The diameter of a circle is 5 ft. Find its circumference in terms of
π

Answer:

an=a1rn−1 a n = a 1 r n - 1

Step-by-step explanation:

multiplying the previous term in the sequence by 2 gives the next term

I hope this helps...

Have a nice day<3

The sum of the given expression from n = 3 to 7 is 241.

The given expression is to be evaluated from n = 3 to 7.  The given expression is,begin{align*}\sum_{n=3}^{7} (n^2 + 2n)\end{align*}Now, we can substitute the values of n and add them up to evaluate the expression. So, the sum of the expression is, \begin{align*}\sum_{n=3}^{7} (n^2 + 2n) &= (3^2 + 2 \cdot 3) + (4^2 + 2 \cdot 4) + (5^2 + 2 \cdot 5) \\&\qquad+ (6^2 + 2 \cdot 6) + (7^2 + 2 \cdot 7)\\&= 9 + 20 + 35 + 72 + 105\\&= \boxed{241}.\end{align*}.

Mathematical statements are called expressions if they have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.

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to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 4 }{ 2 } \implies 2[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 2}(x-\stackrel{x_1}{1}) \\\\\\ y-5=2x-2\implies {\Large \begin{array}{llll} y=2x+3 \end{array}}[/tex]

In a time-series graph, the horizontal axis is marked off in units of time, such as days, months, quarters, or years. The time intervals between the marks on the horizontal axis are usually equal, which allows the graph to show changes in the variable being measured over time.

The vertical axis of the graph shows the values of the variable being measured, and the line or curve connecting the points on the graph represents the trend of the data over time. Time-series graphs are often used to visualize patterns and trends in economic, financial, and other types of data that vary over time.

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Answer:

$21,366.54

Step-by-step explanation:

Assuming that the interest is compounded annually, we can use the formula:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the initial principal (or amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $18,000, r = 0.045, n = 1 (compounded annually), and t = 4. Plugging in these values, we get:

A = 18000(1 + 0.045/1)^(1*4) = $21,366.54

Therefore, Amelia's loan will be $21,366.54 after her 4 years in college.

The volume of the solid enclosed by the two paraboloids is approximately 1365.34π cubic units.

Here, we have to find the volume of the solid enclosed by the two paraboloids [tex]y = x^2 + z^2[/tex] and [tex]y = 32 - x^2 - z^2[/tex],

we need to set up a triple integral in cylindrical coordinates.

In cylindrical coordinates, we have:

x = r cos(θ)

z = r sin(θ)

y = y

The limits of integration for r, θ, and y will depend on the region of integration.

First, let's find the intersection points of the two paraboloids:

[tex]x^2 + z^2 = 32 - x^2 - z^2\\2x^2 + 2z^2 = 32\\x^2 + z^2 = 16[/tex]

This represents a circular region with radius r = 4 in the x-z plane.

Now, let's find the limits of integration for r, θ, and y:

For r:

Since the circular region has a radius of 4, the limits of r will be from 0 to 4.

0 ≤ r ≤ 4

For θ:

The intersection points form a complete circle in the x-z plane, so the limits of θ will be from 0 to 2π.

0 ≤ θ ≤ 2π

For y:

The lower paraboloid is given by [tex]y = x^2 + z^2[/tex], and the upper paraboloid is given by [tex]y = 32 - x^2 - z^2[/tex].

The limits of y will be from the lower paraboloid to the upper paraboloid.

[tex]x^2 + z^2 \leq y \leq 32 - x^2 - z^2[/tex]

Now, we can set up the triple integral to find the volume V:

V = ∫∫∫ (y) dy dθ dr

V = ∫∫∫ [tex](r^2 cos^2(\theta) + r^2 sin^2(\theta)) dy d\theta dr[/tex]

V = ∫∫∫ [tex](r^2) dy d\theta dr[/tex]

V = ∫∫ [tex](r^2) y|_{(x^2+z^2)}^{(32-x^2-z^2)} d\theta dr[/tex]

V = ∫∫ [tex](r^2) (32 - 2x^2 - 2z^2) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^2(x^2 + z^2)) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^2r^2) d\theta dr[/tex]

V = ∫ [tex](32r^2 - 2r^4) d\theta dr[/tex]

Now, integrate with respect to θ from 0 to 2π:

V = ∫(0 to 2π) ∫(0 to 4) [tex](32r^2 - 2r^4)[/tex] dr dθ

Now, integrate with respect to r from 0 to 4:

V = ∫(0 to 2π) [tex][(32/3)r^3 - (1/3)r^5] |_0 ^4[/tex] dθ

V = ∫(0 to 2π) [tex][(32/3)(4^3) - (1/3)(4^5)][/tex] dθ

V = ∫(0 to 2π) [(32/3)(64) - (1/3)(1024)] dθ

V = ∫(0 to 2π) [682.67] dθ

V = 682.67 * (2π) - 682.67 * (0)

V = 1365.34π cubic units

Therefore, the volume of the solid enclosed by the two paraboloids is approximately 1365.34π cubic units.

