Round 29.675 to
the hundredths place.

The new price of the purchase after the 13% discount can also be expressed as 0.87x.

The new price of the purchase after the 13% discount is expressed as x - 0.13x.

We can factor out x as follows to simplify this expression by combining like terms:

x - 0.13x = x(1 - 0.13) (1 - 0.13).

We can simplify the expression in parentheses as follows:

1 - 0.13 = 0.87.

So, by combining like terms, the equivalent expression is:

x - 0.13x = 0.87x.

As a result, the new purchase price after the 13% discount can also be expressed as 0.87x.

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The value of 6½ - 1⅓ is 5 ⅙

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

To solve 6½ - 1⅓ ;

we make the mixed fraction improper fraction

= 13/2 - 4/3

= (39-8)/6

= 31/6

= 5 1/6

therefore The value of 6½ - 1⅓ = 5 1/6

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Step-by-step explanation:

[tex]6 \frac{1}{2} - 1\frac{1}{3} = 5 \frac{1}{6} [/tex]

The height of a cone is equal to 1.91 feet.

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

Volume of a cone, V = 1/3 × πr²h

Making "h" the subject of formula, we have:

Height, h =3V/(πr²)

Substituting the given parameters into the height of a cone formula, we have;

Height, h =3(18)/(3.142 × 3²)

Height, h = 54/(28.278)

Height, h = 1.91 feet.

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Typically, the group of objects in which data is collected from is called the population

The equation that represents the number of miles will be 68.25 = 35 + 0.07m. Then the number of miles will be 475 miles.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the gradient of the line and c is the y-intercept of the line.

Let 'm' be the number of miles. Then the equation is given as,

$68.25 = $35 + 0.07m

Solve the equation for 'm', then we have

68.25 = 35 + 0.07m

33.25 = 0.07m

m = 33.25 / 0.07

m = 475 miles

The equation that represents the number of miles will be 68.25 = 35 + 0.07m. Then the number of miles will be 475 miles.

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Answer:

B

Step-by-step explanation:

It is B because:

21/5x+12-3+5/2x

21/5x+9+5/2x

u then find the lowest common multiple being 10x

42/10x+25/10x+90x/10x

67/10x+9

The factor of the expression x² + 3x - 4 will be (x + 4) and (x - 1). And the variable 'x' represents the length of the rectangle.

The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be

Area of the rectangle = L × W square units

Let 'x' be the length of the rectangle. Then the width will be (x - 5). Then the factors of the expression is given as,

A = x² + 3x - 4

A = x² + 4x - x - 4

A = x(x + 4) - 1(x + 4)

A = (x + 4) · (x - 1)

The factors of the expression x² + 3x - 4 will be (x + 4) and (x - 1). And the variable 'x' represents the length of the rectangle.

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An equation of the line that satisfies the given conditions is x = 2y + 13.

To find the equation of the line that passes through the point (-9, -11) and is perpendicular to the line passing through (-6, 1) and (-2, -1), we can use the slope-point form of a line.

First, we find the slope of the line passing through (-6, 1) and (-2, -1). The slope of this line can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we have:

m = (-1 - 1) / (-2 - (-6)) = -2 / 4 = -1/2

The slope of a line perpendicular to this line has a negative reciprocal, so the slope of the line through (-9, -11) that is perpendicular to this line is 1/2.

Next, we use the point-slope form of a line to find the equation of the line:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line and m is the slope.

Plugging in the values, we have:

y - (-11) = 1/2 (x - (-9))

Expanding and simplifying, we get:

y + 11 = 1/2 (x + 9)

Multiplying both sides by 2, we get:

2y + 22 = x + 9

Subtracting 9 from both sides, we get:

2y + 13 = x

So, the equation of the line that satisfies the given conditions is:

x = 2y + 13

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The square pyramid is having a height of 89 units.

A pyramid is a three-dimensional shape. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid.

As per the given data:

length of the base ([tex]a[/tex]) = 20.8 units

slant height of the pyramid ([tex]s[/tex]) = 89.6 units

Height of the pyramid ([tex]H[/tex]) = [tex]\sqrt{s^2 - (\frac{a}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (\frac{20.8}{2})^2}[/tex]

=  [tex]\sqrt{(89.6)^2 - (10.4)^2}[/tex]

=  [tex]\sqrt{(8028.16) - (108.16)}[/tex]

= [tex]\sqrt{7920}[/tex]

= [tex]89[/tex] units

The height of the square pyramid is 89 units.

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The false statement involving p, and the arbitrary events A and B are e) P(Ac ∩ B) = P(B) - P(A ∩ B).

