Calculate the amount you would pay (including tax) for an item normally priced at $329 on sale for 25% off where sales tax is 7.25%.

The simplified expression after canceling out the 5a^2b term is (4ba - 12)

To cancel out the term 5a^2b in the expression 5a^2b + 4ba - 15a - 12, you need to multiply ab by 5a.

This is because (ab)(5a) = 5a^2b, which cancels out the 5a^2b term in the numerator.

To maintain the equality of the expression, you need to multiply both the numerator and denominator of the fraction by 5a.

This gives:

(ab - 3)(5a^2b + 4ba - 15a - 12) / (ab - 3)(5a)

Now, the 5a^2b term in the numerator cancels out with the 5a term in the denominator, leaving:

(4ba - 12)

Therefore, the simplified expression after canceling out the 5a^2b term is (4ba - 12)

By long division, we have

           5a + 4

ab - 3 | 5a^2b + 4ba - 15a - 12

           5a^2b - 15a

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

             4ba - 12

             4ba - 12

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

             0

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Answer:

We know that the object is in the air for 10 seconds, so we can substitute t = 10 into the formula for h(t) and solve for v0:

h(t) = -1.86t^2 + v0t + 2

h(10) = -1.86(10)^2 + v0(10) + 2

h(10) = -186 + 10v0 + 2

h(10) = 10v0 - 184

Since the object was thrown upward, we know that its height at the end of the 10 seconds is 2 meters (the initial height). So we have:

h(10) = 2

10v0 - 184 = 2

10v0 = 186

v0 = 18.6 m/s

Therefore, the initial velocity of the object was 18.6 m/s.

rate 5stars~ and thanks for more po! your welcome.

Since a circle has a 360° circumference, dividing an arc's degree measurement by 360° yields the percentage of the circle's circumference that the arc represents. The length along the arc is then obtained by multiplying the circle's circumference, which is its total length, by that fraction.

It is a significant arc if the centre angle is larger than or equal to 180°.It is a minor arc if the central angle is less than 180°; to obtain the major arc, take the minor arc's angle from 360°.

What is arc?

In mathematics, an arc is a portion of the boundary of a circle or curve. It also goes by the name "open curve."

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter. The distance between any two places along the arc's perimeter is thus defined as the arc.

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Answer:

62 in

Step-by-step explanation:

5 x 2 = 10

5 x 3 = 15

2 x 3 = 6

2 x 3 = 6

2 x 5 = 10

3 x 5 = 15

Answer:

True

Step-by-step explanation:

divide 21 feet by 4 feet to convert to inches, that is

21 feet ÷ 4 feet = 21 ÷ 4 = 5.25 inches

Answer:

s = [tex]\frac{5\pi }{3}[/tex]

Step-by-step explanation:

arc length is calculated as

s = circumference of circle × fraction of circle

 = 2πr × [tex]\frac{0}{2\pi }[/tex] ( cancel 2π on numerator/ denominator )

 = 3 × [tex]\frac{5\pi }{9}[/tex]

 = [tex]\frac{15\pi }{9}[/tex]

 = [tex]\frac{5\pi }{3}[/tex]

Answer:

(a) Star's surface power.

(b) Star's interior power.

(c) Radius = 6 × 10¹⁰ cm

Step-by-step explanation:

Since the star is a sphere, we can calculate its volume and surface area by using the following formulas:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a sphere}\\\\$V=\dfrac{4}{3} \pi r^3$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]   [tex]\boxed{\begin{minipage}{4 cm}\underline{Surface area of a sphere}\\\\$\vphantom{\dfrac12}SA=4 \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Given the star has a radius of about 7 × 10⁸ cm and its interior generates 3 × 10⁻⁷ watts of power per cubic centimeter, to calculate the power that the interior of the star would generate, multiply the volume of the star (in cubic centimeters) by 3 × 10⁻⁷:

[tex]\begin{aligned} \implies \textsf{Interior power}&=V \times 3 \times 10^{-7}\\&=\dfrac{4}{3} \pi (7 \times 10^8)^3\times 3 \times 10^{-7}\\&=4\pi(7^3 \times 10^{24}) \times 10^{-7}\\&=4\pi(343) \times 10^{24} \times 10^{-7}\\&=1372\pi \times 10^{24-7}\\&=1372\pi \times 10^{17}\\&=4310.265...\times 10^{17}\\&\approx 4.31 \times 10^3 \times 10^{17}\\&\approx 4.31 \times 10^{3+17}\\&\approx 4.31 \times 10^{20}\; \sf watts\end{aligned}[/tex]

Similarly, given each square centimeter of the star's surface shines 6,000 watts of power into space, to calculate how much power the star's surface would shine into space, multiply the surface area (in square centimeters) by 6,000:

[tex]\begin{aligned} \implies \textsf{Surface power}&=SA \times 6000\\&=4 \pi (7 \times 10^8)^2 \times 6000\\&=4 \pi(7^2 \times 10^{16}) \times 6000\\&=24000 \pi(49) \times 10^{16}\\&=1176000 \pi \times 10^{16} \\&=1.176\pi \times 10^6 \times 10^{16}\\&=1.176\pi \times 10^{6+16}\\&=1.176\pi \times 10^{22}\\&\approx 3.69 \times 10^{22}\; \sf watts\end{aligned}[/tex]

.

As the exponent on base 10 increases, the standard notation gets larger. Therefore, the power the star's surface shines into space is greater.

Given the star has a radius of about 5 × 10¹² cm and its interior generates 3 × 10⁻⁷ watts of power per cubic centimeter, to calculate the power that the interior of the star would generate, multiply the volume of the star (in cubic centimeters) by 3 × 10⁻⁷:

[tex]\begin{aligned} \implies \textsf{Interior power}&=V \times 3 \times 10^{-7}\\&=\dfrac{4}{3} \pi (5\times 10^{12})^3\times 3 \times 10^{-7}\\&=4\pi(5^3 \times 10^{36}) \times 10^{-7}\\&=4\pi(125) \times 10^{36} \times 10^{-7}\\&=500\pi \times 10^{36-7}\\&=1570.796... \times 10^{29}\\&\approx 1.57 \times 10^3 \times 10^{29}\\ &\approx 1.57 \times 10^{3+29}\\&\approx 1.57 \times 10^{32}\; \sf watts\end{aligned}[/tex]

Similarly, given each square centimeter of the star's surface shines 6,000 watts of power into space, to calculate how much power the star's surface would shine into space, multiply the surface area (in square centimeters) by 6,000:

[tex]\begin{aligned} \implies \textsf{Surface power}&=SA \times 6000\\&=4 \pi (5 \times 10^{12})^2 \times 6000\\&=4 \pi(5^2 \times 10^{24}) \times 6000\\&=4 \pi(25) \times 10^{24} \times 6000\\&=600000\pi \times 10^{24} \\&=6\pi \times 10^5\times 10^{24}\\&=18.8495...\times 10^{5} \times 10^{24}\\ &\approx 1.88 \times 10^1 \times 10^5 \times 10^{24}\\ &\approx 1.88 \times 10^{1+5+24}\\&\approx 1.88 \times 10^{30}\; \sf watts\end{aligned}[/tex]

.

As the exponent on base 10 increases, the standard notation gets larger. Therefore, the power the star's interior generates is greater.

To calculate the radius of the star that makes the power generated in its interior equal to the power leaving its surface, set the volume formula multiplied by 3 × 10⁻⁷ equal to the surface area formula multiplied by 6,000 and solve for r.

[tex]\begin{aligned}\implies \sf Power\;generated\;in\;interior&=\sf Power\;leaving\;surface\\ V \times 3 \times 10^{-7}&=SA \times 6000\\ \dfrac{4}{3} \pi r^3 \times 3 \times 10^{-7}&=4 \pi r^2 \times 6000\end{aligned}[/tex]

Divide both sides by 4πr²:

[tex]\implies \dfrac{1}{3} r\times 3 \times 10^{-7}=6000[/tex]

Multiply the numbers:

[tex]\implies r \times 10^{-7}=6000[/tex]

Divide both sides by 10⁻⁷:

[tex]\implies r =\dfrac{6000}{10^{-7}}[/tex]

[tex]\implies r =6000 \times 10^7[/tex]

Simplify:

[tex]\implies r =6 \times 10^3 \times 10^7[/tex]

[tex]\implies r =6 \times 10^{3+7}[/tex]

[tex]\implies r =6 \times 10^{10}[/tex]

Therefore, the radius of the star for which the power leaving the surface equals the power generated in the interior is 6 × 10¹⁰ cm.

Answer:

Read step by step explanation

Step-by-step explanation:

Well, it basically shows the angle is 40 degrees, and the circle angle from the angle is 96 degrees. I think so.

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Step-by-step explanation:

tan A = P/B = 36/27 = 4/3

option B is correct.

hope this helps.

The domain of  fof is all real numbers.

(f.f)(x) = f(f(x)) = f(6x+3) = 6(6x+3) + 3 = 36x + 21. The domain of fof is all real numbers.

(a) (f.g)(x) = f(g(x)) = f(x^2) = 6(x^2) + 3 = 6x^2 + 3. The domain of fog is all real numbers.

(b) (g.f)(x) = g(f(x)) = g(6x+3) = (6x+3)^2 = 36x^2 + 36x + 9. The domain of gof is all real numbers.

(d) (g.g)(x) = g(g(x)) = g(x^2) = (x^2)^2 = x^4. The domain of gog is all real numbers.

Therefore, the correct answer is OB. The domain of fog is all real numbers.

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The correct option is, Because 1/36 times 3 equals 1/12, the quotient of the division of 1/12 ÷ 3 gives 1/36.

Given problem is to find the quotient of the division of 1/12 ÷ 3.

The quotient of the given division is some x, such that,

3x = 1/12

That is when we multiply the required quotient with 3, we will get the product as 1/12.

We know that,

3 × 1/36 = 1/12

So the quotient is 1/36.

Hence the required quotient is 1/36.

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The expressions are matched as;

1. Subtract m

2. subtract 2m

3. Add 1

4. subtract 1

5. subtract 2

6. add 2

Algebraic expressions are described as mathematical expressions that are composed of coefficients, factors, constants, variables and terms.

These expressions are also composed of arithmetic operations. These operations are;

From the information given, we have that;

2m = 1 + m

collect like terms

2m - m= 1

m = 1

2. 2m -1 = 3m

2m -3m = 1

-m = 1

m = -1

3. m - 1 = 2

m = 2 + 1

m = 3

4. 3 = 1 + m

collect like terms

m = 3 - 1 = 2

5. 2 + m = 3

m = 3 - 2

subtract 2

m = 1

6. -2 + m = 1

collect like terms

m = 1+ 2 = 3

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Answer:

  148

Step-by-step explanation:

You want to know the number of minutes from 3:32 pm to 6:00 pm.

There are 60 minutes in an hour, so the 2 hours between 3:32 and 5:32 will be a total of 2·60 = 120 minutes.

The number of remaining minutes in the hour between 5 pm and 6 pm is ...

  60 -32 = 28

So, the total number of minutes between 3:32 pm and 6:00 pm is ...

  120 +28 = 148 minutes

There are 148 minutes from 3:32 pm until Emma's gymnastics lesson.

__

Additional comment

Degrees and hours both are subdivided into 60 parts called minutes. Some calculators can use this to do calculations when hours (degrees) and minutes are given. The result will generally be expressed in hours (degrees), which can be converted to minutes by multiplying by 60.

As the linear functions have the same end behavior, the relationship is given as follows:

D. The sign of m and p must be the same. The relationship between the other variables does not matter.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope determines if a linear function is increasing or decreasing, hence the only condition needed for two linear functions to have the same end behavior is that the slopes of the two functions have the same signal.

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The measure of the angle m∠1 for triangle formed by the tangent line BP is equal to 147°

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

we observe a right triangle ABP with a radius perpendicular to the line BP tangent to the circle, with the hypotenuse AK. Hence we can solve for the angle m∠1 as follows:

m∠1 + m∠APB = 180° {sum of interior angles of a triangle}

m∠1 + 33° = 180°

m∠1 = 180° - 33° {collect like terms}

m∠1 = 147°

Therefore, the measure of the angle m∠1 for triangle formed by the tangent line BP is equal to 147°

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The distance that Mr. Stein drove can be represented by the expression: [tex]140 - x[/tex]

A mathematical phrase made up of one or more variables, constants, and arithmetic operations like addition, subtraction, multiplication, and division is known as an algebraic expression. Exponentiation and other mathematical operators could also be present.

Let's assume that Mr. Smith drove "x" miles before Mr. Stein took over the driving.

Then, the total distance they traveled is 140 miles.

So, the distance that Mr. Stein drove can be represented by the expression:

140 - x

Therefore, This is because if Mr. Smith drove "x" miles, then the remaining distance that needed to be covered by Mr. Stein would be the difference between the total distance of 140 miles and the distance already driven by Mr. Smith.

