surface area of Prism A to Prism B

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]\frac{x}{y}=\frac{81}{4}[/tex]

substitute

[tex]z^{2}=\frac{81}{4}[/tex]

[tex]z=\frac{9}{2}[/tex]

step 3

Find the volume ratio of Prism A to Prism B.

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> scale factor

x/y----> volume ratio of Prism A to Prism B

so

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{9}{2}[/tex]

substitute

[tex](\frac{9}{2})^{3}=\frac{x}{y}[/tex]

[tex](\frac{729}{8})=\frac{x}{y}[/tex]

The volume ratio of two similar prisms with a surface area ratio of 81:4 is obtained by cubing the square root of the surface area ratio, resulting in a volume ratio of 729:8.

The question involves finding the volume ratio of two similar prisms when the surface area ratio is given.

Since the surface areas are in a ratio of 81:4, the corresponding linear dimensions will be in the square root ratio, which is 9:2. For two similar three-dimensional shapes, if the ratio of their corresponding lengths is a:b, then the ratio of their surface areas is a^2:b^2, and the ratio of their volumes is a^3:b^3.

Therefore, the volume ratio of Prism A to Prism B can be found by cubing the linear dimension ratio: (9:2)^3 which equals 729:8. Hence, the volume ratio of Prism A to Prism B is 729:8.

Answer:

Option B. 767

Step-by-step explanation:

we know that

75%=75/100=0.75

To find the school’s students who attended the last home

football game, multiply 0.75 by the total students of Central High School

so

0.75*(1,023)=767.25

Round to the nearest whole number

767.25=767 students

Answer:

[tex]R^{2}=0.7744[/tex]

Step-by-step explanation:

r represents the correlation coefficient between two sets of data. It is a measure of the degree of association between the two sets of data and gives insight into the strength and direction of the relationship.

On the other hand, [tex]R^{2}[/tex] is the coefficient of determination for a given data set. It is a measure of the predictive power of a linear model.

Given r, [tex]R^{2}[/tex] is simply the square of r;

in this case we are given, r = 0.88. Therefore, [tex]R^{2}=0.88^{2}\\\\R^{2}=0.7744[/tex]

The possible dimensions of the rectangle are

4 and 1

3 and 2

Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).



We are given that rectangle has a perimeter of 10 meters.

Since we know that the perimeter of the rectangle is twice the sum of the length and width of rectangle.

Thus, perimeter of the rectangle = 2 (L + W)

10 = 2 (L + W)

L +w = 10/2 = 5

Some basic dimensions could be ;

4 and 1

3 and 2

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Answer:

x² + 2x + (3 / (x − 1))

Step-by-step explanation:

Start by setting up the division:

.........____________

x − 1 | x³ + x² − 2x + 3

Start with the first term, x³.  Divided by x, that's x².  So:

.........____x²______

x − 1 | x³ + x² − 2x + 3

Multiply x − 1 by x², subtract the result, and drop down the next term:

.........____x²______

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

Repeat the process over again.  First term is 2x².  Divided by x is 2x.  So:

.........____x² + 2x __

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

Multiply, subtract the result, and drop down the next term:

.........____x² + 2x __

x − 1 | x³ + x² − 2x + 3

.........-(x³ − x²)

...........----------

...................2x² − 2x

.................-(2x² − 2x)

.................---------------

.....................................3

x doesn't divide into 3, so that's the remainder.

Therefore, the answer is:

x² + 2x + (3 / (x − 1))

Answer:

A= 10.5

Step-by-step explanation:

Answer:10.5 yards

Step-by-step explanation:3 x 7 / 2

You must use Pythagorean theorem:

a^2 + b^2 = c^2

You are given the two legs (40 and 9) which you will plug into a and b. That means that you have to find c, the hypotheses

40^2 + 9^2 = c^2

1600 + 81 = c^2

1681 = c^2

To get rid of the squared on the c, square root both sides:

41 = c

Hope this helped!

Answer: The missing length is 41m

Step-by-step explanation:

To find the missing length c, we simply use the Pythagoras thereon.

The Pythagoras theorem states that: in a right-angle triangle,

opposite²   +  adjacent² =  hypotenuse²

In this case

opposite = 40

adjacent = 9

hypotenuse = c (It is the missing length)

Applying the Pythagoras theorem to this;

opposite²   +  adjacent² =  hypotenuse²

          40²    +     9²       =      c²

We will now go ahead and simplify

40²    +     9²       =      c²

        1600    +    81      =  c²

        1681      =  c²

To get the value of c, we will simply take the square root of both-side

√ 1681      = √ c²

      41    =   c

Therefore the missing length is 41 m

Answer:

P(face | Black) = 3/13

Step-by-step explanation:

total number of cards in standard deck of cards = 52

Total number of face cards = 12

Then P(face cards) = 12/52

Total number of black cards = 26

Then P(black cards) = 26/52

Total number of cards that are both black and face cards = 6

Then P(black and face cards) = 6/52

Then conditional probability of getting face card given that the card is black is given by:

P(face | Black) = P( face & Black) / P(Black)

P(face | Black) = (6/52) / (26/52)

P(face | Black) = 6/26

P(face | Black) = 3/13

Answer:

The probability of a face card given that the card is black = 3/26

Step-by-step explanation:

Points to remember

There are total 52 cards. It is divided into 4 suites, 13 each.

