What is the product of 10 and 6/sqrt(96) in simplest radical form?

Answer:

  a) 23.1 million

  b) year 2013

Step-by-step explanation:

Given a population in millions is modeled by A = 23.1e^(0.0152t) for t years after 2000, you want to know the population in year 2000, and the year in which the population is 28.3 million.

When t=0, the exponential factor is 1. The population is given by the coefficient of that factor: 23.1

The population in 2000 was 23.1 millions.

We can solve for t to find the year the population is 28.3 million:

  28.3 = 23.1e^(0.0152t)

  28.3/23.1 = e^(0.0152t) . . . . .divide by 23.1

  ln(28.3/23.1) = 0.0152t . . . . . take natural logs

  t ≈ 13.36

The population will reach 28.3 million in the year 2013.

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A pyramid is a solid shape with a specified shaped base. The required answer is 8.67 cubic feet.

A pyramid is a solid shape with a specified shaped base. While a square based pyramid is a type of pyramid which has its base to be a square.

Volume of a square based pyramid = [tex]\frac{1}{3}[/tex] x base area x height

Also, are of a square = length x length

So that,

i. For the first pyramid;

volume =  [tex]\frac{1}{3}[/tex] x (2 x 2) x 6

            = 8 cubic feet

The volume of the first pyramid is 8 cubic feet.

ii. For the second pyramid, we have;

height = 8 feet

base side = 2.5 feet

So that.

Volume =  [tex]\frac{1}{3}[/tex] x (2.5 x 2.5) x 8

             = 16.6667

Volume = 16.67 cubic meters

The volume of the second pyramid is 16.67 cubic meters.

Therefore, the volume of the second pyramid is greater than the volume of the first pyramid by;

volume of the second pyramid - volume of the first pyramid = 16.67 - 8.0

                                              = 8.67 cubic feet

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The function f(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.

Graph is a mathematical representation of a Networks and it's describes the relation between lines and points.

The graph of the function f(x) is given.

The following steps can be used in order to determine the interval for f(x):

Step 1 - The value of f(x) means the value of y.

Step 2 - The value of f(x) is positive when the graph of f(x) is in the first or in the second quadrant.

Step 3 - So, according to the graph function f(x) is positive when the value of x is in between -3 and 5.

Therefore, the correct option is 3).

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The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

Given that, the dimensions of a rectangle (x-1) and (x+3).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, the area of a rectangle

= (x+3)×(x-1)

= x²+3x-x-3

= x²+2x-3

Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the area of a rectangle with the dimensions (x-1) and (x+3).

Under the same translation as X and X' the coordinates of Y' = (-2, -4) and Z' = (-4, -1)

What is translation of a point in coordinate system?

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

According to the given question:

It is given about the points X (-4, -2) and X' (-6, -5).

We see that the translation is moving -2 units horizontally to the left and -3 units vertically down.

Therefore, the point Y(0,0)  is translated to Y'(0-2,-1-3) = Y'(-2,-4)

and the point Z(-2,2)   is translated to Z'(-2-2,2-3)  = Y'(-4,-1).

Hence, under the same translation Y' = (-2, -4) and Z' = (-4, -1)

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The number of swims that Will swims by using decimal divisions is 16 laps in each hour.

What is decimal division?

When dividing decimals, the divisor must be converted to a whole number by moving the decimal point to the right. The dividend's decimal point is then carried up to the same number of places to the right, and the resulting numbers are divided in the same manner as regular long division.

Given, Will swims a total of 45.6 laps in 2.85 hours

That is, 2.85 hours = 45.6 laps

or, 1 hour = 45.6/2.85 = 16 laps

Hence, he swims 16 laps each hour.

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Amount of computer can be 350 or more than 350.

What do you mean by inequality?

Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilised to compare the numbers, whether it is less than or higher than.

Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.

It is given that Alex has $600 in her checking account and She wants to have at least $250 left in her checking account after buying the computer.

Let the amount of computer be t

According to the question , inequality become:

600 - t ≥ 250

600 - 250 ≥ t

350 ≥ t

Therefore, amount of computer can be 350 or more than 350.

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The length of the two arcs and the area of the two circular sectors can be calculated as follows:

Since the semicircle is divided into two circular sectors, each sector has an angle of 180/2 = 90 degrees. Therefore, the smaller circular sector has an angle of 90 * (4/5) = 72 degrees, and the larger circular sector has an angle of 90 - 72 = 18 degrees.

The length of the arc of a circle is equal to the circumference of the circle multiplied by the ratio of the central angle of the arc to 360 degrees. Therefore, the length of the smaller arc is 18 * pi * (72/360) = 8pi cm, and the length of the larger arc is 18 * pi * (18/360) = 2pi cm.

The area of a circular sector is equal to the area of the circle multiplied by the ratio of the central angle of the sector to 360 degrees. Therefore, the area of the smaller circular sector is 18^2 * pi * (72/360) = 288pi cm^2, and the area of the larger circular sector is 18^2 * pi * (18/360) = 72pi cm^2.

Therefore, the length of the two arcs is 8pi cm and 2pi cm, and the area of the two circular sectors is 288pi cm^2 and 72pi cm^2.

Answer: y= -3x -1

Step-by-step explanation: y=mx+b

The Y-intercept is at (0,-1), so b is -1

The slope is rise/run, and the graph is down 3, right 1, so the slope is -3/1

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The distance between the point and the line is 3 units.

Find the equation for line L

Begin by finding the slope of the line through the given points, (4,-1) and (4,9) ; its intercept:

m = (y₂ - y₁) / (x₂ - x₁)

= (9 - (-1) ) / 4 - 4

= 10 / 0

= Undefined

Because the slope is undefined, then line L is a vertical line which has an x-intercept of (4,0):

x=4

Because, line L is vertical, then the line w perpendicular to it is a horizontal line that passes through (1,6)(1,6) so its equation is y=6. Hence, L and w intersect at (4,6) which we will denote as Q.

The perpendicular distance is the distance from point P(1,6) to point Q(4,6) which is simply the absolute value of the difference of the x-coordinates:

d = | 1 - 4 |

= |-3|

= 3

Hence, The distance between the point and the line is 3 units.

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Answer:

20 boxes

Step-by-step explanation:

12 cans = 1 box

240 = x

apply rule of three

(240/12) x 1 = x

20 = x

Answer:

She will need 20 boxes

Step-by-step explanation:

Take the total number of cans and divide by the number of cans per box

240/12

20

She will need 20 boxes.

If a prestigious program accepts 2 out of every 9 applicants per year than the program will accept 360 applicants out of 1620.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

the ratio is given:

2/9 = 360/x

solving for the value of x;

x/9=360/2

x=(180)9

x=1620

this is the required value of applicants that were not accepted.

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The line AC from the diagrammatic expression of the tangent of the circle shows that line AC is 24.0

A tangent of a circle is a line that intersects the circle at a single point. The site at which the tangent intersects the circle is referred to as the site of tangency.

From the given information:

Line |CD| =  Diameter

Line |EA| = radius = 18

Line |DB| = 12

Then, we can infer that line EA = DE since they are both (radii of the circle.)

Line |DE| = |EA| = 18

By using the formula for Pythagoras' theorem, we can find line |EA|.

hyp² = opp² + adj²

where;

Line |BE| = hypotenuse = DB + BE = 12 + 18 = 30

Line |AB| = opposite (x) = ???

Line |EA| = adjacent = 18

Thus;

30² = x² + 18²

900 = x² + 324

-x²  = -900 + 324

x  = √576

x = 24.0

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Answer:

x=2√10,−2√10

Step-by-step explanation:

Answer:

[tex]\frac{7}{5}[/tex] or 7:5

Step-by-step explanation:

You are going from the smaller triangle to the larger.

Let x = the scale factor.  Find two corresponding sides that you know both lengths.

50x = 70  Divide both sides by 50

x = [tex]\frac{70}{50}[/tex]  Divide both the numerator and denominator by 10

[tex]\frac{7}{5}[/tex]

Answer:

y = - [tex]\frac{5}{4}[/tex] x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-5}{4-0}[/tex] = [tex]\frac{-5}{4}[/tex] = - [tex]\frac{5}{4}[/tex]

the line crosses the y- axis at (0, 5 ) ⇒ b = 5

y = - [tex]\frac{5}{4}[/tex] x + 5 ← equation of line

Answer: $50.25

Step-by-step explanation:

     First, we will write an equation to represent this situation.

C = $2.75 + $5D

     Next, we will substitute 9.5 miles into D and solve.

C = $2.75 + $5D

C = $2.75 + $5(9.5)

C = $50.25

Answer:

(a) c = 2.75 + 5d

(b) $50.25

Step-by-step explanation:

(a)

The information tells us the following:

Cost of a taxi ride = $2.75 + (5 * number of miles travelled)

We can use the variables c and d to represent the descriptions:

c = 2.75 + 5d

(b)

Substitute 9.5 into the equation as d:

c = 2.75 + 5(9.5)

Simplify:

c = 2.75 + 47.5

c = 50.25

Therefore, the cost of a 9.5 mile ride is $50.25.

180 - 57 = 123 ( ALLIED ANGLE )

answer:

step by step explanation:

(4,8); y = 2x — 4 = ?

Answer:

False

Step-by-step explanation:

Subtract the numbers  115 − 10 = 105    

     2.Simplify 12 − 5(2 − 6) : 8

105=8

this shows that the sides are not equal so it is false  

Answer: To find out how long it takes the paddle wheel to complete 100 full revolutions, we need to calculate the circumference of the paddle wheel and divide that by the speed at which the fins along the outer edge are traveling.

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle.

The radius of the paddle wheel is 2 feet (the diameter of 4 feet divided by 2), so the circumference is:

C = 2π * 2 = 8π feet

To find out how long it takes the paddle wheel to complete 100 full revolutions, we divide the number of feet traveled in one revolution (the circumference of 8π feet) by the speed at which the fins are traveling (1.3 feet per second):

100 * 8π feet / 1.3 feet per second = 615.38 seconds

Rounded to the nearest second, it takes approximately 615 seconds for the paddle wheel to complete 100 full revolutions.

The slope of the line that passes through the points (10, 3)(10,3) and (7, 0)(7,0)= 1.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

According to our question-

The slope m using the slope formula

m = y2-y1/x2-x1

with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )

-3/-3 = 1

Hence, the slope is = 1.

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If the ratio of band members in group 1 to band members in group 2 is 1 to 3, then for every 3 band members in group 2, there will be 1 band member in group 1.Therefore, group 2 will have 11 band members.

Comparing two numbers or quantities results in a ratio. Usually, it is expressed in the form "a:b" or "a/b," with a and b standing for the two quantities under comparison. Contrarily, a percentage is an equation that states that two ratios are equal. Alternatively said, a proportion is a claim that one ratio is equal to another.

For example, if the ratio of apples to oranges in a basket is 2:3, this implies that there are three oranges per each two apples. We may alternatively state that the ratio of apples to total number of fruits in the basket is 2:5, because 2 + 3 = 5. The two ratios (2:3 and 2:5) are proportionate in this instance. Also, ratio of band members in group 1 to band members in group 2 to be 1 to 3

How to solve?

If the director wants to divide 44 band members into two groups, with this ratio, then the number of band members in group 2 will be 44 / (1 + 3) = 44 / 4 = 11 band members.

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The smallest integer out of the three integers is 109

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Three consecutive integers:

x, x+1, x+2

The sum of the integers,

x+(x+1)+(x+2) = 330

3x + 3 = 330

3x= 327

x= 327/3

x= 109

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The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

The conditional statement is defined as the two fundamental components that make up a conditional statement Hypothesis (if) and Conclusion (then).

The given conditional statement is "walking in front of a moving car is dangerous to your health."

The converse of the conditional statement is “If dangerous to your health then walking in front of a moving car”.

The inverse of the conditional statement is “If not dangerous to your health then not walking in front of a moving car”.

The contrapositive of the conditional statement is “if not walking in front of a moving car then not dangerous to your health."

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Based on the unit rate of the table, the missing values that shows the cost and the number of tickets are:

$32 and 9 tickets.

To calculate the missing values in the table shown in the attachment below, we have to find the unit rate, which is the cost of 1 ticket.

Given that 3 tickets will cost $12, therefore:

Unit rate = 12 / 3 = $4 per ticket.

Using this rate, find the missing values as explained below.

For 8 tickets, we will have the following cost:

8 × $4 = $32

For $36, we will have the following tickets:

$36/$4 = 9 tickets

Thus, the missing values that will complete the table will be:

$32 and 9 tickets.

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