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Answer:

f(n) = -20 + 4(n - 1)

Step-by-step explanation:

The explicit formula for an arithmetic sequence in function notation is [tex]f(n) = f(1) + d(n - 1)[/tex], where:

We need to find the values of f(1) (the first term) and 'd' (the common difference). The first term in the arithmetic sequence is -20 because it's the beginning number. The common difference is 4 because we add 4 to each term to get the next term (-20 + 4 = -16, -16 + 4 = -12, -12 + 4 = -8...). Now, we can plug in the values of f(1) and 'd' to get the formula of this arithmetic sequence: f(n) = -20 + 4(n - 1).

Answer:

10 students.

Step-by-step explanation:

Considering that 60% of 25 is 15, all we need to do is find 40% of 25

Multiply 25 by 0.4=10.

Hope this helps!

Answer:

10

Step-by-step explanation:

x = students who don't play basketball

[tex]x=25(\frac{100-60}{100} )=25(\frac{40}{100} )=25(0.4)=10[/tex]

Hope this helps.

By answering the presented question, we may conclude that Therefore, rectangle the width οf the οbject is 4.5 cm.

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. Since each οf its angles is equal, it is also referred to as an equiangular quadrilateral. The parallelogram also has the οption οf a straight angle. All four sides οf a square are the same length. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-shaped shape.

To find the width οf the οbject, we can use the formula for volume οf a rectangular solid which is:

Volume = Length x Width x Height

We have the volume οf the οbject as 220.5 cubic centimeters and the length and height are both given as 7 cm. Substituting these values into the formula, we get:

220.5 = 7 x Width x 7

Simplifying this equation, we get:

Width = 220.5 / (7 x 7)

Width = 4.5 cm

Therefore, the width οf the οbject is 4.5 cm.

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Hence the correct option is C. for the fourth term of the expansion of

[tex](a - b)^{10}[/tex].

Either the process of expanding or the condition of expanding. An expanded object, surface, or component. the amount by which anything extends; its degree, extent, or size. an expansion, growth, or development, especially in a company's operations.

An expression that has been raised to any finite power can be expanded using the binomial theorem. A useful expansion technique with applications in  probability theory or probability  and algebra is the binomial theorem. A binomial expression is an algebraic expression with two terms that are not the same.

According to The binomial theorem  to determine the fourth term in the expansion of[tex](a - b)^{10}[/tex], Therefore,

[tex](a - b)^{10}[/tex] = [tex]C(10,0)*a^{10}*b^0 + C(10,1)*a^9*b^1 + C(10,2)*a^8*b^2 + C(10,3)*a^7*b^3 + ...[/tex]

where C(n,r) denotes the variety of options for selecting item(s) r from a set of item(s) n.

So, the term r = 3 equal to the fourth term in the given expansion:

[tex]C(10,3)*a^7*b^3 = (10!)/(3!7!)*a^7*b^3[/tex]

[tex]C(10,3)*a^7*b^3\\ = (10 *9 * 8*7!) /(3*2 * 1*7!)*a^7*b^3\\ = 120*a^7*b^3 C(10,3)*a^7*b^3 \\=(10 *9 * 8) /(3 *2 *1)*a^7*b^3 =\\ =120*a^7*b^3[/tex]

hence [tex]120*a^7*b^3[/tex] is the fourth term in the given expansion of [tex](a - b)^{10}[/tex]

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The value of given quadrant is cos(5π/3) = -1/2 and sin(5π/3) = -√3/2.

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths. There are six trigonometric ratios, namely sine, cosine, tangent, cotangent, secant, and cosecant of a reference angle.

The reference angle 5π/3 is π/3.

To find the quadrant where 5π/3 is, we can divide the angle by π/2. Since 5π/3 is between 4π/3 and 2π, it is in the third quadrant.

We can use the unit circle or trigonometric identities to find the exact values ​​of sin(5π/3) and cos(5π/3).

In the unit circle, we start from the positive x-axis (cosine) and rotate clockwise 5π/3 radians, which corresponds to  π/3 radians counterclockwise. This takes us to (-1/2, -√3/2).

Therefore cos(5π/3) = -1/2 and sin(5π/3) = -√3/2.

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Answer:

you didn't provide exact question so here's some help

Step-by-step explanation:

To find the total monthly cost, we need to know how many client sessions the sports trainer has in a month.

Let's say he trains 15 clients in a month.

The cost for client sessions would be:

$10 x 15 = $150

So the total monthly cost would be:

$70.59 (phone) + $40.16 (website/advertising) + $150 (client sessions) = $260.75

The Area of the shaded region is 20.86 in²

The area of a circle is calculated using the formula A = πr², where "A" is the area of the circle.

We know,
Area of Rectangle = l × w,      where l = length and w = width
Area of Circle = [tex]\pi r^{2}[/tex],                where r = radius.

find the area of the rectangle,
length = 6 in and width = 4 in
Area of Rectangle = 6 × 4 = 24 inch²

Here given the circle radius is 1 inch, and we use π as 3.14

Area of Circle = [tex]\pi r^{2}[/tex]
Area of Circle = 3.14 × 1² = 3.14 in²  

The area of the shaded region as per figure below is:

Area of the shaded region = Area of Rectangle - Area of Circle

Area of the shaded region = 24 - 3.14 = 20.86 in²

Therefore, the answer is D.  20.86 square inches.

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We have used the calculation below to sow that the definition to show that lim (x,y)→(3,4) f(x, y) = 3 / 26

In order to show that lim (x,y)→(3,4) f(x, y) = 3 / 26, we need to show that for any ε > 0, there exists a δ > 0 such that if 0 < √((x-3)² + (y-4)²) < δ, then |f(x,y) - 3/26| < ε.

Using the given function, we have:

|f(x,y) - 3/26| = |x/(x²+y²+1) - 3/26|

= |(26x - 3(x²+y²+1)) / 26(x²+y²+1)|.

To simplify this expression, we can use the fact that x² + y² ≥ 0 for any x and y. Therefore,

26(x²+y²+1) ≥ 26(0+0+1) = 26.

Using this inequality, we can write:

|f(x,y) - 3/26| = |(26x - 3(x²+y²+1)) / 26(x²+y²+1)|

≤ |(26x - 3(x²+y²+1)) / 26|

≤ |26x / 26| + |3(x²+y²+1) / 26x²+26y²+26|

= |x| + 3(x²+y²+1) / (26(x²+y²+1))

= |x| + 3 / 26 (1 + 1 / (x²+y²+1)).

Now, we choose δ = ε / (1 + 3/26). Then, if 0 < √((x-3)² + (y-4)²) < δ, we have:

|x| ≤ √((x-3)² + (y-4)²) < δ,

and also

1 < 1 + 1 / (x²+y²+1) ≤ 1 + 1 / δ².

Therefore, |f(x,y) - 3/26| ≤ δ + 3 / 26 (1 + 1 / δ²)

< ε / (1 + 3/26) + 3 / 26 (1 + δ²)

≤ ε / (1 + 3/26) + 3 / 26 (1 + ε² / (1 + 3/26)²).

Since the last term does not depend on x and y, we can choose ε sufficiently small such that ε / (1 + 3/26) + 3 / 26 (1 + ε² / (1 + 3/26)²) < ε. Therefore, we have shown that lim (x,y)→(3,4) f(x, y) = 3 / 26.

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Mark needs a ladder that is 13 feet long in order to reach the second floor windows of the building.

Length is a measurement of distance or space from one point to another. It is typically measured in units such as meters, feet, or inches. Length is a scalar quantity, meaning it has magnitude but no direction. Length is a fundamental property of physical objects and can be used to measure the size of an object or the distance between two points.

To properly calculate the ladder length Mark needs, we must use the Pythagorean Theorem. The Theorem states that for the triangle formed by the ladder and the building, the square of the hypotenuse (the ladder length) is equal to the sum of the squares of the other two sides. Therefore, the ladder length Mark needs is equal to the square root of the sum of the squares of 5 feet and 12 feet, which is equal to the square root of 169, or 13 feet. Therefore, Mark needs a ladder that is 13 feet long in order to reach the second floor windows of the building.

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Answer: 120 yd^2

Step-by-step explanation:

First find the area of the square using the l*l=A: 10*10=100

Then, find the area of the triangle using the formula (b*h)/2: (4*10)/2=40/2=20

Now add the area of the 2 shapes: 100+20=120

Therefore the area of the figure is 120

The pre-split market cap for Rockville was $145.912 billion.

What is pre-split?

Pre-split refers to the process of dividing each outstanding share of a company's stock into multiple shares, effectively increasing the number of shares outstanding and reducing the price per share. This is often done to make the shares more affordable and accessible to investors.

According to the given information

To calculate the pre-split market cap for Rockville, we need to multiply the number of shares outstanding by the market share price.

Before the split, the market share price was $63.44 per share and the corporation had 2.3 billion shares outstanding.

So the pre-split market cap can be calculated as:

Market cap = Market share price * Number of shares outstanding

= $63.44 * 2.3 billion

= $145.912 billion

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