Tennis balls are packaged into cylindrical cans to ship and sell. Three tennis balls fit into one cylinder so that the height of the three balls is equal to the height of the cylinder. and the diameter of one ball is equal to the diameter of the cylinder. The radius of one tennis ball is 1.3 inches. How much air space is in the cylinder around the tennis balls?

Answer:

Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical and horizontal stretch with reflection

- A vertical stretching is the stretching of the graph away from the

 x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

 by multiplying each of its y-coordinates by k.

- If k should be negative, the vertical stretch is followed by a reflection

 across the x-axis  

- A horizontal stretching is the stretching of the graph away from

 the y-axis

- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally

 stretched by dividing each of its x-coordinates by k.

- If k should be negative, the horizontal stretch or shrink is followed

 by a reflection in the y-axis

* Lets solve the problem

∵ G(x) = sin x

∵ F(x) = -5.8 sin x

∴ F(x) = -5.8 G(x)

- From the rule above

∴ G(x) is stretched vertically by scale factor -5.8

∵ The scale factor is negative

∴ The vertical stretch is followed by a reflection across the x-axis  

* The transformation is:

  Vertical stretch by a factor of 5.8 , reflection across x-axis

To obtain the graph of f(x) = -5.8sin x from g(x) = sin x, a vertical stretch by a factor of 5.8 and a reflection across the x-axis are required.

To transform the graph of the function g(x) = sin x into the graph of f(x) = -5.8sin x, two main transformations are required:

Option B (vertical stretch by a factor of 5.8 and reflection across the x-axis) correctly describes the required transformations to obtain the graph of f(x) from the graph of g(x).

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the first 3 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]\bf A=20000\left(1+\frac{0.06}{1}\right)^{1\cdot 3}\implies A=20000(1.06)^3\implies \boxed{A=2382.032} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Compound Interest Earned Amount \underline{for the next 4 years}}[/tex]

[tex]\bf A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2382.032\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]\bf A=2382.032\left(1+\frac{0.08}{1}\right)^{1\cdot 4}\implies A=2382.032(1.08)^4\implies \boxed{A\approx 3240.73} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{amount for this period}}{2382.032+3240.73}\implies 5622.762[/tex]

Answer:

  180 minutes

Step-by-step explanation:

Starting with the distance formula ...

  d = rt

dividing by the coefficient of t will give an equation for t:

  t = d/r

Ryan's rate of 4 miles per hour can be expressed in minutes as 4 miles per 60 minutes. The Ryan's time is ...

  t = (12 mi)/(4 mi/60 min) = 12·60/4 min = 180 min

Ryan's time is 180 minutes.

Answer:

180 MINUTES

Step-by-step explanation:

I TOOKTHE TEST ON FLVS

Hello There!

Divide by 3 each time

so

#1 is 9, because 27/3 = 9

#2 is 3, because 9/3 = 3

#3 is 1, because 3/3 = 1

So your answer is 9, 3, 1

Answer:

x² + 8x + 16

Step-by-step explanation:

You can draft the Pascal's Triangle as below;

                                             Exponent

                  1-----------------------0

               1     1  -------------------1

             1   2    1 ------------------2

            1  3   3   1 -----------------3

According to the question, we use values for exponent 2 because (a+b)²

Given  (x+4)²...................................expand

x² × 4⁰ + x¹ × 4¹+ x⁰ × 4²

x² × 1 + x × 4 + 1 × 16

x² + 4x + 16---------------------------------introduce values in exponential 2 of the table which are 1  2  1

x² × 1 + 2 × 4x + 16 × 1

⇒ x² + 8x + 16

Answer:

The answer is the 2nd one

Step-by-step explanation:

A dilation is a transformation in which the lines connecting every point P with its image P' all intersect at a point C.

C is called the center of dilation, and CP'/CP is the same for every point P.

The only picture where the objects are similar and the image has not been rotated or reflected is

It is also seen from the picture that all the faces of the first figure appears to be parallel to all the faces of the second figure. Thus, CP'/CP is the same for every point P.

Therefore, the transformation in the picture above appears to be a dilation.

The transformation in the picture above appears to be a dilation is option 2nd.

Dilation of a figure will leave its sides get scaled (multiplied) by same number. That number is called the scale factor of that dilation.

Its also called scaling of a figure, but due the involvement of coordinates, it involves a center of a dilation, which is like a pinned point which stays at same place after dilation.

Its like we enlarge or shorten the size of the figure (or keep it same, when scale factor = 1).

C is called the center of dilation, and CP'/CP is the same for every point P.

It is also seen from the picture that all the faces of the first figure appear to be parallel to all the faces of the second figure.

Thus, CP'/CP is the same for every point P.

Therefore, the transformation in the picture above appears to be a dilation is option 2nd.

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Answer: D

Step-by-step explanation:

Answer:  The correct option is

(D) x represents the number of level 1 tickets; y represents the number of level 2 tickets

Step-by-step explanation:  Given that a sports team came to town. The stadium filled all 10,000 seats at two-level pricing. Level 1 tickets are $50 each, and level 2 tickets are $150 each. The stadium made $75,000 in ticket sales.

The system of equations that models this scenario is:

x + y = 10,000

50x + 150y = 75,000

We are to find the terms that x and y represents.

Since the total number of seats is 10000 and it is given that x + y = 10000, so x and y represents the number of tickets.

Also, since the price of one level 1 tickets is $50 and that of one level 2 ticket is $150 and 50x + 150y = 75000, so

x represents the number of level 1 tickets; y represents the number of level 2 tickets.

Thus, (D) is the correct option.

Answer:

B

Step-by-step explanation:

The area of the shaded sector Rounded to the nearest tenth, is 22.5

Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.

If the entire circle was shaded the radius sweeping out the circle would go through 360 degrees.

Too solve this problem is to multiply the entire area of the circle by (81/360)

Area of the sector = (81/360) x  π x r^2

π = 3.14

r = cm

Area of the sector = (81/360) x 3.14 x 8.91^2

Area of the sector = 22.5

The area is 22.5 m2

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Answer:

  (-2, 2)

Step-by-step explanation:

You can graph the equations and points and see which points fall into the doubly-shaded area. The only one that does is (-2, 2).

___

You can also evaluate the inequalities at the given points to see which might work. The inequality y > x is the simplest to evaluate, and it immediately eliminates the last two choices:

  -3 > -1 . . . not true

  -1 > 0 . . . not true

So, we can check the first two choices in the first inequality:

  -(-3) +1 > 5 . . . not true

  -(-2) +1 > 2 . . . TRUE

The ordered pair (-2, 2) makes both inequalities true.

Answer:

2nd Option is correct.

Step-by-step explanation:

Given Inequalities are,

y < x + 1  .....................(1)

y > x .....................(2)

To find: Ordered pair which makes he inequalities true.

Pair 1:

x = -3 , y = 5

Inequality (1),

LHS = 5

RHS = -(-3) + 1 = 4

⇒ LHS > RHS

Thus, this pair does not satisfy the pair of inequalities.

Pair 2:

x = -2 , y = 2

Inequality (1),

LHS = 2

RHS = -(-2) + 1 = 3

⇒ LHS < RHS

Inequality (2),

LHS = 2

RHS = -2

⇒ LHS > RHS

Thus, this pair satisfies the pair of inequalities.

Pair 3:

x = -1 , y = -3

Inequality (1),

LHS = -3

RHS = -(-1) + 1 = 0

⇒ LHS < RHS

Inequality (2),

LHS = -3

RHS = -1

⇒ LHS < RHS

Thus, this pair does not satisfy the pair of inequalities.

Pair 4:

x = 0 , y = -1

Inequality (1),

LHS = -1

RHS = -(0) + 1 = 1

⇒ LHS < RHS

Inequality (2),

LHS = -1

RHS = 0

⇒ LHS < RHS

Thus, this pair does not satisfy the pair of inequalities.

Therefore, 2nd Option is correct.

Answer:

1/2 is the answer (actually, it's ±1/2)

Step-by-step explanation:

The identity you need here is for a half angle of tangent.  That identity is as follows:

[tex]tan(\frac{\theta }{2})=[/tex]±[tex]\sqrt{\frac{1-cos\theta }{1+cos\theta } }[/tex]

If we need the cos of that angle, we need to find the missing hypotenuse.  Applying Pythagorean's Theorem to that right triangle, we get that the hypotenuse is 5.  The cos of the angle is 3/5.  Filling in the formula, using only the principle root since you have not allowed for the negative in the choices you gave:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1-\frac{3}{5} }{1+\frac{3}{5} } }[/tex]

Turning each one of those 1's into 5/5 we combine the fractions to simplify to:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{\frac{2}{5} }{\frac{8}{5} } }[/tex]

Bringing up the lower fraction and flipping to multiply gives us:

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{2}{5}*\frac{5}{8}  }[/tex]

Canceling out the 5's and reducing the remaining fraction gives us

[tex]tan(\frac{\theta }{2})=\sqrt{\frac{1}{4} }[/tex]

and since the square root of 4 is 2, we end with a solution of 1/2

Answer:

1/36

Step-by-step explanation:

Bonnie uses 12×6" = 72" of wire to make her cube.

Roark uses 12×1" = 12" of wire to make each of his cubes. He must make 6³ = 216 cubes to match the volume of Bonnie's cube.

The ratio of wire lengths is then ...

72/(12×216) = 6/6³ = 1/6² = 1/36

Answer: 2l+2w

Step-by-step explanation:

Answer:21 plus 2w

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

Here we are given that the number of convertibles cars. Total number of cars owned by the dealers is 90. We have to draw the pie graph for above ratio. The pie chart is a circular statistical graph , where the different portion in form of sectors on the circle showing the amount of different entities.

The angle covered by an entity is in the same proportion as its number is in ration to the total number of all the entities.

Hence

[tex]\frac{15}{90}=\frac{\theta}{360}\\\\\theta=\frac{15*360}{90}\\\theta=\frac{15*4}{1}\\\theta=60\\[/tex]

Hence we will represent 60 degrees in order to represent 15 cars in our chart.

To represent convertibles on the pie graph, calculate the proportion of convertibles sold to the total number of cars sold (15/90) and multiply by the total degrees in a circle (360). Convertibles should be represented by a 60-degree slice on the pie graph.

The question is asking how to calculate the degree measure for the convertibles slice in a pie chart based on the total sales in a month. We know that a pie chart represents 100% of a data set, with the entire chart being a 360-degree circle. To find the degree measure for the convertibles, we would perform a proportion calculation based on the number of convertibles sold (15) out of the total number of cars sold (90). The calculation is as follows:

Proportion of convertibles to total sales = (Number of convertibles sold / Total cars sold) = 15 / 90

Now, multiply this proportion by the total degrees in a circle to get the degree measure for convertibles:

Degree measure for convertibles = Proportion of convertibles imes Total degrees in a circle = (15 / 90) * 360 = 1/6 * 360 = 60 degrees

Therefore, the convertibles should be represented by a 60-degree slice on the Pie Graph.

Answer: [tex]15.57\°[/tex]

In order to understand better this problem, we can use the figure attached, in which we have a right triangle (with a 90 degree angle), where [tex]c[/tex] is its hypotenuse, [tex]a[/tex] is the adjacent side to the angle of elevation [tex]\theta[/tex] from the boat to the top of the lighthouse and [tex]b[/tex] is the opposite side to [tex]\theta[/tex].

Knowing this, we will use the tangent trigonometric function to find [tex]\theta[/tex]:

[tex]tan\theta=\frac{oppositeside}{adjacentside}=\frac{b}{a}[/tex]   (1)

[tex]tan\theta=\frac{34m}{122m}[/tex]   (2)

[tex]tan\theta=0.278[/tex]   (3)

[tex]\theta={tan}^{-1} (0.278)[/tex]   (4)

Finally:

[tex]\theta=15.572\°[/tex]  

Answer:

16

Step-by-step explanation:

A boat is 122 meters from the base of a lighthouse that is 34 meters above sea level. What is the angle of elevation from the boat to the top of the lighthouse? Round to the nearest degree.

Answer:

the first one is 350 inches (350 in) and the second on is 350 square inches (350 in2)

Step-by-step explanation:

Answer:

-1/10, -1/5 , -2/5 or -2/5, -1/5 , -1/10

Step-by-step explanation:

let a/r, a, ar  be the first 3 terms of the geometric series

their product would be equal to a^3

a^3=-1/125

a=-1/5

Substitute a=-1/5 into the first 3 terms

-1/5r + -1/5+-r/5=-7/10

Multiply the terms such that they have a common denominator:

-1/5r +-r/5r + -r^2/5r = -3.5r/5r

Multiply both sides by 5r

-r^2-r-1=-3.5r

Add 3.5r to both sides and multiply the equation by 2

-2r^2 + 5r -2=0

Factorize the equation

(2r-1)(r-2)=0

r=0.5 or r-2

For the first three terms where r=0.5

-2/5, -1/5 , -1/10

For the first three terms where r=2

-1/10, -1/5 , -2/5

Answer:

C:  (x + 4)(x - 1)

Step-by-step explanation:

Please use " ^ " to indicate exponentiation.  Thanks.

x2 + 3x – 4 →  x^2 + 3x - 4 = (x + 4)(x - 1)      This matches Answer C.

ANSWER

a=3, b=5

EXPLANATION

The given equation is

[tex] \frac{3}{x} + \frac{5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]

We simplify the left hand side.

We collect LCD to obtain:

[tex] \frac{3x + 5}{ {x}^{2} } = \frac{ax + b}{ {x}^{2} } [/tex]

Both sides of the equation are now the same.

By comparing the coefficients of x, we have

[tex]a = 3[/tex]

By comparing the constant terms

[tex]b = 5[/tex]

Answer:

For the first part

A=3

B=5

For the second part

M=3

N=14

P=2

Step-by-step explanation:

Right on edge 2020

1. The first step to solving this problem is to find the values of x and y. This can be done in a multitude of different ways, however I will go with the method of substitution.

Thus, the first thing we must do is write out both equations and rearrange one of them so that either x or y is the subject of the equation. Looking at the two equations, I can see that in the second equation this would be easier, and that we could also simplify the first equation a little further. Thus:

a) Collecting like terms to simplify equation 1:

4x + 3y = 14 - y

4x + 4y = 14 (Add y to both sides)

b) Rearranging equation 2 to make x the subject:

x - 5y = 2

x = 2 + 5y (Add 5y to both sides)

Now, we can substitute x = 2 + 5y into the first equation:

4x + 4y = 14

if x = 2 + 5y:

4(2 + 5y) + 4y = 14

8 + 20y + 4y = 14 (Expand 4(2 + 5y))

8 + 24y = 14 (Add 20y and 4y)

24y = 6 (Subtract 8 from both sides)

y = 1/4 (Divide both sides by 24)

Now that we know that y = 1/4, we can substitute this back into x = 2 + 5y:

x = 2 + 5y

if y = 1/4: x = 2 + 5(1/4)

x = 2 + 5/4

x = 13/4

2. So now we know that x = 13/4 and y = 1/4. Given these values, we can now solve x - y as such:

x - y = 13/4 - 1/4

= 12/4

= 3

Thus, the value of x - y is 3 (answer C).

Check the picture below.

Answer:

(m-5) (n-4)

Step-by-step explanation:

mn - 4m - 5n + 20

We will factor by grouping

mn -5n  -4m +20

Factor an n out of the first 2 terms and a -4 out of the last 2 terms

n (m-5) -4(m-5)

Now factor out a m-5

(m-5) (n-4)

Answer:

B.

Step-by-step explanation:

The function is positive when it is above the x-axis

The following x values are where the function has positive y coordinates:

(-2,0)

(4,inf)

The function is negative when it is below the x-axis

The following x values are where the function has negative y coordinates:

(-inf,-2)

(0,4)

So you should see all of these intervals listed in choice B

Answer:

B

Step-by-step explanation:

Answer:

B-10=N

Step-by-step explanation:

N is the lesser number. So if B is the greater number & there is a difference of 10 this would be your expression

Expressions do not have an equal sign (although they can have operators such as plus or minus).

[tex]2x+1[/tex] is an expression.

[tex]2x+1=1[/tex] is an equation since it has an equal sign.

Answer:

Since we know that ABCD is an isosceles trapezoid, we can also asume that its diagonals have the same length, which means:

AC = BD

=> 7x - 21 = 5x + 13

=> 7x - 5x = 21 + 13

=> 2x        = 34

=> x           = 34/2 = 17

So the answer is C.

Since we know that ABCD is an isosceles trapezoid, the value of Option C. x= 17

we can also assume that its diagonals have the same length, which means:

AC = BD

=> 7x - 21 = 5x + 13

=> 7x - 5x = 21 + 13

=> 2x        = 34

=> x          = 34/2 = 17

So the answer is C.

An isosceles trapezoid is a trapezoid with congruent base angles and congruent non-parallel sides. A trapezoid is a quadrilateral with only one of its sides parallel. An isosceles trapezoid has many interesting properties that make it unique and help us differentiate it from the other quadrilaterals

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Answer:

b.

Step-by-step explanation:

We have to look at sign changes in f(x) to determine the possible positive real roots.

[tex]f(x)=-3x^4-5x^3-x^2-8x+4[/tex]

There is only one sign change here, between the -8x and the +4.  So that means there is only 1 possible real positive root.

Now we have to look at sign changes in f(-x) to determine the possible negative real roots.

[tex]f(-x)=-3x^4+5x^3-x^2+8x+4[/tex]

There are 3 sign changes here.  That means there are either 3 negative roots or 3-2 = 1 negative root.  So we have:

1 positive

3 or 1 negative

We need to pair them up now with all the possible combinations.

If we have 1 positive and 1 negative, we have to have 2 imaginary

If we have 1 positive and 3 negative, we have to have 0 imaginary

Keep in mind that the total number or roots--positive, negative, imaginary--have to add up to equal the degree of the polynomial.  This is a 4th degree polynomial, so we will have 4 roots.

Answer:

5 year  = $2,400

20 year = $18,560

Step-by-step explanation:

Firstly,

You have to identify the cash value per unit. so It 'll be  5 years = 30 dollars per unit.

Secondly,

Now, take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. so It'll be 80 times 30 is $2,400

Answer: $2,400

Now,

Just like the previous one identify the cash value per unit. so It'll be 20 years= 232 dollars per unit.

Next,

take the face value of the policy divided by 1000, to find how many units the person has. 80,000 divided by 1000 is 80. Now take the # of units time the cash value it has. 80 times 232 is $18,560

Answer:  $18,560

Answer:

Output = 8- input

Step-by-step explanation:

The first point is  (1,7)

The input is 1 and the output is 7

The lines goes down, so we know that this is subtraction

Output = 8- input

7 = 8-1

Lets check another point

(5,3)

3 = 8-5

This checks

Answer: I think it is A.

Step-by-step explanation: