A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or . Since the area of the circle is the area of the square, the volume of the cylinder equals the volume of the prism or (2r)(h) or πrh. the volume of the prism or (4r2)(h) or 2πrh. the volume of the prism or (2r)(h) or r2h. the volume of the prism or (4r2)(h) or r2h.

Answer:

The value of  annuity is [tex]P_v = \$ 32058[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 1500[/tex]

     The  interest rate  is   [tex]r = 8\% = 0.08[/tex]

     Frequency at which it occurs in a year is  n = 2 (semi-annually )

      The number of years is  [tex]t = 22 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex](reference EDUCBA website)

 substituting values

             [tex]P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ][/tex]

             [tex]P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ][/tex]

             [tex]P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ][/tex]

            [tex]P_v = \$ 32058[/tex]

Answer:

4:00 pm

Step-by-step explanation:

To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.

5:30 minus 1 hour is 4:30.

Now, subtract 30 minutes.

4:30 minus 30 minutes is 4:00.

Malik started working on his English essay at 4:00 pm.

Hope that helps.

Answer:

pleasse elaborate more

Step-by-step explanation:

First, let's figure out the pattern that this series follows. We can see that the first number is increased by 1/2 to get to 2 1/2. Then, the second number is decreased by 1 to get to 1 1/2. Finally, the pattern repeats.

So, let's apply this pattern to find the next number in this series.

2, 2 1/2, 1 1/2, 2, 1

The next number in this series is 1.

Hope this helps!! :)

Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

Answer:

  0

Step-by-step explanation:

The determinant of this matrix is zero (0).

Answer:

x = 3 ± sqrt(11)

Step-by-step explanation:

x^2 - 6x + 9 = 11

Recognizing  that this is a perfect square trinomial

(x-3) ^2 =11

Taking the square root of each side

sqrt((x-3) ^2) = ± sqrt(11)

x-3 =± sqrt(11)

Add 3 to each side

x = 3 ± sqrt(11)

Answer:

[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]

Step-by-step explanation:

Hello,

   [tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]

Do not hesitate if you have any question

Hope this helps

Answer:

The simple pendulum should be 15.9 m long.

Step-by-step explanation:

Approximately (for small amplitudes), the period of a simple pendulum is

T = 2*pi * sqrt (L/g), L=length

using pi = 22/7, and g=9.8 m/s^2

8 = 2* 22/7 * sqrt(L/9.8)

solve for L

L = (8*7/(2*22))^2 * 9.8

= 15.874 m

That's quite a long pendulum!

Answer: Diverging

Step-by-step explanation:

Find explanations in the attached file

Complete question is;

Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2005 and 2006 are as follows:

2005 Season: 73 77 78 76 74 72 74 76

2006 Season: 70 69 74 76 84 79 70 78

​A) Calculate the mean (to the nearest whole number) and the standard deviation (to decimals) of the golfer's scores, for both years.

B) What is the primary difference in performance between 2005 and 2006? What improvement,

if any, can be seen in the 2006 scores?

Answer:

A) 2006 mean = 75

2005 mean = 75

2006 standard deviation = 5.2644

2005 standard deviation = 2.0702

B)The primary difference is that variation is higher in the 2006 season than the 2005 season.

Step-by-step explanation:

A) Mean is the sum of all scores divided by the number of scores.

Thus;

μ_2005 = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8 = 75

Similarly;

μ_2006 = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8 = 75

Now, variance is calculated by the sum of the square of mean deviations divided by (n - 1)

Thus;

2005 Variance = ((73-75)² + (77-75)² + (78-75)² + (76-75)² + (74-75)² + (72-75)² + (74-75)² + (76-75)²)/(8-1) = 4.2857

2006 Variance = ((70-75)² + (69-75)² + (74-75)² + (76-75)² + (84-75)² + (79-75)² + (70-75)² + (78-75)²)/(8 - 1) = 27.7143

Now, standard deviation is the square root of variance.

Thus;

2005 standard deviation = √4.2857 = 2.0702

2006 standard deviation = √27.7143 = 5.2644

B) The primary difference is that variation is higher in the 2006 season than the 2005 season.

Also,

Answer:

The scores are equal

Step-by-step explanation:

The z-score for any normal distribution is:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

(i) Score (X) = 40

Mean (μ)= 50

Standard deviation (σ) = 10

[tex]z=\frac{40-50}{10}\\ z=-1[/tex]

(ii) Score (X) = 45

Mean (μ)= 50

Standard deviation (σ) = 5

[tex]z=\frac{45-50}{5}\\ z=-1[/tex]

Both scores have the same z-score, which means that, relative to their respective distributions, the scores are equal.

Answer:

Hey there!

An equilateral triangle has all sides equal to each other, so the perimeter would be 3x, where x is the length of one side.

Thus, the perimeter for this equilateral triangle would be 3(12)=36

Hope this helps :)

Answer:

[tex]\boxed{Perimeter = 36 \ units}[/tex]

Step-by-step explanation:

Perimeter = sum of all sides

Perimeter = 12 +12 + 12

Perimeter = 36 units

Answer:

b = 4

Step-by-step explanation:

3 - b = 6 - 7

3 - b = -1

-b = -1 -3

-b = -4

b = 4

Answer:

B y ≥ 4x + 2

Step-by-step explanation:

1. find slope of the line: (y² - y¹) / (x² - x¹)

(0, 2) and (-1, -2)

(-2 - 2) / (-1 - 0) = -4 / -1 = 4

y = 4x + 2*

*+2 because that is the y-intercept as shown by point (0, 2)

2. the line is solid, therefore the inequality is ≤ or ≥. dashed line would mean < or >

3. the shaded region is on the right side of the line, so the values are greater than. therefore, you use ≥

4. final equation: y ≥ 4x + 2

Answer:

1) 18

2) P

Step-by-step explanation:

1) Multiply the top number by itself and then reverse the digits!

9*9 = 81 reversed is 18

2) Seems to be the number of line ends a letter has when you write it down. P only has one end, at the bottom.

Answer:

P

Step-by-step explanation:

2.

The number of strokes of the letter that come to an end.

The bottom of the A has two sticks that come to an end.

A = 2

The B has no sticks coming to an end.

B = 0

The C and an upper and a lower stroke coming to an end.

C = 2

D has none.

D = 0

E has 3 sticks coming to an end.

E = 3

etc.

M has 3.

N has 2.

O has 0.

P has 1 stick coming to an end.

Q has none.

R has 2.

S has 2.

T has 3.

U has 2.

V has 2.

W has 3.

X has 4.

Y has 3

Z has 2.

Of all letters after L, only P has exactly 1 stroke coming to an end.

Answer: P

Answer:

1st blank: X axis reflection

2nd blank: Y axis reflection

Step-by-step explanation:

If you drew the first triangle and then the second triangle on a piece of paper, you would notice that it would reflect across the corresponding axis.

So the solution is to just draw it out.

Answer:

reflection across the x axis and the second is a reflection across the y axis.

Answer: (a) When he turns 68 , the account will have = $1,179,415.39

(b) $ 288,000

Step-by-step explanation:

Formula: Future value of annuity =[tex]P[\dfrac{(1+r)^n-1}{r}][/tex], where P+ periodic payment, r = rate of interest per period, n= number of periods.

As per given, we have

P= $1800

rate of interest = 6% = 0.06

(a) n= 68-28 = 40

Rate per period : r= [tex]\dfrac{0.06}{4}=0.015[/tex]  

Number of periods: n = 4x 40 =160

Now, Future value of amount when Mr. Pink turns 28 years = [tex]1800(\dfrac{(1+0.015)^{160}-1}{0.015})[/tex]

[tex]=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\$1179415.39[/tex]

Hence, when he turns 68 , the account will have = $1,179,415.39

(b) Total contribution = P × n

=1800 × 160

=$ 288,000

Hence, Total contribution =$ 288,000

Answer:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]

[tex](f/g)(2)=-4[/tex]

Step-by-step explanation:

[tex](f/g)(x)=\frac{x^4-x^3-7x^2+9x-2}{x-1} =x^3-7x+2\,\,\,for\,\,x\neq 1[/tex]  and undefined for x = 1.

Notice that (x-1) is in fact a factor of f(x), so the quotient of the two functions introduces a "hole" for the new function at x = 1.

f(2) can be found by simply evaluating the expression for x = 2:

[tex](f/g)(2)=2^3-7(2)+2=-4[/tex]

Answer: Smokers pay less attention to driving while trying to light a cigarette.

Step-by-step explanation:

( A ) reasons for, why the given statement was misleading.

Following are the reasons for accidents

(i) Drunk Driving.

(ii) Driving during the night.

(iii) Smoking.

(iv) Unsafe lane changes.

(v) Driving the wrong way.

(vi) Bad weather e.g fog.

From the list above, it is shown that, smoking is also one of the major cause of car accidents on the roads.

( B.) Smokers tends to pay less attention to driving why trying to light a cigarette.

Answer:

  φ ≈ 1.19029 radians   (≈ 68.2°)

Step-by-step explanation:

There are simple formulas for A and φ in this conversion, but it can be instructive to see how they are derived.

We want to compare ...

  y(t) = Asin(ωt +φ)

to

  y(t) = Psin(ωt) +Qcos(ωt)

Using trig identities to expand the first equation, we have ...

  y(t) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Matching coefficients with the second equation, we have ...

  P = Acos(φ)

  Q = Asin(φ)

The ratio of these eliminates A and gives a relation for φ:

  Q/P = sin(φ)/cos(φ)

  Q/P = tan(φ)

  φ = arctan(Q/P) . . . . taking quadrant into account

__

We can also use our equations for P and Q to find A:

  P² +Q² = (Acos(φ))² +(Asin(φ))² = A²(cos(φ)² +sin(φ)²) = A²

  A = √(P² +Q²)

_____

Here, we want φ.

  φ = arctan(Q/P) = arctan(5/2)

  φ ≈ 1.19029 . . . radians

Answer:

A. Cone

D. Rectangular Prism

E. Cylinder

F. Sphere

Step-by-step explanation:

Rectangular Prism is a solid three dimensional shape. It has six faces which are sides of a rectangle. It is also known as Cuboid. The rectangular prism cannot be formed with two dimensional shapes. Sphere is a geometrical object which is a three dimensional circle. This shape has a circumference so this shape cannot be formed with two dimensional shapes.

To make it easier, you can convert 7/20 to a decimal, and as a decimal it is 0.35. 0.42*0.35=0.147, so .42*7/20=0.147.

Answer:

0.147

Step-by-step explanation:

0.42 * 7/20

Well, 0.42 = 42/100. Now we have both numbers as fractions.

We can simplify 42/100 to 21/50

Therefore we have 7/20 * 21/50

To multiply fractions multiply the numerators together and multiply the denominators together.

This gives: 147 / 1000

Which is equal to 0.147

Therefore 0.42 * 7/20 = 0.147

Answer:

Optimal production = 600 gold pens

Revenue  = 600*7 = $4200 gold pens

Step-by-step explanation:

The Fine Line Pen Company makes two types of ballpoint pens: a silver model and a gold model.

A. The silver model requires 1 minute in a grinder and 3 minutes in a bonder.

B. The gold model requires 3 minutes in a grinder and 4 minutes in a bonder.

Because of maintenance procedures,

C. the grinder can be operated no more than 30 hours per week and

D. the bonder no more than 50 hours per week.

The company makes

E. $5 on each silver pen and

F. $7 on each gold pen.

How many of each type of pen should be produced and sold each week to maximize profits?

Solution:

We will solve the problem graphically, with number of silver pens, x, on the x axis, and number of gold pens, y, on the y axis, i.e.

1. From A and C, the maximum number of silver pens

x <= 30*60 / 1 = 1800 and

x <= 50*60 /3 = 1000  ....................(1)   bonder governs

2. from A & D, the maximum number of gold pens

y <= 30*60 / 3 = 600 .....................(2) grinder governs

y <= 50*60 / 4 = 750

3. From D,

x + 3y <= 30*60 = 1800  ...................(limit of grinder) ..... (3)

3x + 4y <= 50*60 = 3000 .................(limit of bonder)  .......(4)

Need to maximize profit,

Z(x,y) = 5x+7y, represented by parallel lines y = -5x/7 + k such that all constraints of (3) and (4) are satisfied.

The maximum is obtained when Z passes through (360,480), i.e. at intersection of constraints (3) and (4).  Using slope intercept form,

(y-480) = -(5/7)(x-360)

or y=-(5/7)x + (737+1/7)    [the purple line] which violates the red line, so not a solution.

Next try the point (0,600)

(y-600) = -(5/7)(x-0), or

y = 600 - (5/7)x   [the black line]

As we can see all point on the black (in the first quadrant) satisfy the constraints, so it is a feasible solution, and is the optimal solution, with a revenue of

Revenue  = 600*7 = 4200 gold pens

Answer:

Simply plug in the polynomial into a graphing calc.

Step-by-step explanation:

Answer:

(1400)(1+0.029/12)3(1+0.221/12)9

Step-by-step explanation:

A p e x

Answer:

Step-by-step explanation:

Just so you know how it looks on the page

Answer:

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all, let's find the factors of these two numbers and I will put in boxes the common factors.

[tex]15a^2b^2=\boxed{3}\cdot 5\cdot \boxed{a} \cdot a \cdot \boxed{b} \cdot b \\ \\ \\-24ab=(-1)\cdot 2 \cdot \boxed{3} \cdot 4 \cdot \boxed{a} \cdot \boxed{b}[/tex]

The Highest Common Factor (HCF) is found by finding all common factors and selecting the largest one. So, in this case, it gives

[tex]\large \boxed{\sf \ \ \ 3\cdot a \cdot b \ \ \ }[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The width of the model will be  2.5 inches

Step-by-step explanation:

The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.

Step One: Determine the scale factor from the tower height.

The scale factor is obtained from the formula:

Scale factor = model size / observed size

This will be

Height of model tower/ height of the real tower.

The height of the model tower is 5 inches which is the same as 0.416667 ft

Scale factor = 0.416667 ft/ 40ft = 0.0104

Step two:  Multiply the width of the real-life tower by the scale factor to get the model width.

Width of model =20ft X 0.0104 = 0.208ft

Step three:  Convert your answer back to inches.

We will now have to convert 0.208 ft back to inches by multiplying by 12

This will be 0.208 X 12 =2.5 inches.

The width of the model will be  2.5 inches

Answer:

  C. g(-13) = 20

Step-by-step explanation:

Let's check the offered statements:

  A. g(0) = 2 . . . . . . doesn't match g(0) = -2

  B. g(7) = -1 . . . . . . 7 is not in the domain of g

  C. g(-13) = 20 . . . could be true

  D. g(-4) = -11 . . . . -11 is not in the range of g