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The missing side (the adjacent side) is approximately 13.257 units long.

To find the missing side, we can use the cosine function which relates the cosine of an angle to the adjacent side and the hypotenuse of a right triangle.

cos(28°) = adjacent side / hypotenuse

We are given the measure of the angle and the length of one side, so we can plug in those values and solve for the missing side.

cos(28°) = adjacent side / 15

adjacent side = 15 cos(28°)

Using a calculator to evaluate cos(28°) to four decimal places:

cos(28°) ≈ 0.8838

Substituting into the equation:

adjacent side ≈ 15 × 0.8838

adjacent side ≈ 13.257

Therefore, the missing side (the adjacent side) is approximately 13.257 units long.

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The volume of the cone in terms of π is 168π in³

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is one- third of a volume of a cylinder. Therefore;

The volume of a cone is expressed as;

V = 1/3 πr²h

where r is the radius and h is the height

r = 6 in

h = 14 in

V = 1/3 × π × 6² × 14

V = 504π/3

V = 168π in³

Therefore the volume of the cone in terms of π is 168π in³

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The directions of the parabola are:

Other solutions are below

The equation of a parabola is represented as

y = ax² + bx + c

If a > 0, then the parabola will open up

If a < 0, then the parabola will open down

Using the above as a guide, we have the following:

This is calculated as (h, k)

Where

h = -b/2a

So, we have

1. f(x) = x² + 6x +2

2. f(x) = 2 - 5x + 2x²

3. f(x) = -0.25x² + 8x - 2

4. f(x) = 4x² + 3x -5

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The calculated volume of the solid is 335.10 cubic feet

From the question, we have the following parameters that can be used in our computation:

Radius = 4 feet

Height = 10 fet

The angle is given as

Angle = 120 degrees

Using the above as a guide, we have the following:

Volume = (360 - Angle)/360 * πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = (360 - 120)/360 * π * 4² * 10

Evaluate

Volume = 335.10

Hence. the volume of the solid is 335.10 cubic feet

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The value of the original price is, $1,029

We have to given that;

At a sale this week a desk is being sold for $247 this is a 24% discount from the original price.

Let us assume that, the original price is x

Hence, we can formulate;

24% of x = 247

Solve for x;

24/100 × x = 247

24x = 24700

x = 24700/24

x = 1,029

Thus, The value of the original price is, $1,029

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Answer:

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

First, find the common ratio:

Next, use the formula for the nth term of a geometric sequence:

Plugging in the values we have:

The Volume of a cone is,

⇒ V = 50π units³

We have to given that;

In a cone,

Diameter = 10 feet

Height = 6 feet

Hence, Radius of cone,

r = 10/2 = 5 feet

Since, Volume of cone is,

V = 1/3 (πr²h)

V = 1/3 (π × 5² × 6)

V = 50π units³

Thus, The Volume of a cone is,

⇒ V = 50π units³

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The slope of the line is 3.

Given are the coordinates of points on a line, we need to find the slope of the line,

Considering the points (2, 7) and (4, 13).

We know that the slope = y₂-y₁ / x₂-x₁

slope = 13-7 / 4-2 = 6/2

Slope = 3

Hence the slope of the line is 3.

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The solution is, the angles of the right triangle are approximately:

A = 12° 33'

B ≈ 1.03°

C ≈ 76° 27'

We are given angle A = 12° 33' and side c = 283 ft. Let's first find angle C using the sine ratio:

sin C = opposite / hypotenuse

sin C = a / c

a = c * sin C

Using a calculator:

sin C = sin(90° - A) ≈ 0.996

a ≈ 282.95 ft

Therefore, we have side a ≈ 282.95 ft. To find the remaining side b, we can use the Pythagorean theorem:

b² = c² - a²

b² = (283 ft)² - (282.95 ft)²

b ≈ 0.79 ft

(Note that we may have some rounding error in the last digit due to using approximate values for a and c, but it should be insignificant.)

Now let's find the angles:

Angle B = 90° - A ≈ 77° 27'

Using the sine ratio again:

sin B = opposite / hypotenuse

sin B = b / c

B ≈ 1.03°

(Note that we may have some rounding error here due to using an approximate value for b, but it should be insignificant compared to the precision of the given angles.)

Therefore, the angles of the right triangle are approximately:

A = 12° 33'

B ≈ 1.03°

C ≈ 76° 27'

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The area of the bumper sticker is 28.3 square inches.

To find the area of the bumper sticker, we need to use the formula for the area of a circle, which is A=πr^2, where π is a constant value of 3.14 and r is the radius of the circle. In this case, we can see that the diameter of the circle is 6 inches, so the radius would be half of that, which is 3 inches.
Substituting these values into the formula, we get:
A=3.14 x 3^2
A=3.14 x 9
A=28.26
Therefore, the area of the bumper sticker to the nearest tenth is 28.3. This means that the bumper sticker covers an area of approximately 28.3 square inches.
In conclusion, to find the area of the bumper sticker, we used the formula A=πr^2 and substituted the given values. The answer we obtained was 28.3 square inches.

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Based on the above, the area of the bumper sticker is 98.91 square inches.

To find the area of the bumper sticker, we need to use the formula for the area of a circle,

Where:

π = 3.14

r = the radius of the circle.

r = 1.5 ft ->  that is half the diameter of 3 ft.

h = 6

Area of the cylinder bumper  = 2π r h + 2π r²

Substituting these values into the formula, we get:

A =  2 x 3.14 x 1.5² x 6 + 2 x 3.14  x  1.5²

A= 2 x 3.14 x 2.25 x 6 + 2 x 3.14  x  2.25

A=98.91

Therefore, the area of the bumper sticker to the nearest tenth is 98.91

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Answer: D

Step-by-step explanation:

If u know that the total is 423, u can narrow the options down. They mention the variables with each food. Substitute and find the answer. Hope it helps!

You have $2.30 and would like to buy some rice flour buy 9.2 ounces of rice flour with $2.30.

To arrive at this answer, we need to first convert the price per pound to price per ounce. There are 16 ounces in a pound, so the price per ounce is $4/16 = $0.25 per ounce.

Next, we divide the amount of money you have ($2.30) by the price per ounce ($0.25).

$2.30/$0.25 = 9.2 ounces.

Therefore, the conclusion is that you can buy 9.2 ounces of rice flour with $2.30.
Hi! I'm happy to help you with your question.


You can buy 9.2 ounces of rice flour.


1. First, we need to find out how many dollars you have per ounce of rice flour: $4 per pound / 16 ounces per pound = $0.25 per ounce.
2. Next, we'll determine how many ounces of rice flour you can buy with $2.30: $2.30 / $0.25 per ounce = 9.2 ounces.


With $2.30, you can buy 9.2 ounces of rice flour at the given price of $4 per pound.

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Answer:

Step-by-step explanation:

If the perimiter is 2X+2Y=36

then area should be X x Y=???

I dont know what the sides are so that is all I can come up with.

Answer:

gradient = - 2 , y- intercept = 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope (gradient) and c the y- intercept )

given

2x + y = 1 ( subtract 2x from both sides )

y = - 2x + 1 ← in slope- intercept form

with gradient m = - 2 and y- intercept c = 1

∠FGK and ∠FGH are the pairs of non-overlapping angles that share a ray to make a right angle. option C

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

In the given figure, we need to find the pairs of non-overlapping angles that share a ray to make a right angle.

We can see that ∠EGF and ∠HGF make a right angle but line FG is overlapping or common in both the angles.

∠FGK and ∠FGH make a right angle and pairs of non-overlapping angles.

So, this is the correct pair for the condition.

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There are 34,650 distinct ways to order the letters of "mississippi" subject to the requirement that no two S's are adjacent and no two P's are adjacent.

To find the number of ways to order the letters of the word "mississippi" while satisfying the given conditions, we can use the principle of inclusion-exclusion.

First, we consider all the ways to order the letters without any restrictions. There are 11 letters in "mississippi", so there are 11! ways to order them.

Next, we consider the cases where two S's are adjacent and the cases where two P's are adjacent. To count these cases, we can treat each pair of adjacent S's or P's as a single letter. So we have 10 letters to order in the case of adjacent S's, and 9 letters to order in the case of adjacent P's.

For the case of adjacent S's, we have 10! ways to order the letters. However, we have overcounted the cases where both pairs of S's are adjacent, so we need to subtract those out. There are 9 letters in this case (M, I, S1, S2, I, P, P, I), so there are 9! ways to order them. Therefore, the number of cases where two S's are adjacent is 10! - 9!.

Similarly, for the case of adjacent P's, we have 9! ways to order the letters. But we have overcounted the cases where both pairs of P's are adjacent, so we need to subtract those out. There are 8 letters in this case (M, I, S1, S2, I, P1, P2, I), so there are 8! ways to order them. Therefore, the number of cases where two P's are adjacent is 9! - 8!.

Now we need to add back in the cases where both pairs of S's and both pairs of P's are adjacent, because we subtracted them out twice. There are 8 letters in this case (M, I, S1, S2, P1, P2, I, I), so there are 8! ways to order them. Therefore, the number of cases where both pairs of S's and both pairs of P's are adjacent is 8!.

Finally, we subtract all these cases from the total number of ways to order the letters:

11! - (10! - 9!) - (9! - 8!) + 8! = 34,650

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1. The x-intercepts are: x = -1/2 and x = 2

2. The vertex is at (3/4, 19).

3. To graph the function f(x) = -16x² + 24x + 16,

1. Solve for x:

-16x² + 24x + 16 = 0

Dividing both sides by -8, we get:

2x² - 3x - 2 = 0

Using the quadratic formula, we have:

x = [3 ± ✓ (3² - 4(2)(-2))]/(2(2))

x = [3 ±  ✓ (25)]/4

x = [3 ± 5]/4

The x-intercepts are: x = -1/2 and x = 2

2. The vertex of the graph of f(x) can be found by using the formula x = -b/(2a) and plugging it into the function to find the corresponding y-value.

In this case, we have:

x = -24/(2(-16)) = 3/4

f(3/4) = -16(3/4)² + 24(3/4) + 16 = 19

Therefore, the vertex is at (3/4, 19).

3 To graph the function f(x) = -16x² + 24x + 16, you can follow these steps:

Find the vertex of the parabola: The vertex is given by the formula x = -b/2a, where a = -16 and b = 24.

Find the y-intercept: The y-intercept is the value of f(x) when x = 0. Therefore, f(0) = -16(0)² + 24(0) + 16 = 16. The y-intercept is (0, 16).

Find the x-intercepts: The x-intercepts are the values of x for which f(x) = 0. To find them, solve the quadratic equation -16x² + 24x + 16 = 0.

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A clockwise rotation about the origin preserves distance, a dilation of 3/5 Preserves angle measures, a reflection in the y-axis and dilation of 3  angle measures and a translation down 2 units and right 4 units Preserves distance and angle measures.

A clockwise rotation about the origin:

Preserves distance, but not angle measures.

A dilation of 3/5:

Preserves angle measures, but not distance.

A reflection in the y-axis and dilation of 3:

Preserves angle measures, but not distance.

A translation down 2 units and right 4 units:

Preserves distance and angle measures.

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Answer:

1231.5 units^2

Step-by-step explanation:

The formula for volume of a cone is

V = 1/3πr^2, where

We see from the diagram that the height is 24 cm and the radius is 7 cm.  Now, we can plug these values in for h and r respectively in the volume formula:

V = 1/3π(7)^2(24)

V = 1/3π(49)(24)

V = 1/3π*1176

V = 392π

V = 1231.50432

V = 1231.5 cm^3

Answer:

90 square feet

Step-by-step explanation:

area of rectangle = 12 X 30 = 360 square feet

look at the green triangle in top left. it has area 0.5 X (12 - 3) X (30)

= 0.5 X 9 X 30 = 135

area of other green triangle is equal (they are congruent)

so, the area of the path is 360 - 2 (135) = 360 - 270 = 90 square feet

Answer:

A

Step-by-step explanation:

Range = Highest value - Lowest value

At Park Zoo:

R = 44 - 38

= 6

At Countryside Zoo;

R = 45 - 38

= 7

So, it cannot be D, because the ranges are not the same and it cannot be B because the range is greater at countryside zoo

The mode is the value that appears the moat frequently.

At Park zoo, the mode is 41 since it has the most dots.

At Countryside zoo, the mode is 40, since it has the most dots

So, it cannot be C because Park zoo has a greater Mode.

so, the only answer is A

The value of x in the equation x - 3(x - 3 + x + 1) = 6(6 + 15) is -24

From the question, we have the following parameters that can be used in our computation:

x-3(x-3+x+1)=6(6+15)

Express properly

So, we have

x - 3(x - 3 + x + 1) = 6(6 + 15)

Evaluate tje like terms

This gives

x - 3(2x - 2) = 126

Open the brackets

x - 6x + 6 = 126

So, we have

-5x = 120

Divide

x = -24

Hence the value of x is -24

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The event that covers the entire sample space of the experiment is given as follows:

D. The number is even or less than 12.

In probability theory, a sample space is the set of all possible outcomes of a random experiment.

The outcomes for this problem are given as follows:

2, 3, 4 and 10.

Hence the statement covering the entire sample space is given by option D, as:

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