find the value of the following expression. Write your answers without any exponents.

The volume of metal is the difference of the overall volume of the cylinder and the volume of the hole in it. The formula for the volume of a cylinder is ...

... V = π·r^2·h . . . . . radius r and height h

For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm, so the volume in mm³ will be ...

... V_overall -V_hole = π(10)^2(21) -π(6)^2(21)

... = 21π·10^2 -21π·6^2 . . . . . . . matches the first selection

... = 2100π -756π . . . . . . . . . . . matches the third selection

... = 1344π . . . . . . . . . . . . . . . . doesnt' match any selection

The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,

⇒ 21π(10)² – 21π(6)²

⇒ 2,100π – 756π

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters.

And,  A cylindrical hole cut out of the center has a radius of 6 millimeters.

Hence, The formula for the volume of a cylinder is,

V = π·r²·h

Where, radius r and height h.

Now, For the overall dimensions, the radius is half the diameter, so is 10 mm. The hole is said to have a radius of 6 mm. The overall "height" is 21 mm,

so the volume in mm³ will be;

V (overall) -V (hole) = π(10)²(21) -π(6)²(21)

= 21π·10² -21π·6²

= 2100π -756π

= 1344π

Thus, The correct expressions for the volume of metal needed, in cubic millimeters, to make the pipe are,

⇒ 21π(10)² – 21π(6)²

⇒ 2,100π – 756π

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See the attachment for a labeled graph.

_____

I find it convenient to use "technology" to draw the graph. A spreadsheet, graphing calculator, or on-line graphing program can do this for you.

1/3, 1/4, 1/5

40% = 40/100 = 2/5

Any fraction with a numerator of 2 and a denominator larger than 5 will be less than 40%, for example.

So, we can choose 2/6 = 1/3, 2/8 = 1/4, and 2/10 = 1/5 as some such values.

_____

We could also choose something like 39.99% = 3999/10000, or 1% = 1/100.

Answer:

19

Step-by-step explanation:

b - 7 = 12

b = 7 + 12

b = 19

Hi there! :)

Answer:

b=19

*The answer must have a positive sign.*

Step-by-step explanation:

First, you add by 7 from both sides of an equation.

[tex]b-7+7=12+7[/tex]

Then, you add by the numbers from left to right.

[tex]12+7=19[/tex]

Final answer is b=19

I hope this helps you!

Have a nice day! :)

:D

-Charlie

Thank you so much! :)

Answer:

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Step-by-step explanation:

Answer:

The distance from he ball to the goal is 11.85 feet (Approx) .

Step-by-step explanation:

As given

The angle of elevation from a soccer ball on the ground to the top of the goal is 34° .

If the goal is 8 feet tall.

Now by using the trigonometric identity .

[tex]tan \theta = \frac{Perpendicular}{Base}[/tex]

As shown in the diagram given below

[tex]\theta = 34^{\circ}[/tex]

Perpendicular = AB = 8 feet

Base = BC

Put all the values in the identity .

[tex]tan\ 34^{\circ} = \frac{AB}{BC}[/tex]

[tex]tan\ 34^{\circ} = \frac{8}{BC}[/tex]

[tex]tan\ 34^{\circ} = 0.675\ (Approx)[/tex]

[tex]BC = \frac{8}{0.675}[/tex]

BC = 11.85 feet (Approx)

Therefore the distance from he ball to the goal is 11.85 feet (Approx) .

To calculate the distance from the soccer ball to the goal with an angle of elevation of 34 degrees and a goal height of 8 feet, use the tangent trigonometric ratio. The distance is found to be approximately 11.86 feet.

Given the angle of elevation is 34 degrees and the goal's height is 8 feet, we're looking to calculate the adjacent side (distance from the ball to the goal) in a right-angled triangle where the opposite side (goal's height) and the angle are known.

To calculate the distance (let's call it d), we use the tangent function:

So, d = 8/tan(34 degrees).

Calculating this, we find:

Therefore, the distance from the soccer ball to the goal is approximately 11.86 feet.

Using the smallest number she has, 9 daisies..

18/9 = 2

45/9 = 5

She can make 9 bouquets with 2 roses, 1 daisy and 5 tulips in each.

That means each bouquet would have 8 total flowers.

The number of rooms booked to produce maximum revenue is required.

The number of rooms booked to produce the maximum revenue is 250.

The revenue function is

[tex]R(x)=200x-0.4x^2[/tex]

Differentiating with respect to x we get

[tex]R'(x)=200-0.8x[/tex]

Equating with zero

[tex]0=200-0.8x\\\Rightarrow x=\dfrac{-200}{-0.8}\\\Rightarrow x=250[/tex]

Double derivative of the function is

[tex]R''(x)=-0.8x[/tex]

Substituting the value of [tex]x=250[/tex]

[tex]R''(250)=-0.8\times 250=-200[/tex]

Since, it is negative the maximum value of x will be 250.

The number of rooms booked to produce the maximum revenue is 250.

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The number of rooms that produces the maximum revenue for Fred's Estates LLC is 250 rooms, calculated using the formula -b/2a, where a and b are the coefficients of the quadratic revenue function.

To calculate the maximum revenue for Fred's Estates LLC, we need to find the value of x that maximizes the function [tex]R(x)=200*-0.4x2.[/tex]

The maximum value of a quadratic function can be found using the formula -b/2a, where a and b are the coefficients of x² and x in the function. Here, a=-0.4 and b=200.

Using the formula, [tex]x=-b/2a = -200/(2*(-0.4)) = 250[/tex] rooms. Therefore, booking 250 rooms results in the maximum revenue for Fred's Estates LLC.

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9 students did not study in either the cafeteria or the student lounge.

How to find the number

To find the number of students who did not study in either the cafeteria or the student lounge, we solve as follows

Let

C = 92

L = 86

C ∩ L = 40

We find the number in either C, L or C ∩ L

= (92 - 40) + (86 - 40) + 40

= 52 + 46 + 40

= 138

The number  did not study in either the cafeteria or the student lounge

= 147 - 138

= 9

Answer:

So the value of x=3  and y =3

Step-by-step explanation:

5x + 3i = 15 + yi

To find out x   , set the constant terms  equal to each other and solve for x

5x= 15

Divide by 5 on both sides

x= 3

To find out y   , set the ';i' terms  equal to each other and solve for y

3= y

So the value of x=3  and y =3

Answer:  The required value of x is 3 and that of y is 3.

Step-by-step explanation:  We are given to find the values of x and y that satisfies the following equation :

[tex]5x+3i=15+yi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

[tex]a+bi=c+di~~~~~~~~~\Rightarrow a=c,~b=d.[/tex]

That is, the real and parts on both sides of the equation are equal.

From equation (i), we have

[tex]5x+3i=15+yi.[/tex]

Equating the real and imaginary parts on both sides of the above equation, we get

[tex]5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3[/tex]

and

[tex]3=y\\\\\Rightarrow y=3.[/tex]

Thus, the required value of x is 3 and that of y is 3.

Answer:

21d +25 ≤ 115

Step-by-step explanation:

Jim's cost will be ...

... 21.00·d + 0.10·250 = 21d +25

He wants his cost not to exceed his budget, so ...

... 21d +25 ≤ 115

_____

The solution is ...

... 21d ≤ 90 . . . . subtract 25

... d ≤ 90/21 ≈ 4.3

so Jim can rent the car a maximum of 4 days.

The inequality that can be used to express this scenario is

115 ≤  21*d+ 25

Given data

Charges = $21 per day

Cost per driven distance = $0.10

Distance he will travel = 250 miles

Amount her has to spend = $115

Let the maximum number of days Jim can rent a car with $115 be "m"

Hence

Total amount = 21*d+ 0.1*250

Substituting and Simplifying we have

115 ≤  21*d+ 25

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Answer:

B. -9/4 -4i

Step-by-step explanation:

Collect terms the way you would with any algebraic expression.

= (-3 +2 -3)i + (3/4 -3)

= -4i +(3/4 -12/4)

= -9/4 -4i

The product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is [tex]\( 5 - 4i \)[/tex].

To find the product of two complex numbers, we multiply them as we would with binomials, remembering that [tex]\( i^2 = -1 \)[/tex]. Let's perform the multiplication step by step:

Given complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex], we multiply them directly:

[tex]\[(3 - 2i) \cdot (1 + i) = 3 \cdot 1 + 3 \cdot i - 2i \cdot 1 - 2i \cdot i. \][/tex]

Now, we simplify the expression by combining like terms and using the fact that [tex]\( i^2 = -1 \)[/tex]:

[tex]\[ = 3 + 3i - 2i - 2i^2 = 3 + i - 2(-1) = 3 + i + 2. \][/tex]

Finally, we combine the real parts and the imaginary parts:

[tex]\[ = (3 + 2) + i = 5 - 4i. \][/tex]

Therefore, the product of the complex numbers [tex]\( (3 - 2i) \)[/tex] and [tex]\( (1 + i) \)[/tex] is[tex]\( 5 - 4i \)[/tex].