Spades, Clubs, Hearts and Diamonds

Spades and  Clubs are black.

Hearts and Diamonds are red

In each suites there are 3 face cards.

To find the probability

There are total 52 cards. And 6 black face cards

The  probability of a face card given that the card is black =6/52

 = 3/26

Answer:

1218.75

Step-by-step explanation:

7.5 x 5 = 37.5

37.5 x 3250 = 121875

121875 ÷ 100 = 1218.75

Answer:

9

Step-by-step explanation:

Just remove the DECIMALS

Therefore you get 63/7 which is obviously 9.

Answer:

9

Step-by-step explanation:

Long division (in diagram)

Answer: Third option

[tex]-x + 2 = 3x - 4.[/tex]

Step-by-step explanation:

One of the ways of solving a system of equations is by equating the equations and solving for one of the variables.

In this case we have the system:

[tex]y = -x + 2\\\\y = 3x - 4[/tex]

Note that if [tex]y[/tex] is equal [tex]-x + 2[/tex] and also [tex]y[/tex] equals [tex]3x - 4[/tex]

Then logically [tex]-x + 2[/tex] must be equal to [tex]3x - 4[/tex].

We write equality.

[tex]-x + 2 = 3x - 4.[/tex]

Then the correct answer is the third option.

We can also solve for the variable x

[tex]-4x = -6\\\\4x = 6\\\\x = \frac{6}{4}\\\\x = \frac{3}{2}[/tex]

To calculate the area Tia needs to waterproof, find the perimeter of the triangular base and multiply it by the height of the prism.

To find the area Tia will waterproof, we need to calculate the lateral surface area of the triangular prism. The lateral surface area is given by the formula:

Lateral Surface Area = Perimeter of Base × Height

First, find the perimeter of the triangular base by adding up the lengths of all three sides. Then, multiply this perimeter by the height of the prism. This will give you the area Tia needs to waterproof.

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To determine the area Tia needs to waterproof for her triangular prism tent with base dimensions 14 ft, 8 ft, and side lengths 8 ft, the total area is calculated as the sum of the areas of the two triangular bases.

To find the area that Tia needs to waterproof, we can calculate the surface area of the triangular prism. The formula for the surface area of a triangular prism is given by:

A = 2B + Ph

where:

- B is the area of the triangular base,

- P is the perimeter of the base, and

- h is the height of the prism.

First, calculate the area of one triangular base (either base 1 or base 2). The area B of a triangle is given by:

[tex]\[ B = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

For base 1:

[tex]\[ B_1 = \frac{1}{2} \times 14 \times 8 = 56 \, \text{ft}^2 \][/tex]

Now, find the perimeter P of the base, which is the sum of the three sides:

[tex]\[ P = \text{side}_1 + \text{side}_2 + \text{side}_3 \][/tex]

[tex]\[ P_1 = 8 + 8 + 14 = 30 \, \text{ft} \][/tex]

Now, substitute these values into the formula for the surface area:

[tex]\[ A_1 = 2 \times 56 + 30 \times h \][/tex]

Similarly, calculate the area [tex]\( A_2 \)[/tex] for base 2.

Tia needs to waterproof both bases, so the total area to be waterproofed is [tex]\( A_1 + A_2 \).[/tex]

Answer:

1: It's I think 2+2

2: If I got your accent right then it's 4

3: count 2 and 2 makes 4

4: YAYYY YOU GOT IT PRACTICE MORE

Step-by-step explanation:

PLZZZZ MARK BRAINLIST!! REALLY FUNNY QUESTION AND MADE MY DAY!!!

Applying the definition of negative exponents, we have

[tex]3^{-2}\cdot 27 = \dfrac{1}{3^2}\cdot 27 = \dfrac{27}{9} = 3[/tex]

The value of x in the equation sin 40 = x/12 is found by multiplying both sides by 12 and then by the sine of 40 degrees, resulting in x being approximately 7.7136.

To find the value of x in the equation sin 40 = x/12, we need to isolate x on one side of the equation. To do this, we multiply both sides of the equation by 12 to get x on its own. So, the steps are as follows:

Multiply both sides of the equation by 12 to eliminate the denominator on the right side, which gives us 12 * sin 40 = x.

Calculate sin 40 using a calculator.

Finally, multiply the value of sin 40 by 12 to find the value of x.

Carrying out these steps:

sin 40 approximately equals 0.6428 (rounded to four decimal places).

Then we calculate 12 * 0.6428 = 7.7136 (rounded to four decimal places).

Therefore, the value of x is approximately 7.7136.

Answer:

37

Step-by-step explanation:

To start out, if you know that the digits add to 10, then the number must me around 46-37, as 28 and 82 wouldn't make sense, and 55 is a palindrome.

37-->73, 73-37=36.

Step-by-step explanation:

10y + x = 10x + y + 36

x+y = 10

so we have to find y and x

10y - y = 10x - x + 36

9y = 9x + 36

Answer:

Step-by-step explanation:

Problem One

All quadrilaterals have angles that add up to 360 degrees.

Tangents touch the circle in such a way that the radius and the tangent form a  right angle at the point of contact.

Solution

x + 115 + 90 + 90 = 360

x + 295 = 360

x + 295 - 295 = 360 - 295

x = 65

Problem Two

From the previous problem, you know that where the 6 and 8 meet is a right angle.

Therefore you can use a^2 + b^2 = c^2

a = 6

b =8

c = ?

6^2 + 8^2 = c^2

c^2 = 36 + 64

c^2 = 100

sqrt(c^2) = sqrt(100)

c = 10

x = 10

Problem 3

No guarantees on this one. I'm not sure how the diagram is set up. I take the 4 to be the length from the bottom of the line marked 10 to the intersect point of the tangent with the circle.

That means that the measurement left is 10 - 4 = 6

x and 6 are both tangents from the upper point of the line marked 10.

Therefore x = 6

10 mm = 1 cm.

Divide total mm by 10 to get total cm's.

500/10 = 50 centimeters.

500/10 = 50

The answer here is 50 cm

Answer:

20 harnesses

36 leashes

Step-by-step explanation:

h = number of harnesses

l = number of leashes

set up two equations based on the information provided:

h + l = 56; since the number of harnesses and leashes made up the total item sold, which is 56

7.5h + 3.25l = 267; the same concept as the last step

h = 56 - l; let one of the variable stand by itself

7.5(56 - l) + 3.25l = 267; substitute the variable h into the other equation

420 - 7.5l + 3.25l = 267; solve

420 - 4.25l = 267; add common variables, remember you take the sign in front of the number when doing math

-4.25l = -153; subtract 420 from both side

l = 36; divide both side by -4.25

36 leashes were sold last month; 56 - 36 = 20, which means 20 harnesses were sold.

Answer:

t = 0.93 years

Step-by-step explanation:

Simple interest: I = prt

Given:

Interest(I)= $900, Investment(p) = $21,000, Rate(r) = 4.6% = 0.046

900 = 21000 × 0.046 × t

900 = 966 × t

[tex]\frac{900}{966}[/tex] = t

t = 0.93 years

Answer:

Because some applicants volunteer and meet the GPA requirements the events are NOT MUTUALLY exclusive. Thus, the probability is 65%

The probability that an applicant meets the GPA requirements or volunteers is 65%.

To find the probability that an applicant meets the GPA requirements or volunteers, we need to determine the number of applicants who meet either requirement. From the given information, there are 950 applicants who meet the GPA requirements and 600 applicants who volunteer for community service. However, there are 250 applicants who meet both requirements, so we count them only once.

To find the total number of applicants who meet either requirement, we add the number of applicants who meet the GPA requirements and the number of applicants who volunteer and subtract the number of applicants who meet both requirements:

Total number of applicants who meet either requirement = 950 + 600 - 250 = 1300

The probability that an applicant meets the GPA requirements or volunteers is the number of applicants who meet either requirement divided by the total number of applicants:

Probability = Number of applicants who meet either requirement / Total number of applicants = 1300 / 2000 = 0.65 = 65%

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18/40 = 9/20 =

Simplified

Answer:

9/20 is the simplified 18/40

Answer:

Negatively skewed

Step-by-step explanation:

Arrange this data in ascending order:

46, 50, 57, 58, 59, 59, 65, 66, 77, 80

and draw the bar chart as shown in attached diagram.

The data distribution appears to be negatively skewed (or left skewed), because the scores fall toward the higher side of the scale and there are very few low scores. The mean is also to the left of the peak.

Answer:

Negatively skewed

Step-by-step explanation:

Arrange this data in ascending order:

46, 50, 57, 58, 59, 59, 65, 66, 77, 80

and draw the bar chart as shown in attached diagram.

The data distribution appears to be negatively skewed (or left skewed), because the scores fall toward the higher side of the scale and there are very few low scores. The mean is also to the left of the peak.

Answer:

Step-by-step explanation:

A(1,4), B(4, -2), C(-1, 2)

In the first transformation, we multiply each x coordinate by -2, and each y coordinate by 1/2.

A(1*-2, 4/2) = A(-2, 2)

B(4*-2, -2/2) = B(-8, -1)

C(-1*-2, 2/2) = C(2, 1)

In the second transformation, we take each new x coordinate and subtract 2, and each new y coordinate and add 3:

A(-2-2, 2+3) = A(-4, 5)

B(-8-2, -1+3) = B(-10, 2)

C(2-2, 1+3) = C(0, 4)