Partial qoutients 231÷11

Answer:

104 cm^3

Step-by-step explanation:

The ratio of volumes is the cube of the ratio of linear dimensions for similar figures. Since the height of B is 2 times the height of A, the volume of B will be 2^3 = 8 times the volume of A, so is ...

8·13 cm^3 = 104 cm^3

Answer:

The volume of B is 39cm³

Step-by-step explanation:

Volume of cylinder A

Va = 1/3πr²ha ...(1)

Where height of A is ha

If the height of B is twice the corresponding height of A

hb = 3ha

Volume of B Vb = 1/3πr²(3ha)...(2)

If volume of A is 13cm³ and

Va = 1/3πr²ha

Then 13 = 1/3πr²ha

39 = πr²ha

πr² = 39/ha ... (3)

To get Vb, we wil substitute equation 3 into 2 to have;

Vb = 1/3(39/ha)(3ha)

Vb = 39/ha × ha

Vb = 39cm³

Answer:

B. 3¹²

Step-by-step explanation:

To solve this we need to apply the following laws of exponents:

1. [tex](a^n)^m=a^{n*m}[/tex]

2. [tex]a^{-n}=\frac{1}{a^n}[/tex]

Let's apply the first law to the numerator of our fraction and the second law to the denominator. For the numerator, [tex](3^5)^2[/tex], [tex]a=3[/tex], [tex]n=5[/tex], and [tex]m=2[/tex]. For the denominator [tex]3^{-2}[/tex], [tex]a=3[/tex] and [tex]n=-2[/tex]

Replacing values

[tex]\frac{(3^5)^2}{3^{-2}} =\frac{3^{5*2}}{\frac{1}{3^2} } =\frac{3^{10}}{\frac{1}{3^2} }[/tex]

Now, remember that to divide fractions we just need to invert the order of the second fraction and multiply:

[tex]\frac{3^{10}}{\frac{1}{3^2} }=3^{10}*\frac{3^2}{1} =3^{10}*3^2[/tex]

Finally, we can use the law of exponents for multiplication to get our answer:

[tex]a^n*a^m=a^{n+m}[/tex]

[tex]3^{10}*3^2=3^{10+2}=3^{12}[/tex]

We can conclude that the correct answer is B. 3¹²

Answer:

B. The sum function is linear but the volume function is not

Step-by-step explanation:

We are given that f(x) and g(x) are linear. Due to this, the sum function S(x) is linear.

And we know the shape of our figure, so we just need to multiply the dimensions for V(x) but the product of three linear functions results in a cubic function, and we conclude V(x) is not linear.

Glad to answer.

Answer:

$63.36

Step-by-step explanation:

First we need to determine how many pencils are needed

8 pencils times 96 students

8*96 =768 pencils

A dozen is 12 pencils

Divide the number of pencils needed by 12 to determine how many dozen pencils are needed

768/12 =64

We need 64 dozen pencils

They cost .99 per dozen

64*.99 =63.36

It will cost $63.36 for  the pencils

Answer:

$112

Step-by-step explanation:

Reduced price of $89.60 = 80% (100% - 20%)

You can get the original price (100%) by dividing $89.60 with 80% = $112

The original price is $112.

Given:

A store has 20% off sale.

Reduced price of an item = $89.60

We have to find the original price of an item.

Now, the store has 20% off sale. Hence, the reduced price of an item $89.60 is the 80% of the original price.

Form the given information we can find the original price of an item.

⇒ (80/100) × original price = 89.60

Multiply both sides by 100, we get:

⇒ 80 × original price = 8960

Divide both the sides by 80, we get:

⇒ Original Price = $112

Therefore, the original price of an item is $112.

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Answer:

294.5 sq meters

Step-by-step explanation:

I found the area of the circle, subtracted away the area of the sector, then had to add back in the area of the triangle.  The areas for each is as follows:

[tex]A_{c}=\pi (11.1)^2[/tex]

A = 387.0756 sq m

[tex]A_{s}=\frac{130}{360}*\pi (11.1)^2[/tex]

A = 139.7773

[tex]A_{t}=\frac{1}{2}(11.1)(11.1)sin(130)[/tex]

A = 47.1922

Now taking the area of the circle - area of sector + area of triangle:

387.0756 - 139.7773 + 47.1922 = 294.5 sq m

Answer:

294.5

Step-by-step explanation:

Answer: regular hexagon

Step-by-step explanation:

The polygon shown is a regular hexagon.

A regular hexagon is a six-sided polygon with all its sides of equal length and all its interior angles of equal measure. The term "regular" signifies the uniformity and symmetry of this geometric shape. Each side of a regular hexagon is congruent to the others, and each interior angle measures 120 degrees.

Regular hexagons can be found in various contexts, from nature to man-made structures. Honeycombs, for instance, are often composed of hexagonal cells. The six-sided structure allows for efficient packing and maximizes space utilization, which is why it's a prevalent shape in the natural world.

In geometry, a regular hexagon can be divided into equilateral triangles, demonstrating its versatility and ease of partitioning. This feature makes it a fundamental shape in tessellation patterns and various geometric designs.

Additionally, regular hexagons possess rotational symmetry. You can rotate a hexagon by 60 degrees, and it will align perfectly with its original position, making it a key element in tessellation art and certain engineering applications.

Overall, the regular hexagon is an elegant, balanced, and harmonious shape with numerous real-world and mathematical applications, valued for its regularity and aesthetic appeal.

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The answer would be A

If a  coin is flipped 10 times  then the probability that it will show all heads or all tails is 1/512.

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of getting all heads or all tails on 10 flips in a row is the sum of the probabilities of getting all heads and getting all tails.

P(all heads or all tails) = P(all heads) + P(all tails)

Since the coin flips are independent events, we can use the multiplication rule to find the probability of getting all heads or all tails:

P(all heads) = (1/2)¹⁰ = 1/1024

P(all tails) = (1/2)¹⁰ = 1/1024

So, the probability of getting all heads or all tails is:

P(all heads or all tails) = P(all heads) + P(all tails)

= 1/1024 + 1/1024

= 1/512

Therefore, if a  coin is flipped 10 times  then the probability that it will show all heads or all tails is 1/512.

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Answer: D) 0, one real solution

A quadratic function is given of the form:

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

We can find the roots of this equation using the quadratic formula:

[tex]x_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

Where [tex]\Delta=b^2-4ac[/tex] is named the discriminant. This gives us information about the roots without computing them. So, arranging our equation we have:

[tex]4a^2-4a-6=-7 \\ \\ Adding \ 7 \ to \ both \ sides \ of \ the \ equation: \\ \\ 4a^2-4a-6+7=-7+7 \\ \\ 4a^2-4a+1=0 \\ \\ Then \ the \ discriminant: \\ \\ \Delta=(-4)^2-4(4)(1) \\ \\ \Delta=16-16 \\ \\ \boxed{Delta=0}[/tex]

Since the discriminant equals zero, then we just have one real solution.

Answer: D) -220, no real solution

In this exercise, we have the following equation:

[tex]-r^2-2r+14=-8r^2+6[/tex]

So we need to arrange this equation in the form:

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

Thus:

[tex]-r^2-2r+14=-8r^2+6 \\ \\ Adding \ 8r^2 \ to \ both \ sides \ of \ the \ equation: \\ \\ -r^2-2r+14+8r^2=-8r^2+6+8r^2 \\ \\ Associative \ Property: \\ \\ (-r^2+8r^2)-2r+14=(-8r^2+8r^2)+6 \\ \\ 7r^2-2r+14=6 \\ \\ Subtracting \ 6 \ from \ both \ sides: \\ \\ 7r^2-2r+14-6=6-6 \\ \\ 7r^2-2r+8=0[/tex]

So the discriminant is:

[tex]\Delta=(-2)^2-4(7)(8) \\ \\ \Delta=4-224 \\ \\ \boxed{\Delta=-220}[/tex]

Since the discriminant is less than one, then there is no any real solution

Answer: C) 144

What we need to find is the value of [tex]c[/tex] such that:

[tex]x^2+24x+c=0[/tex]

is a perfect square trinomial, that are given of the form:

[tex]a^2x^2\pm 2axb+b^2[/tex]

and can be expressed in squared-binomial form as:

[tex](ax\pm b)^2[/tex]

So we can write our quadratic equation as follows:

[tex]x^2+2(12)x+c \\ \\ So: \\ \\ a=1 \\ \\ b=12 \\ \\ c=b^2 \therefore c=12^2 \therefore \boxed{c=144}[/tex]

Finally, the value of [tex]c[/tex] that completes the square is 144 because:

[tex]x^2+24x+144=(x+12)^2[/tex]

Answer: C) [tex]\frac{121}{4}[/tex]

What we need to find is the value of [tex]c[/tex] such that:

[tex]z^2+11z+c=0[/tex]

So we can write our quadratic equation as follows:

[tex]z^2+2\frac{11}{2}z+c \\ \\ So: \\ \\ a=1 \\ \\ b=\frac{11}{2} \\ \\ c=b^2 \therefore c=\left(\frac{11}{2}\left)^2 \therefore \boxed{c=\frac{121}{4}}[/tex]

Finally, the value of [tex]c[/tex] that completes the square is [tex]\frac{121}{4}[/tex] because:

[tex]z^2+11z+\frac{121}{4}=(x+\frac{11}{2})^2[/tex]

In this problem, we need to find the length and width of a rectangle. We are given the area of the rectangle, which is 45 square inches. We know that the formula of the area of a rectangle is:

[tex]A=L\times W[/tex]

From the statement we know that the length of the rectangle is is one inch less than twice the width, this can be written as:

[tex]L=2W-1[/tex]

So we can introduce this into the equation of the area, hence:

[tex]A=L\times W \\ \\ \\ Where: \\ \\ W:Width \\ \\ L:Length[/tex]

[tex]A=(2W-1)(W) \\ \\ But \ A=45: \\ \\ 45=(2W-1)(W) \\ \\ Distributive \ Property:\\ \\ 45=2W^2-W \\ \\ 2W^2-W-45=0 \\ \\ Quadratic \ Formula: \\ \\ x_{12}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{1}=\frac{-(-1)+ \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{1}=\frac{1+ \sqrt{1+360}}{4} \therefore W_{1}=5 \\ \\ W_{2}=\frac{-(-1)- \sqrt{(-1)^2-4(2)(-45)}}{2(2)} \\ \\ W_{2}=\frac{1- \sqrt{1+360}}{4} \therefore W_{2}=-\frac{9}{2}[/tex]

The only valid option is [tex]W_{1}[/tex] because is greater than zero. Recall that we can't have a negative value of the width. For the length we have:

[tex]L=2(5)-1 \\ \\ L=9[/tex]

Finally:

[tex]The \ length \ is \ 9 \ inches \\ \\ The \ width \ is \ 5 \ inches[/tex]

The distance in miles between mars and a satellite is given by the equation:

[tex]d=-9t^2+776[/tex]

where [tex]t[/tex] is the number of hours it has fallen. So we need to find when the satellite will be 452 miles away from mars, that is, [tex]d=452[/tex]:

[tex]d=-9t^2+776 \\ \\ 452=-9t^2+776 \\ \\ 9t^2=776-452 \\ \\ 9t^2=324 \\ \\ t^2=\frac{324}{9} \\ \\ t^2=36 \\ \\ t=\sqrt{36} \\ \\ \boxed{t=6h}[/tex]

Finally, the satellite will be 452 miles away from mars in 6 hours.

Answer:

  7.  x=8

  8.  x=7

Step-by-step explanation:

7.  The segment marked 30 is bisected by the segment marked x. So, you have a right triangle with legs x and 15 and hypotenuse 17. The Pythagorean theorem applies:

  x^2 + 15^2 = 17^2

  x^2 = 289 -225 = 64

  x = √64 = 8

__

8. The arc subtended by the chord x is 360° -230° -65° = 65°. Since this is the same measure as the arc subtended by the chord of length 7, x will also be of length 7.

___

In fact, this geometry is impossible. The combination of circle radius, arc measure, and chord length cannot be obtained all in the same circle. The answer you get will depend on how you work the problem.

Answer:

  64

Step-by-step explanation:

From a given point outside the circle, the two tangents to the circle are the same length. This means: JB = JA, CL = AL, and BK = CK.

The perimeter is the sum of all these segments, so is ...

  P = JB +JA +CL +AL +BK +CK = 8 +8 +13 +13 +11 +11

  = 2(8 +13 +11) = 2(32)

  P = 64

The perimeter of the triangle is 64 units.

Answer:

See explanation

Step-by-step explanation:

1. R is the set of all integers with absolute value less than 10, thus

[tex]R=\{a\in \mathbb{Z}\ :\ |a|<10 \}=\\ \\=\{-9,\ -8,\ -7,\ -6,\ -5,\ -4,\ -3,\ -2,\ -1,\ 0,\ 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9\}[/tex]

2. A is its subset containing all natural numbers less than 10, thus

[tex]A\subset R\\ \\A=\{b\in \mathbb{N}\ :\ b<10\}=\{1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9\}[/tex]

3. B is the set of all integer solutions of inequality 2x+5<9 that are less than 10 by absolute value (and therefore, it is also a subset of R). First, solve the inequality:

[tex]2x+5<9\\ \\2x<9-5\\ \\2x<4\\ \\x<2[/tex]

Thus,

[tex]B\subset R\\ \\B=\{c\in \mathbb{Z}\ :\ 2c+5<9,\ |c|<10\}=\{c\in \mathbb{Z}\ :\ c<2,\ |c|<10\}=\\ \\=\{-9,\ -8,\ -7,\ -6,\ -5,\ -4,\ -3,\ -2,\ -1,\ 0,\ 1\}[/tex]

See the diagram in attached diagram.

Note that

[tex]A\cup B=R\\ \\A\cap B=\{1\}.[/tex]

8 squared=(x+12)x

8 squared = x squared + 12x

52 = x squared

So x= the square root of 52

Answer:

The rate of change of the area of the circle when the radius is 4 meters = 2 meters²/minute ⇒ answer 4

Step-by-step explanation:

* Lets revise the chain rule in the derivative

- If dy/da = m and dx/da = n, and you want to find dy/dx

∴ dy/dx = dy/da ÷ dx/da = m ÷ n = m/n

* In our problem we have

- The rate of increasing of the circumference dC/dt = 0.5 meters/minute

- We need the find the rate of change of the area of the circle

 when the radius is 4 meters

- The common element between the circumference and the area

 of the circle is the radius of the circle

* We must to find dC/dr and dA/dr and use the chain rule to

 find dA/dr

- Find the rate of change of the radius dr/dt

∵ C = 2πr

- Find the derivative of C with respect to r

∴ dC/dr = 2π ⇒ (1)

∵ dC/dt = 0.5 meters/minute ⇒ (2)

- Divide (1) by (2) to get dr/dt by using chain rule

∵ dC/dt ÷ dC/dr = 0.5 ÷ 2π

∴ dC/dt × dr/dC = 0.5 × 1/2π ⇒ cancel dC together and change

   0.5 to 1/2

∴ dr/dt = 1/2 × 1/2π = 1/4π ⇒ (3)

- Find the rate of change of the area dA/dt

∵ A = πr²

- Find the derivative of A with respect to r

∴ dA/dr = 2πr

∵ r = 4

∴ dA/dr = 2π(4) = 8π ⇒ (4)

- Multiply (4) by (3) to get dA/dt by using chain rule

∵ dA/dr × dr/dt = 8π × 1/4π ⇒ divide 8 by 4 and cancel π

∴ dA/dt = 2 meters²/minute

* The rate of change of the area of the circle when the radius is

  4 meters = 2 meters²/minute

The rate of change of the area of the circle when the radius is 4 meters is 2m²/min

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

where:

r is the radius of the circle

The rate of change of circumference is expressed as:

[tex]\frac{dC}{dt} = \frac{dC}{dr} \times \frac{dr}{dt} \\0.5=2 \pi \times \frac{dr}{dt}\\ \frac{dr}{dt} = \frac{0.5}{2\pi} \\ \frac{dr}{dt} = 0.0796 m/min[/tex]

The change in area of the circle is expressed as:

[tex]\frac{dA}{dt} = \frac{dA}{dr} \times \frac{dr}{dt}\\ \frac{dA}{dt} =2 \pi r\times 0.0796\\ \frac{dA}{dt} = 2(3.14)(4)\times 0.0796\\ \frac{dA}{dt} = 2m^2/min\\[/tex]

Hence the rate of change of the area of the circle when the radius is 4 meters is 2m²/min

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Answer:

  Equations A and C are equivalent, and of those, equation C is in the form most useful ...

Step-by-step explanation:

In standard form, the equations are ...

Equation A: y = 3x² -6x +21

Equation B: y = 3x² -6x +18

Equation C: y = 3x² -6x +21 . . . . equivalent to A

Equation D: y = 3x² -6x +24

__

Equation C is in vertex form, so the vertex (extreme value) can be read directly from the equation. It is (x, y) = (1, 18).

Equations A and C are equivalent; equation C is most useful for finding the vertex.

Answer with explanation:

→→Two equations or two polynomials are said to be equivalent, if written in distinct ways, and real value of variables is substituted in both equivalent and Original Polynomial, the numerical value of both the polynomials are Same.

→→The four Quadratic Polynomials are:

[tex]1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\2.\text{Equation} B: y = 3x^2 - 6 x + 18\\\\3.\text{Equation} C: y = 3(x-1)^2 +18=3(x^2-2 x +1)+18\\\\y=3x^2 - 6 x +18+3\\\\y=3x^2 - 6 x +21\\\\3.\text{Equation} C: y = 3(x-1)^2 +21[/tex]

→→If you will look at Equation A and Equation C, both the equation are Quadratic, Coefficient of x², Coefficient of x, as well as , constant term is same in both the equation.So, Equation A, and Equation C, are equivalent.

→→If you will look at the function,

[tex]y=3\times (x-1)^2+18\\\\y-18=3\times(x-1)^2[/tex]

at, x=1, y=18, which is extreme value of the function, as at vertex of the parabola , Parabola attains it's Maximum value.

⇒⇒Equations A and C,

[[tex]1.\text{Equation} A: y = 3x^2 - 6 x + 21\\\\3.\text{Equation} C: y = 3(x-1)^2 +18[/tex]]

are equivalent, and of those, equation is in the form most useful for identifying the extreme value is [tex]3.\text{Equation} C: y = 3(x-1)^2 +18[/tex]]  function it defines.

Hello there! The x-intercept is 6.

The x-intercept is when the y value id equal to zero, and the line crosses the x axis. In this example, you can see that the line passes through x at the value of 6, making that your answer.

I hope this was helpful and have a great rest of your day!

Answer: LAST OPTION.

Step-by-step explanation:

You need to remember that a line intercepts the x-axis when y is equal to zero ([tex]y=0[/tex])

Knowing this and given the graph of the line [tex]2x -3y = 12[/tex], you can observe in the figure attached that this line intercepts the x-axis at this point:

[tex](6,0)[/tex]

Where:

 [tex]x=6[/tex] and  [tex]y=0[/tex]

Therefore, you can identify that the x-intercept is the x-coordinate of this point, which is:

[tex]x=6[/tex]

This matches with the last option.

Answer:

Step-by-step explanation:

Let t represent the time driving at 50 mi/h. Then her total distance driven (in miles) is ...

  distance = speed · time

  290 = 50t + 45(6-t)

  20 = 5t . . . . . . . . . . . subtract 270, collect terms

  4 = t . . . . . . divide by the coefficient of t

Taylor drove 4 hours at 50 miles per hour, then 2 hours at 45 miles per hour.

Answer:

  about 0.254

Step-by-step explanation:

The light is red for 0.3 of the period, so that is the probability one car is stopped. Probability 3 cars are stopped and 5 are not is 0.3^3·0.7^5, about 0.004538. In the group of 8 cars, there are 56 different ways 3 of the cars can be stopped, so your overall probability could be 56·0.004538 ≈ 0.254.

_____

Comment on the question

Many factors go into a driver's decision to stop at a light. Many factors go into the distribution of arrival times at a light. Here, the problem is only tractable if we assume that cars arrive at the light individually and at random times with respect to the light's fixed 50-second cycle. (This is possibly the case only early in the morning hours when traffic is at its lightest (not associated with bar closings or night shift changes).)

Explanation:

Each row in Pascal's triangle is a listing of the values of nCk = n!/(k!(n-k)!) for some fixed n and k in the range 0 to n. nCk is the number of combinations of n things taken k at a time.

If you consider what happens when you multiply out the product (a +b)^n, you can see where the coefficients nCk come from. For example, consider the cube ...

  (a +b)^3 = (a +b)(a +b)(a +b)

The highest-degree "a" term will be a^3, the result of multiplying together the first terms of each of the binomials.

The term a^b will have a coefficient that reflects the sum of all the ways you can get a^b by multiplying different combinations of the terms. Here they are ...

Adding these three products together gives 3a^2b, the second term of the expansion.

For this cubic, the third term of the expansion is the sum of the ways you can get ab^2. It is essentially what is shown above, but with "a" and "b" swapped. Hence, there are 3 combinations, and the total is 3ab^2.

Of course, there is only one way to get b^3.

So the expansion of the cube (a+b)^3 is ...

  (a +b)^3 = a^3 + 3a^2b +3ab^2 +b^3 . . . . . with coefficients 1, 3, 3, 1 matching the 4th row of Pascal's triangle.

__

In short, the values in Pascal's triangle are the values of the number of combinations of n things taken k at a time. The coefficients of a binomial expansion are also the number of combinations of n things taken k at a time. Each term of the expansion of (a+b)^n is of the form (nCk)·a^(n-k)·b^k for k =0 to n.

The values in Pascal's triangle are the coefficients in the binomial expansion of (x+y)^n. Each row in the triangle represents the coefficients for a certain power of the binomial being expanded.

In mathematics, Pascal's triangle is a triangular array of numbers where each number is the sum of the two immediately above it. Each row of Pascal's Triangle corresponds to the coefficients in the binomial expansion of (x+y)n. For example, the third row of the Pascal's triangle is 1, 2, 1, which are the coefficients for the expansion of (x+y)2, yielding x2 + 2xy + y2. To put it differently, the values in Pascal's triangle provide the coefficients for each term in the binomial expansion. The index of the row in the triangle indicates the power of the binomial being expanded. So, effectively, the values in Pascal’s triangle connect directly to the coefficients in an algebraic binomial expansion.

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Answer:

2 4/16 = 2 1/4 lb

Step-by-step explanation:

The pointer is 4 of the smallest units above 2. There are 16 of those small units. Each 2 of those units is 1/8 pound, so when the pointer is on a multiple of 2 units, it is on a multiple of 1/8 pound. No guesswork is required to choose the correct weight to the nearest 1/8 pound.

2 4/16 = 2 1/4 lb . . . . the scale reading to the nearest 1/8 pound.

D. it is correct because the length of the unknown side is the difference of the squares of the sides.

Answer:

It is correct because the length of the unknown side is the difference of the squares of the sides.

Step-by-step explanation:

Answer:

The answer is 3 8/15 miles.

Hope I helped ; )

Answer:

your answer will be 3 8/15

Step-by-step explanation:

Area of parallelogram(A) = base×hight

=4.7×3.3=15.51 sq. cm

Answer:

[tex]Area=15.51cm^2[/tex]

Step-by-step explanation:

The given figure is a parallelogram.

The area of a parallelogram is calculated using the formula:

[tex]Area=b\times h[/tex]

The base of the 4.7 cm.

The height is 3.3 cm.

We substitute the given values into the formula to obtain;

[tex]Area=4.7\times 3.3[/tex]

We multiply out to obtain;

[tex]Area=15.51cm^2[/tex]

Answer:

[tex]9\ years[/tex]

Step-by-step explanation:

Let

P----> the initial price of the ticket

y ---> the price of the ticket after t years

t---> the time in years

we know that

100%+8%=108%=108/100=1.08

so

[tex]y=P(1.08)^{t}[/tex] ----> equation A

If the price is doubled

then

[tex]y=2P[/tex] -----> equation B

equate equation A and equation B and solve for t

[tex]2P=P(1.08)^{t}[/tex]

Simplify

[tex]2=(1.08)^{t}[/tex]

Apply log both sides

[tex]log(2)=t*log(1.08)[/tex]

[tex]t=log(2)/log(1.08)=9\ years[/tex]

It will take approximately 9 years for the price of theater tickets to double at an annual increase of 8%.

To solve this problem, we can use the Rule of 70, which is a quick and easy way to estimate the number of years required for a quantity to double at a constant growth rate. The Rule of 70 is given by the formula:

[tex]\[ \text{Years to double} \approx \frac{70}{\text{Annual growth rate}} \][/tex]

Given that the annual growth rate is 8%, we can apply this formula:

[tex]\[ \text{Years to double} \approx \frac{70}{8} \] \[ \text{Years to double} \approx 8.75 \][/tex]

Since we cannot have a fraction of a year in this context, we round to the nearest whole number. Therefore, it will take approximately 9 years for the price to double.

Answer:

The parent function for a concave up parabola with its vertex at the origin is

y=a(x-h)^2+k.

+a points the parabola concave up

-a points the parabola concave down

h moves the vertex along the x axis that many times

k moves the vertex along the y axis that many times.

if you need more clarification comment on this question.

Answer:

The required functions are [tex]f(x)=x^2+3[/tex], [tex]g(x)=2x^2-3[/tex], [tex]h(x)=x^2-3[/tex] and [tex]j(x)=-2x^2-3[/tex].

Step-by-step explanation:

The vertex from of a parabola is

[tex]y=a(x-h)^2+k[/tex]

Where, (h,k) is the vertex of parabola is a is the vertical stretch factor.

If a is negative, then it is downward parabola and if a is positive then it is an upward parabola.

If |a|<1, then it is compressed vertical and if |a|>1, then it is stretched vertically.

The graph of f(x) has vertex at (0,3) and it is not stretch vertically so the value of a is 1. So, the function f(x) is defined as

[tex]f(x)=1(x-0)^2+3[/tex]

[tex]f(x)=x^2+3[/tex]

The graph of g(x) has vertex at (0,-3) and it is stretch vertically by factor 2 so the value of a is 2. So, the function g(x) is defined as

[tex]g(x)=2(x-0)^2-3[/tex]

[tex]g(x)=2x^2-3[/tex]

The graph of h(x) has vertex at (0,-3) and it is not stretch vertically so the value of a is 1. So, the function h(x) is defined as

[tex]h(x)=1(x-0)^2-3[/tex]

[tex]h(x)=x^2-3[/tex]

The graph of j(x) has vertex at (0,-3) and it is stretch vertically by factor 2 and it is downward so the value of a is -2. So, the function j(x) is defined as

[tex]j(x)=-2(x-0)^2-3[/tex]

[tex]j(x)=-2x^2-3[/tex]

Therefore the required functions are [tex]f(x)=x^2+3[/tex], [tex]g(x)=2x^2-3[/tex], [tex]h(x)=x^2-3[/tex] and [tex]j(x)=-2x^2-3[/tex].

Answer:

  16/(3(x+1))

Step-by-step explanation:

We can factor the denominator of the second term, which lets us see how to combine terms:

[tex]\displaystyle\frac{7}{x+1}-\frac{5}{3x+3}=\frac{7}{x+1}-\frac{5}{3(x+1)}\\\\=\frac{3\cdot 7}{3(x+1)}-\frac{5}{3x+3}=\frac{21-5}{3(x+1)}=\frac{16}{3(x+1)}[/tex]

Answer:

D

Step-by-step explanation:

9.6 is a floating-point number, therefore, not a integer.

Answer:

d

Step-by-step explanation:

Answer:

Alyssa walked 200 ft more than Miki.

Step-by-step explanation:

According to the Pythagorean theorem formula if we square the a(400) and b(300) and add them both we would get 250,000. From then you square root it to 500. So Miki walked 500ft and Alyssa walked 700ft (400+300). Subtract 500 from 700 and you would get 200ft.

Answer:

  A. Step 1: Multiply 1 × 5.

  Step 2: Multiply 2 × 3.

  Step 3: Add the two products.

Step-by-step explanation:

The total number of miles hiked will be the sum of the numbers of miles hiked each day. Each day, the number of miles hiked can be computed by multiplying time by speed:

  distance = speed × time

So, the total number of miles hiked is ...

  total miles = miles on day 1 + miles on day 2 . . . . . (sum, not a difference—eliminates choice B)

  total miles = (speed on day 1)×(time on day 1) + (speed on day 2)×(time on day 2) . . . . . (sum of products—eliminates choices C and D)

Choice A correctly describes the computation.

if you want to find out how money you have left then you are supposed to subtract the spent money from the total money.

$42.69-$9.45= $33.24

$33.24- $14.35= $18.89

you have $18.89 of your money left and you have spent $23.80.

Hope this helps