Answer:

A = 4200 ft^2

Step-by-step explanation:

We know the formula for area is

A = l*w

We need to have the same units

convert yd to ft

1 yd = 3ft

Multiply each by 70

70 yds = 210 ft

A = 210 *20

A = 4200 ft^2

The area of the pavement section is 4200 square feet, computed by converting the length to the same unit as the width and multiplying width by length.

The subject of this question is the calculation of the area of a rectangle. The rectangle in question is a section of pavement with a width of 20 ft and a length of 70 yd. Before calculating, it's important to have the measurements in the same units. Converting 70 yards to feet (since 1 yard equals 3 feet) we get 210 feet. The formula to calculate the area of a rectangle is Area = Width x Length. Substituting the given values into the formula, we get: Area = 20 ft x 210 ft which equals 4200 square feet. Therefore, the pavement section's area is 4200 square feet.

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Answer:

The cost of the wristband for 8 rides is $35.

Step-by-step explanation:

The expression for the cost, C, for r rides is

C = 2.5r + 15

Since she wants to go on 8 rides, r is 8.

Substitute r with 8 in the cost equation and evaluate it.

C = 2.5r + 15

C = 2.5 * 8 + 15

C = 20 + 15

C = 35

The cost of the wristband for 8 rides is $35.

Answer:

2

Step-by-step explanation:

1/2 cup = 2/4 cups = 2 × 1/4 cup

Alonzo can make 2 batches that each require 1/4 cup.

Answer :

The proof is as follows :

Step-by-step explanation:

Let NC = x

⇒ AB = 3x and AN = 2x

In Δ ABN, By using Pythagoras theorem,

AB² = BN² + AN²

⇒ BN² = AB² - AN²

⇒ BN² = (3x)² - (2x)²

⇒ BN² = 5x²

⇒ BN = x√5  .......................(1)

Now in ΔANC , Using Pythagoras theorem We have,

AC² = NC² + AN²

⇒ AC² = x² + (2x)²

⇒ AC² = 5x²

⇒ AC = x√5   ....................(2)

From equations (1) and (2) We get,

AC = BN , which is our required result

Answer:

BN=AC=√5 x.

The proof is explained in step-by-step explaination.

Step-by-step explanation:

Let NC=x. It is given that AB=3NC & AN=2NC

⇒ AB=3x & AN=2x

By applying Pythagoras theorem

In triangle ANC,

[tex]AC^{2}=AN^{2}+NC^{2}[/tex]

⇒ [tex]AC^{2} = (2x)^{2}+x^{2}[/tex]

⇒ [tex]AC^{2}=4x^{2}+x^{2} =5x^{2}[/tex]

⇒ [tex]AC=\sqrt{5}x[/tex]   →    (1)

Similarly, In triangle ABN,

[tex]AB^{2}=AN^{2}+BN^{2}[/tex]

⇒ [tex](3x)^{2}=BN^{2}+x^{2}[/tex]

⇒ [tex]9x^{2} = (BN)^{2}+4x^{2}[/tex]

⇒ [tex]BN^{2}=5x^{2}[/tex]

⇒ [tex]BN=\sqrt{5}x[/tex]   →   (2)

From eq (1) & (2),    AC=BN

The correct option is the last:

[tex] a_n = -2a_{n-1}+1 [/tex]

In fact, every term in the sequence is one more than twice the opposite of the previous one:

We start with 3. Twice its opposite is -6. Plus one, we get -5.

We start with -5. Twice its opposite is 10. Plus one, we get 11.

We start with 11. Twice its opposite is -22. Plus one, we get -21.

The recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

To find a recursive formula for the given sequence, we need to determine the relation between consecutive terms.

Let's denote the sequence as an, where:

[tex]a_1 = 3\\a_2 = -5\\a_3 = 11\\a_4 = -21\\[/tex]

First, let's calculate the differences between consecutive terms:

[tex]a_2 - a_1 = -5 - 3 = -8\\a_3 - a_2 = 11 - (-5) = 16\\a_4 - a_3 = -21 - 11 = -32[/tex]

We observe that each difference is a multiple of 8 and that each difference is twice the previous difference but with alternating signs.

The recursive formula can be defined as:

[tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Thus the recursive formula is: [tex]a_n-a_{n-1} = (-8)(-1)^n \times (2)^{n-2}[/tex]

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

The definition of a line segment is the set of points on a line between two given end points, including those end points. The best description is the one that matches the definition.

Answer:

the set of all points between point F and point G, including point F and point G

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

-0.2(x-20)=4-x

The first step is to distribute the -.2

-.2 x -.2 * -20 = 4-x

-.2x +4 = 4-x

Add x to each side

x-.2x +4 = 4-x+x

.8x +4 = 4

Subtract 4 from each side

.8x +4-4 = 4-4

.8x=0

Divide by .8

.8x/.8 = 0/.8

x =0

[tex]\displaystyle x^{\frac{2}{3}}[/tex]

The rules of exponents tell you ...

... (a^b)(a^c) = a^(b+c) . . . . . . applies inside parentheses

... (a^b)^c = a^(b·c) . . . . . . . . applies to the overall expression

The Order of Operations tells you to evaluate inside parentheses first. Doing that, you have ...

... x^(4/3)·x^(2/3) = x^((4+2)/3) = x^2

Now, you have ...

... (x^2)^(1/3)

and the rule of exponents tells you to multiply the exponents.

... = x^(2·1/3) = x^(2/3)

Answer:

x^(2/3)

Step-by-step explanation:

(x^a.x^b)^c = x^[c*(a+b)]

using the above eqn, u can simplify the given expression to

x^[1/3*(4/3+2/3)]

=x^[1/3*(6/3)]

=x^(2/3)

ans is the 2nd choice

2/5

There are 2 units of green and 5 units of "pink," so the ratio is ...

... green/pink = 2/5

Answer:

$6.40 because 32 ounces is the difference 128 and 96 hence 32 is 1/3 of 96 so divide $4.80 by 3 which is $1.60 then add $1.60 + $4.80 =$6.40

Step-by-step explanation:

Answer:

$300

Step-by-step explanation:

Let x represent the side length of the square base in feet. Then the height of each side is ...

... h = (50 ft³)/(x ft)² = (50/x²) ft

The cost of the sides of the box is then ...

... (4 sides) × (x ft)(50/x² ft)/side × $2/ft² = $400/x

The cost of the bottom is ...

... (x ft)² × $25/ft² = $25x²

So, the total dollar cost is

... C = 400/x + 25x²

This will be a minimum where its derivative with respect to x is zero.

... 0 = -400/x² +50x

... 400/50 = 8 = x³ . . . . . add 400/x²; multiply by x²/50

... x = ∛8 = 2

For this value of x, the minimum cost is ...

... C = 400/2 + 25·2² = 300

The minimum possible cost is $300.

_____

Comments on the problem

1) Cardboard boxes are usually made of cardboard. They are rarely made of wood and alumninum.

2) The cost of the bottom is half the cost of the sides. When the dimensions are unconstrained, you will find (as here) the cost is shared equally between the bottom and pairs of opposite sides—each being 1/3 the total cost.

9.9 years

A = P(1 + rt) . . . . account balance after time t at rate r starting with principal P

... 3000 = 2500(1 + 0.0202t) . . . . filling in the given numbers

... 1.2 = 1 + 0.0202t . . . . divide by 2500

... 0.2 = 0.0202t . . . . . . subtract 1

... 0.2/0.0202 = t ≈ 9.901

It will take about 9.9 years for the account balance to reach $3000.

Answer:

216 cupcakes

Step-by-step explanation:

81 = 0.375 × order

81/0.375 = order = 216 . . . . . divide by the coefficient of the variable

_____

About percentages

% means /100

37.5% = 37.5/100 = 375/1000 = 0.375

3 ft

The statue's height is 1.5 times the length of its shadow, so we expect the same relationship for the globe.

... 1.5 × 2 ft = 3 ft

_____

Comment on the problem

As a practical matter, with the sun high enough in the sky to cast a shadow shorter than the object's height, it will be quite difficult to measure the length of the shadow of the point at the top of the globe. The shadow of other parts of the globe will interfere.

Answer:

see attached

Step-by-step explanation:

Each of the pie slices can be cut in half different ways. An easy way to do it and to understand it is to draw another cut from the center to the middle of the edge.

The result of cutting these slices is that instead of 8 equal pieces (of which 3 are colored), there will be 16, of which 6 are colored.

The new fraction is 6/16.

ANSWER:

Your answer is the 3rd one: y - 8 = -3/7(x - 5)

ABOUT POINT SLOPE FORM:

ABOUT PROBLEM:

y - Y1 = m (x - X1)

y - 8 = -3/7(x - 5) --- IN POINT SLOPE FORM

Hope this helps you!!! :)

The line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)

The equation of a straight line is given by:

y = mx + b;

where y,x are variables, m is the slope of the line and b is the y intercept.

Since the line has a slope -3/7 and passes through the point (5, 8), the equation of the line is:

[tex]y-y_1=m(x-x_1)\\\\y-8=-\frac{3}{7} (x-5)[/tex]

Hence a line with a slope -3/7 and passes through the point (5, 8) has an equation of y - 8 = (-3/7)(x - 5)

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