When two events cannot happen simultaneously or at the same time, they are said to be mutually exclusive in probability theory. In other words, discontinuous occurrences are described as being mutually exclusive. The likelihood of two occurrences occurring simultaneously is 0 if they are regarded as separate events. based on an impulse, notion, or chance rather than on logic: Despite being a random pick, her clothing was ideal. 1. Dependent solely upon one's discretion; open to individual will or judgment without limitations. a choice made at random. 2. made by a court or arbitrator as opposed to a law or statute.

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The graph of the slope-intercept form y = -x + 2 is a linear graph with the slope = -1, and the y-intercept = 2

The slope intercept form is an approach for figuring out the straight line of a linear equation on the coordinate plane. We need to have the slope of the line and the y-intercept where the line crosses the y-axis in order to use the slope-intercept formula.

The slope-intercept form can be expressed by using the formula:

y = mx + b;

where,

Given that:
y = -x + 2

The graph of the linear equation  (y) means that the slope = - 1, and the y-intercept = 2.

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Answer:

Step-by-step explanation:

The first step is to find the slope of the tangent line. To do that, we need to find the derivative of f(x):

f(x) = sin(x) + 2cos(x)

f'(x) = cos(x) - 2sin(x)

Now we can find the slope of the tangent line at x=0 by plugging in x=0 into f'(x):

f'(0) = cos(0) - 2sin(0) = 1

Therefore, the slope of the tangent line at x=0 is 1.

Next, we need to find the y-coordinate of the point on the graph where x=0. To do that, we simply plug in x=0 into f(x):

f(0) = sin(0) + 2cos(0) = 2

Therefore, the point on the graph where x=0 is (0, 2).

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in m=1 and (x1, y1) = (0, 2), we get:

y - 2 = 1(x - 0)

Simplifying, we get:

y = x + 2

Therefore, the equation of the tangent line is y = x + 2.

Answer:

The equation of the tangent line at x = 0 can be found by differentiating the function f(x) and using the point-slope form of a line.

The derivative of f(x) is f'(x) = cos(x) - 2sin(x). Substituting x = 0 into f'(x) gives f'(0) = cos(0) - 2sin(0) = 1 - 0 = 1.

Therefore, the equation of the tangent line is y = 1x + b, or y = x + b.

To find the value of b, we can plug in x = 0 and y = f(0) = sin(0) + 2cos(0) = 2 into the equation. Solving for b, we get 2 = 0 + b, so b = 2.

Therefore, the slope-intercept equation of the line tangent to the graph of y = f(x) at the point (0,2) is y = x + 2.

Answer:

So Ms. Shaw will completely fill 6 fish tanks and have 1 fish left.

Step-by-step explanation:

Ms. Shaw has 16 fish and each fish tank can hold 3 fish. To find out how many fish tanks she needs, we can divide the total number of fish by the capacity of each tank:

16 fish / 3 fish per tank ≈ 5.33 tanks

Since we cannot have a fraction of a tank, we need to round up to the nearest whole number. Therefore, Ms. Shaw needs 6 fish tanks to completely fill all her fish.

To find out how many fish are left, we need to subtract the number of fish in the full tanks from the total number of fish:

16 fish - (5 tanks * 3 fish per tank) = 1 fish left

So Ms. Shaw will completely fill 6 fish tanks and have 1 fish left.

Answer:

B

Step-by-step explanation:

The graph has to start at  - 4   and get  smaller ( more negative...'less than')   but NOT INCLUDE -4   ( should be hollow dot at -4)

Answer:

it is the 4th and 5th

Step-by-step explanation:

by following the laws of BODMAS

Brackets

of

Division

Multiplication

Addition

Subtraction

(5×6)+2=5×6+2

(30)+2=30+2

32=32

5×6+2=2+5×6

30+2=2+30

32=32

The formula to calculate the magic number in MLB is: Magic number = 163 - (number of wins by leading team) + (number of losses by trailing team) - 1.

The "magic number" in Major League Baseball (MLB) represents the combination of wins by the leading team and losses by the trailing team required for the leading team to clinch a playoff spot. To calculate the magic number, follow these steps:

1. Determine the total number of games in the season. In MLB, this is typically 162 games.

2. Subtract the number of games in the season from 163. For example, 163 - 162 = 1.

3. Subtract the number of wins by the leading team from 163. For example, if the leading team has 90 wins, 163 - 90 = 73.

4. Add the result from step 2 to the result from step 3. For example, 73 + 1 = 74.

5. Finally, subtract the number of losses by the trailing team from the result of step 4. For example, if the trailing team has 80 losses, 74 - 80 = -6. In this case, the magic number is zero, meaning that the leading team has already clinched a playoff spot.

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" The value of the mean is always greater than the value of the standard deviation" is not a characteristic of the normal distribution

The curve of a normal distribution is known as the bell curve. The curve in statistical analysis represents the occurrence of some particular result as a product of the experiment. The normal curve is always symmetrical. This implies that the results of the trials will produce results near the mean value of the distribution.

Characteristics of a normal distribution involve:

1. The total area beneath the symmetric curve is 1: Since the area under the curve represents the chances of all the experiments; hence the summation must be 1.

2. The two tails of the curve extend indefinitely: The tails of the normal distribution never touch the horizontal axis; it is extended indefinitely.

4. The curve is symmetric about the mean: In a normal curve, the mean value of the distribution lies in the centre dividing the distribution curve into two symmetric parts.

Not a characteristic of a normal curve:

3. The value of the mean is always greater than the value of the standard deviation. The mean of the data can be negative as well as positive, but the value of the standard deviation is always positive. The small value of standard deviation implies the presence of more clustered data around the mean. The large value of the standard deviation indicates that the data is more spread out.

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Answer:

Step-by-step explanation:the answer is 0.14 pounds

If the length of OB was 3/4, then the length of OB' after dilation is; Option B: 3 units.

Dilation of an object simply means enlarging or shrinking the object by a scale factor.

We are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄. What this means is that it was enlarged by a scale factor of 4 with point O as the centre of dilation.

Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;

                    Scale factor = new dilated length OB'/(3/4)

                    New dilated length OB' = (3/4) × 4

                    New dilated length OB' = 3 units

The question is incomplete. The complete question:

"Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the centre of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'?"

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We can write the quadratic equation as -

y = 3(x - 2)² - 7.

A function is a relationship between a dependent {y} and independent variable {x}.

An expression is a combination of terms both constants and variables.

Given is the quadratic function as shown in the image.

The general equation of a quadratic equation is -

y = ax² + bx + c

We can writ the equation of a parabola from the vertex as -

y = a(x - h)² + k

We have (2, - 7) as the coordinates of vertex. So, we can write -

y = a(x - 2)² - 7

For the point (3, - 4), we can write -

- 4 = a(3 - 2)² - 7

- 4 = a x 1 - 7

a = - 4 + 7

a = 3

So, we can write the quadratic equation as -

y = 3(x - 2)² - 7

Therefore, we can write the quadratic equation as -

y = 3(x - 2)² - 7.

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It is impossible to get 8 aces from a standard 52 cards deck.

What is probability and its formula?

The formula for probability states that the possibility of an event happening, or P(E), equals the ratio of the number of favorable outcomes to the number of total outcomes. Mathematically, it looks like this: P(E) = favorable outcomes/total outcomes.

Now, According to the question:

There are four aces in total in a 52 card deck.

Therefore the probability of getting 8 aces can be expressed as:

P(8A) = 7/52 × 6/51 × 5/50 × 4/49 × 3/48 × 2/47 × 1/46 × 0/45 = 0

The probability getting is zero.

Therefore, it is impossible to get 8 aces from a standard 52 cards deck.

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The number of ribbons of length  [tex]1\frac{2}{3}[/tex]  that can be cut out of a piece of ribbon that is 35 ft long, is 21

A division is a process of splitting a specific amount into equal parts.

Given that, a piece of ribbon that is 35 feet long, we need to find that how many [tex]1\frac{2}{3}[/tex] foot pieces of ribbon can you cut from it,

For this we will use the concept of division,

The number of ribbon cut from it = total length / small ribbons length

= 35 /  [tex]1\frac{2}{3}[/tex]

= 35 / 5÷3

= 35×3 / 5

= 21

Hence, the number of ribbons of length  [tex]1\frac{2}{3}[/tex]  that can be cut out of a piece of ribbon that is 35 ft long, is 21

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The equation of the function is g(x) = √(x + 5) - 2

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

f(x)=√(x + 2) - 3

The transformation is given as:

3 units left and 1 unit up

This is represented as

(x + 3, y + 1)

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

g(x) = √(x + 2 + 3) - 3 + 1

Evaluate

g(x) = √(x + 5) - 2

Hence, the equation is g(x) = √(x + 5) - 2

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The algebraic expression is 2x - 5 > 6

The given equation can be written in a verbal phrase as:

"Twice a number, decreased by five, is equal to a number greater than negative six."

When represented as an expression, we have

Hence, the expression is 2x - 5 > 6

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The electric potential at the center of the circle formed by the plastic rod is -1.644V.

We know that the formula to find the electric potential V = KQ/R,

where K is Coulombs constant, Q is the charge, and R is the radius of the circle.  

According to the question,

The radius of the circle formed by the plastic rod on bending = 8.20 cm

(Converting cm to m by dividing by 100)               = (8.20)/100 = 0.082m

We know that Coulombs constant (K) =  8.99 × 10 ^ 9 N m^2/C^2

It is given that along one quarter of its circumference (Q1) =  +3.00 pC

and along the remaining circumference, the charge (Q2) = -6Q1

Therefore, electric potential (V) = K (Q1+KQ2) /R

= (8.99 × 10 ^ 9) (Q1 + (-6Q1)) / 0.082 = (8.99 × 10 ^ 9) (-5Q1)/ 0.082

= -5 (8.99 × 10 ^ 9) (3 X 10 ^ -12) / (0.082) = -1.644512V ≈ -1.644V

The given question is incomplete, the complete question is:

A plastic rod has been bent into a circle of radius R = 8.20 cm. It has a charge Q1 = +3.00 pC uniformly distributed along one-quarter of its circumference and a charge Q2 = -6Q1 uniformly distributed along the rest of the circumference. Take V = 0 at infinity.

What is the electric potential at the center C of the circle?

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The area of rectangle in expanded quadratic form is; is 20x² - 10x - 30.

The area of rectangle is given by the formula;

Area = length × width.

Area = 5  × (4x² - 2x - 6)

= (5 × 4x²) - (5 × 2x) - (5 × 6)

= 20x² - 10x - 30

Therefore, the area of rectangle is 20x² - 10x - 30.

Upon solving the above quadratic equation, we get,

20x² - 10x - 30 = 0

2x² - x - 3 = 0

x = 3/2, x = -1

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Complete question is;

A rectangle has a height of 5 and a width of 4x² - 2x - 6. Find the area of rectangle.

Answer:

20x² - 10x - 30

Step-by-step explanation:

Answer:

v = 1.165

Step-by-step explanation:

To find the value of v in the equation 0.4 = 0.167 + 0.2v, we can isolate v by subtracting 0.167 from both sides:0.4 - 0.167 = 0.2v0.233 = 0.2vNext, we can divide both sides by 0.2 to find the value of v:0.233 / 0.2 = 0.2v / 0.2v = 0.233 / 0.2v = 1.165So the value of v is 1.165.In conclusion, by subtracting 0.167 from both sides of the equation and dividing both sides by 0.2, we found that the value of v is 1.165.

Answer: The value of v that satisfies the equation 0.4 = 0.167 + 0.2v is 1.165.

Step-by-step explanation:

To find the value of v in the equation 0.4 = 0.167 + 0.2v, we can isolate v by subtracting 0.167 from both sides:

0.4 - 0.167 = 0.2v

0.233 = 0.2v

Next, we can divide both sides by 0.2 to solve for v:

0.233 / 0.2 = 0.2v / 0.2

v = 1.165

So, the value of v that satisfies the equation 0.4 = 0.167 + 0.2v is 1.165.

The 59th term of the given arithmetic sequence, is -496

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called the common difference of that arithmetic progression.

Given that, an arithmetic sequence 26, 17, 8, we are asked to find the 59th term,

nth term of an arithmetic sequence, is given by :-

aₙ = a₁+(n-1)d

Where n is the asked term, d is the common difference,

Here d = 17-26 = 8-17 = -9

Therefore,

a₅₉ = a₁+(59-1)(-9)

a₅₉ = 26+58×(-9)

a₅₉ = -496

Hence, the 59th term of the given arithmetic sequence, is -496

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The hypotenuse of the right triangle has a length of 19.24 cm.

For a right triangle whose catheti are A and B, and the hypotenuse is C, then the Pythagorean's theorem says that:

A^2 + B^2 = C^2

The lengths of the legs are:

A = 9cm

B = 17cm

Then the length of the hypoten use is given by:

(9cm)^2 + (17cm)^2 = C^2

√((9cm)^2 + (17cm)^2) = C

19.24 cm = C

The length of the hypotenuse is 19.24 cm.

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Answer:

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

Every 3 clovers out of 10 have four leaves and the rest 7 have three leaves.

This gives us the ratio of clovers with four leaves by the total number:

If the total number is 100, then Lucy has:

If there are 200 clovers, then the number of four-leaf clovers is doubled: