Determine the limit using what you know about special limits:

Answer: CHINA

Step-by-step explanation:

IAS CHINADU

Answer:

Bhutan is the answer.

The best description of the expression 6(x + 10) is given as follows:

The product of a constant factor 6 and a 2-term factor x + 10.

The expression for this problem is defined as follows:

6(x + 10).

The 6 before the parenthesis means that the distributive property is applied, meaning that we have a product of two amounts, which are given as follows:

Meaning that the second option is the correct option.

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Answer:

193 1/3

Step-by-step explanation:

First, we need to convert [tex]\frac{145}{3}[/tex] into a mixed number.

Now, we can add them together:

Therefore, the answer is [tex]193\frac{1}{3}[/tex].

The least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:

Length = 24 feet + 6 inches = 24.5 feet

Width = 4 feet + 6 inches = 4.5 feet

Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)

The volume of the sidewalk is then:

Volume = Length x Width x Depth

= 24.5 feet x 4.5 feet x 1/3 feet

= 3.25 cubic feet

Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:

Number of bags = Volume of sidewalk / Volume per bag

= 3.25 cubic feet / 0.6 cubic feet per bag

= 5.42 bags

Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

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Answer:

the sale price of the one-terabyte external hard drive is $274.13.

Step-by-step explanation:

To find the sale price of the one-terabyte external hard drive, we can use the following formula:

Sale price = Original price - Discount amount

where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.

Substituting the given values into the formula, we get:

Discount amount = 0.21 * $347 = $72.87

To find the sale price, we subtract the discount amount from the original price:

Sale price = $347 - $72.87 = $274.13

Therefore, the sale price of the one-terabyte external hard drive is $274.13.

Answer:

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

How to get the measures of the other two sides of the right triangle?

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

sin(a) = (adjacent cathetus)/(hypotenuse).

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

hypotenuse = AC

opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

Step-by-step explanation:

Here, we let n be the number of sides of the regular polygon. Polygon area = n(12sh). As n increases, h approaches r so that rh approaches r² and hence, this statement is true. So, option 4 is the correct option.

When ns equals circumference or 2r, the polygon will turn into a circle.

A polygon must be converted into a circle.

Let s represent the polygon's side length, r represent the hypotenuse of the right triangle,

Let n be the regular polygon's number of sides and h be the height of the triangle.

The polygon's area is now specified as polygon area = n(1/2sh).

Now, we must suppose that the polygon's sides are infinite in order to obtain a circle. In order to do this, we must assume that the polygon's perimeter is the same as the circle's perimeter.

That's why when the number of sides of the polygon will increase its perimeter will become closer to 2πr and its area will become close to a circle.

The complete question that you might be looking for is-

A regular polygon inscribed in a circle can be used to derive the formula for the area of a circle. The polygon area can be expressed in terms of the area of a triangle. Let s be the side length of the polygon, let r be the hypotenuse of the right triangle, let h be the height of the triangle, and let n be the number of sides of the regular polygon. polygon area = n(12sh) Which statement is true?

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The maximum possible value of the result is 8.

How to solve Linear Equations?

We are given the linear equation;

4x - x = 0

From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;

The first step to solving the equation is to; C. add x to both sides

The second step  to solving the equation is to; C. cube both sides

Solving the equation for x initially yields; C. two possible values

Checking the solutions shows that; D. none are valid solutions

4x - x + x = 0 + x

4x = x

Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;

(4x)³ = x³

4³x = x³

64x = x³

Divide both sides by x to get;

x² = 64

Take square root of both sides to get;

x = ±√64

x = ±8

Hence, The maximum possible value of the result is 8.

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Answer:

10x-610x6

The equation 10x-610x6 has no real solutions because it cannot be solved for any value of x. The left side of the equation is 10x-6, and the right side is 10x+6. Since the left side is greater than the right side, no value of x can make the equation true.

Answer:

6

Step-by-step explanation:

the numerator of the fraction is

6(t+h) +1 -(6t +1) = 6h

so the fraction is 6h/h =6

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

Answer:

The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".

Answer:

1 - cos θ

Step-by-step explanation:

a) The linear function is defined as follows: y = 1 - 0.2x.

b) The slope and the intercepts are interpreted as follows:

c) The battery power is at 75% after 1.25 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:

m = -1/5

m = -0.2.

Hence the function is:

y = -0.2x + 1.

The battery power is of 75% = 0.75 when y = 0.75, as follows:

0.75 = -0.2x + 1

0.2x = 0.25

x = 0.25/0.2

x = 1.25 hours.

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Answer:

15.4 is the answer

Stepson

The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have

[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]

Therefore, the two roots of the quadratic equation in exact square root form are:

[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]

Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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The correct sketch is B

The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.

This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.

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The slope of x - 3y = -9 is, m = 1/3, while the y-intercept (b) is 3.

The sketch of x - 3y = -9 is shown below.

To determine the slope and y-intercept of the line given by the equation x - 3y = -9, we can rewrite it in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To do this, we can solve for y:

x - 3y = -9

-3y = -x - 9

y = (1/3)x + 3

Now we can see that the slope of the line is m = 1/3, and the y-intercept is b = 3.

To sketch the line, we can use the slope and y-intercept. We can start by plotting the y-intercept (0,3) on the y-axis. From there, we can use the slope of 1/3 to find additional points on the line. For example, if we move 3 units to the right along the x-axis, we can move up 1 unit (since the slope is 1/3) to get another point on the line, which is (3,4). We can repeat this process to find more points on the line and then connect them to sketch the line.

The sketch is shown below in the attachment.

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The approximate percent of total students that receive no allowance and do not have a cell phone is this:

C. 47%

First, we are given some figures that stand for the number of students who receive no allowance and have no cell phones. We have to calculate the total number of students as follows:

45 + 21 + 35 + 49 = 150

The number of students who receive no allowance = 49

The number of students who have no cell phones =21

So, the percentage is = The Total number of students that receive no allowance and have no cell phones / Total number of students.

= 49 + 21 = 70

70/150 × 100

= 46.6%

Approximately this is 47%.

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Answer: D = √2

(please respond if im wrong)

Step-by-step explanation:

The fold is made along BE. A folds onto A′.

A′B = AB =√2 ⇒ A′C = 1

(by Pythagoras)

ΔA′BC

is therefore a right-angled isosceles triangle.

⇒∠BA′C=45∘ ⇒∠EA′D=45∘

⇒ ED = A′D = √2−1

Answer:

Step-by-step explanation:

A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:

For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).

For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)

B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:

(1/2x,1/2y) = (1/22, 1/20) = (1,0)

Therefore, the point (2,0) will go to the ordered pair (1,0).

C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.

Answer: y = 2x - 7

Step-by-step explanation:

Slope-intercept form is y=mx+b

Substitute variables with their given values.

 y = 2x + b

In order to find the y-intercept, or b, we can plug the point provided, (4,1) , into y = 2x + b and solve for b.

 1 = 2(4) + b

 1 = 8 + b

-7 = b

Now we can put the y-intercept into the equation, and get y = 2x - 7 .

Answer:

Customers are charged $0.003 per gallon of water used.

Step-by-step explanation:

In the given function, T = 35 + 0.003w, the coefficient of w (which is 0.003) represents the rate at which the total cost (T) increases per unit increase in the amount of water used (w). In other words, it is the cost per gallon of water used.

Therefore, the slope of the function is 0.003, and it represents the rate of change of the cost with respect to the amount of water used. Each additional gallon of water used will increase the monthly bill by $0.003.

Answer:

Step-by-step explanation:

Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:

Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,

h = (2 + 8) / 2 = 5

k = (3 + 1) / 2 = 2

Donc, le centre de l'ellipse est (5, 2).

La distance a est la moitié de la longueur du grand axe, donc

a = (8 - 2) / 2 = 3

La distance b est la moitié de la longueur du petit axe, donc

b = (3 - 1) / 2 = 1

Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

En substituant les valeurs trouvées précédemment, nous avons:

(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1

Ce qui est la forme standard de l'équation de l'ellipse.

Answer:

$ 2,484.23

Step-by-step explanation:

The formula for scrap value is

S(n) = C( 1- r)ⁿ

where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years

First convert r to a decimal by dividing by 100

r = 13/100 = 0.13

S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423

= $ 2,484.23

Answer:

5pi (use the pi character button on your screen)

Step-by-step explanation:

Arc length formula is the shortest formula in all of all math!

Arc length = r•theta

r is the radius. In your question, it is 6.

"theta" is the angle in radians, which was given in your question as 5pi/6.

Fill in these given values to the formula.

Arc length

= r • theta

= 6 • 5pi/6

Simplify (the 6's cancel)

= 5pi

Answer:

To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:

g(x) = cos((1/6)x)

To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:

g(x) = cos((1/6)x) - 5

So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.

Answer:

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

    |          /

    |        /

    |      /

    |    /

-----|------------------

    | /         \

    |/            \

    /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

   |          /

   |        /

   |      /

   |    /

-----|------------------

   | /         \

   |/            \

   /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

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The solution is, the total surface area is 92 sq. inches.

Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.

here, we have,

Total paper required = total surface area

Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],

Where 'l' is the length, 'b' is the breadth and 'h' is the height

For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]

=2[24 + 6 + 16]

=2[46]

= 92 sq. inches

Hence, The solution is, the total surface area is 92 sq. inches.

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(a) The probability that exactly 10 of the first 15 graded projects are from the second section can be calculated using the binomial probability formula:

P(X = 10) = (15 choose 10) * (35/60)^10 * (25/60)^5 = 0.0361

(b) The probability that at least 10 of the first 15 graded projects are from the second section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15:

P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 = 0.0536

(c) The probability that at least 10 of the first 15 graded projects are from the same section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15 from both sections:

P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 + 0.0019 + 0.0003 + 0.0000 + 0.0000 + 0.0000 + 0.0000 = 0.0556

(d) The mean value and standard deviation of the number among these 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution:

mean = np = 15 * (35/60) = 8.75
standard deviation = sqrt(np(1-p)) = sqrt(15 * (35/60) * (25/60)) = 1.568

(e) The mean value and standard deviation of the number of projects not among these first 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution, with n = 45 (the remaining number of projects) and p = 35/60 (the probability of a project being from the second section):

mean = np = 45 * (35/60) = 26.25
standard deviation = sqrt(np(1-p)) = sqrt(45 * (35/60) * (25/60)) = 2.714

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Answer:12

Step-by-step explanation: