what was the total amount of all checks vera deposited

Answer:

64π/5 cubic units.

Step-by-step explanation:

The line x = 2 and y = x^3 intersect at the point (2 , 2^3) = (2, 8).

The required volume = volume of the cylinder with height 8 and radius 2 - the volume of shape form between the curve and the y axis when revolved about the y-axis.

Using the disk method for volumes of revolution:

Note that x = y^1/3 so:

the second volume =   Integral  π ((y^1/3)^2) dy  between y = 0 and y = 8.

=  3/5 y^5/3 * π between 0 and 8

= 96π/5.

The required volume = π 2^2 *8 - 96π/5

= 32π - 96π/5

= 64π/5.

Answer:

The volume of the prism = 27√3/2 inches³ (≅ 23.38 inches³)

Step-by-step explanation:

* Lets revise the volume of the triangular prism

- The prism has 5 faces

- Two triangular bases

- Three rectangular side faces

- The rule of its volume = Area of its base × its height

* Now lets solve the problem

- The bases of the prism are equilateral triangles of side 3 inches

- The side faces of the prism are rectangles of dimensions 3 and 6 inches

∵ Its volume = Area of the its base × its height

- The bases are equilateral triangles

∵ The area of the equilateral triangle = √3/4 s² , where s is the

   length of its side

∵ The length of the side = 3 inches

∴ The area of the base = √3/4 (3)² = 9√3/4 inches²

∵ Its height = 6 inches

∴ Its volume = 9√3/4 × 6 = 27√3/2  inches³

* The volume of the prism = 27√3/2 inches³ (≅ 23.38 inches³)

Answer:

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Step-by-step explanation:

30 ft perimeter:  P = 30 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  30 ft - 16 ft = 14 ft.  The minimum width, W, is 14 ft.

32 ft perimeter:  

P = 32 ft = 2L + 2W = 2(8 ft) + 2W

Solving for W, we get:  32 ft - 16 ft = 16 ft.  The minimum width, W, is 16 ft.

The appropriate compound inequality is then 14 ft ≤ W ≤ 16 ft

Answer:

Range of width = [7,8]

Step-by-step explanation:

Let w be the width of garden,

The length of garden, l = 8 feet

We have perimeter = 2 x ( length + width)

Perimeter = 2 x ( 8 + w)

The perimeter of the garden must be at least 30 feet and no more than 32 feet.

That is

             30 ≤ 2 x ( 8 + w) ≤ 32

             15 ≤ 8 + w ≤ 16

              7 ≤ w ≤ 8

So range of width = [7,8]

Answer:

Both a and b are independent (see explanation)

Step-by-step explanation:

Events A and B are independent when

[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]

a) A - "winning"

B - "playing at home"

From the table,

[tex]P(A)=0.25\\ \\P(B)=0.8\\ \\P(A\cap B)=0.2[/tex]

Since

[tex]0.25\cdot 0.8=0.2[/tex]

events are independent.

b) A - "losing"

B - "playing away"

From the table,

[tex]P(A)=0.75\\ \\P(B)=0.2\\ \\P(A\cap B)=0.15[/tex]

Since

[tex]0.75\cdot 0.2=0.15[/tex]

events are independent.

Answer:

E = 151 2/3

Step-by-step explanation:

We need to set up a system of equations to solve for the 2 unknowns.  The first equation is very basic, taken from the sentence "...their total weight is 225 pounds..."

This is

B + E = 225 in equation form.

Next, we know that E is twice the weight of B plus 5 (wording it a little differently helps eliminate the seeming ambiguity of the order things go in).  That looks like this algebraically:

E = 2B + 5

From above, we know that E + B = 225, so let's sub in the equivalent statement for E to get an equation with only one unknown:

B + (2B + 5) = 225 which simplifies to 3B = 220 and B = 73 1/3 pounds.

E can be found now by plugging the value of B:

E = 2(73 1/3) + 5

E = 151 2/3 pounds

The weight of E and B is calculated given their total weight and the relationship between their weights.

The weight of E can be represented as 2B + 5. Given that the total weight of E and B is 225 pounds, we can set up the equation: 2B + 5 + B = 225. Solving this equation, we find B = 70 and E = (2 × 70) + 5 = 145 pounds.

I’m not sure but I think it might be the second one, 6x^3y^6

the answer is b the second choice

Answer:

2,520 pounds

Step-by-step explanation:

Step 1: For this question, all you have to do is multiply 4,000 * 0.63. In other words, you are multiplying the amount you have by the conversion rate. 4,000 * 0.63 is 2,520. That's our answer.

- 1 <= sin (a) <= 1

-2+5*(-1)<= -2+5sin(pi/12)(x-2)<= -2 +5*(1)

so

the minimum value of y is

y = - 2 + 5 * ( - 1 ) = - 7

hope this would help you

Answer:

[tex]\Large \boxed{-7}[/tex]

Step-by-step explanation:

We can find the minimum of the function by plotting the function on the graph.

[tex]\displaystyle \mathrm{y=-2+5 \cdot sin(\frac{\pi }{12}(x-2) )}[/tex]

The minimum value is the y value of the lowest point on the graph.

Answer:

The answer would be division (B)

Step-by-step explanation:

4x equals the total amount

x equals the cost of one item

Therefore you'd divide total cost by 4 and that would find the cost of one item

Answer:

We will use division operation

Step-by-step explanation:

Let x be the cost of 4 items

So, cost of 1 item = [tex]\frac{x}{4}[/tex]

So, we have used division operation

So, to find out how much one costs, we will use division operation

So, Option B is true

Hence we will use division operation

Answer:

1. modulus: 2; argument: 3π/2 (radians)

2. modulus: 5; argument: π (radians)

Step-by-step explanation:

The modulus is the magnitude of the number. When the number is aligned with one of the axes, it is simply the absolute value of the non-zero component. The argument is the arctangent of the imaginary part divided by the real part, with respect given to signs. Again, when the number is aligned with one of the axes, that angle will be some multiple of π/2 radians, where arg(i) = π/2; arg(-1) = π; arg(-i) = 3π/2; arg(1) = 0.

1. the number is aligned with the negative imaginary axis. Its magnitude is |-2| = 2, and its argument is 3π/2.

__

2. the number is aligned with the negative real axis. Its magnitude is |-5| = 5, and its argument is π.

Angles TOS and ROQ are congruent, so [tex]m\angle ROQ=m\widehat{RQ}=28^\circ[/tex].

RT is a diameter of the circle, so [tex]m\widehat{RT}=180^\circ[/tex], and in particular

[tex]m\angle ROQ+m\angle QOP+m\angle POT=180^\circ\implies m\angle QOP=62^\circ[/tex]

Then

[tex]m\widehat{RPS}=28^\circ+62^\circ+90^\circ+28^\circ=\boxed{208^\circ}[/tex]

The measure of arc RPS = [tex]208^{\circ}$$[/tex].

The measure of an inscribed angle is half the measure of the intercepted arc.

(The measure of the arc is twice the measure of the angle)

Arc length is a measurement of distance, so it cannot be in radians.

Angles TOS and ROQ are congruent,

so [tex]$m \angle R O Q=m \widehat{R Q}=28^{\circ}$[/tex].

RT is the diameter of the circle,

so [tex]$m \widehat{R T}=180^{\circ}$[/tex], and in particular [tex]$m \angle R O Q+m \angle Q O P+m \angle P O T=180^{\circ}[/tex]

[tex]\Longrightarrow m \angle Q O P=62^{\circ}$[/tex]

Then

[tex]$$m \widehat{R P S}=28^{\circ}+62^{\circ}+90^{\circ}+28^{\circ}=208^{\circ}$$[/tex]

[tex]$$m \widehat{R P S}=208^{\circ}$$[/tex]

The measure of arc RPS = [tex]208^{\circ}$$[/tex].

Therefore, the correct answer is option (b) [tex]208^{\circ}$$[/tex].

To learn more about the measure of arc

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The following integers from the greatest to least are as follows:

+3, 0, -3, -2, -8

The answer is +3,0,-2,-3,-8

Answer:

y = 57, PQ = 60, RS = 28

Last option is the answer

Step-by-step explanation:

3 * y = 9 * 19

3y = 171

y = 57

PQ = 3 + 57 = 60

RS = 9 + 19 = 28

Answer:

y = 57; PQ = 60; RS = 28

Step-by-step explanation:

The product of lengths of parts of a chord is a constant, so ...

PT·TQ = RT·TS

TQ = y = RT·TS/PT = 9·19/3 = 57

Of course the total chord length is the sum of its parts, so ...

PQ = PT +TQ = 3 +57 = 60

RS = RT +TS = 9 +19 = 28

Then your answer choice is ...

y = 57; PQ = 60; RS = 28.

Answer:

  800,000,000

Step-by-step explanation:

Subtract the known numbers from the sum to find the missing number:

  800,903,402 - 900,000 -2 -3,000 -400 = 800,000,000

Answer:

A = 146.624 cm

Step-by-step explanation:

Variable a, is one base and variable b is the other base. Variable h is the hight of the trapezoid.

Answer:

146.624cm^2

Step-by-step explanation:

do the split method again :D (10.5cm+21.1cm)(9.28cm/2)

Answer:

The answer in the procedure

Step-by-step explanation:

we know that

One tricycle has one seat, three wheels and two pedals

so

The number of seats is equal to 288*1=288 seats

The number of wheels is equal to 288*3=864 wheels

The number of pedals is equal to 288*2=576 pedals

Answer:

$123.25

Step-by-step explanation:

A selling price reflecting a 45% markup can be found by multiplying the wholesale price ($85) by (1 + 0.45), or  1.45:

1.45($85) = $123.25

Answer:

  A.)  285

Step-by-step explanation:

The sum of an arithmetic series is the sum of the first and last terms multiplied by half the number of terms.

  (10 +85)·6/2 = 285 . . . sum of 6 terms

Answer:

The sum of the first 499 terms is 249001

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

 between each two consecutive terms n is the position of the

 number

- The sum of first n terms of an Arithmetic sequence is calculate from

 Sn = n/2[a + l], where a is the first term and l is the last term

* Now lets solve the problem

∵ The terms of the sequence are 1 , 3 , 5 , 7 , ......... , 997

∵ The first term is 1 and the second term is 3

∴ The common difference d = 3 - 1 = 2

∵ The first term is 1

∵ The last term is 997

∵ The common difference is 2

- Lets find how many terms in the sequence

∵ an = a + (n - 1) d

∴ 997 = 1 + (n - 1) 2 ⇒ subtract 1 from both sides

∴ 996 = (n - 1) 2 ⇒ divide both sides by 2

∴ 498 = n - 1 ⇒ add 1 for both sides

∴ n = 499

∴ The sequence has 499 terms

- Lets find the sum of the first 499 terms  

∵ Sn = n/2[a + l]

∵ n = 499 , a = 1 , l = 997

∴ S499 = 499/2[1 + 997] = 499/2 × 998 = 249001

* The sum of the first 499 terms is 249001

Final answer:

The sum of the series 1+3+5+7+...+997 is calculated using Gauss's approach for arithmetic series, resulting in a sum of 249500.

Explanation:

To find the sum of the series 1+3+5+7+...+997 using Gauss's approach, we first recognize that this is an arithmetic series where each term increases by a constant difference, in this case, 2. The first term, a, is 1 and the last term, l, is 997. We can find the number of terms, n, in the series using the formula: n = (l - a) / common difference + 1, which in this case is (997 - 1) / 2 + 1 = 499. Then, the sum of an arithmetic series can be found using the formula: Sum = n/2 * (a + l), so the sum of this series is 499/2 * (1 + 997) = 249500.

1.Make y the subject

k = xy

k/x = xy/x

y = k/x

2.Substitute

y = k/x

y = 7/9

y = 0.777......

y = 0.8 (Answer)

To confirm

k = xy

k = 9 × 0.8

k = 7.2

k = 7 (constant)

Hope it helps☺

Answer:

7/9

Step-by-step explanation:

Answer:

A. x < 6 and x > - 28

Step-by-step explanation:

We have been given the following inequality;

| x+11 | < 17

We can replace the absolute value function by re-writing the inequality as;

-17< x+11<17

subtract 11 from both sides;

-17-11<x+11-11<17-11

-28<x<6

splitting this we have;

x<6

x>-28

Answer:

A. x < 6 and x > - 28

Step-by-step explanation:

| x+11 |< 17

x + 11 < 17

x < 6

-(x + 11) < 17

-x - 11 < 17

-x < 28

x > - 28

Answer

6 > x > -28 (x < 6 and x > - 28)

Answer:

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft

Step-by-step explanation:

The equation for the volume of a pyramid of base area B and height h is

V = (1/3)·B·h.  Here, V = 432 ft³, B = (12 ft)² and h (height of the pyramid) is unknown.  First we find the height of this pyramid, and then the slant height.

V = 432 ft³ = (144 ft²)·h, so h = (432 ft³) / (144 ft²) = 3 ft.

Now to find the slant height of this pyramid:  That height is the length of the hypotenuse of a right triangle whose base length is half of 12 ft, that is, the base length is 6 ft, and the height is 3 ft (as found above).

Then hyp² = (3 ft)(6 ft) = 18 ft², and the hyp (which is also the desired slant height) is hyp = √18, or √9√2, or 3√2 ft.

The slant height of the pyramid is 3√2 ft, or to the nearest tenth ft,

4.2 ft

Answer:

the answer is the 3 one I'm 90% sure

The volume and the surface area of the hemisphere in terms of π are 3888π in³ and 972π in² respectively.

The volume of a hemisphere can be found using the formula given below:

Volume = (2/3)πr^3

The surface area of a hemisphere can be found using the formula given below:

Surface Area = 3πr^2

The figure is provided. From the figure, we can see that the radius of the hemisphere is 18 inches.

The volume of the hemisphere can be found as shown below:

Volume = (2/3)π*18*18*18 in³

= 3888π in³

The surface area of a hemisphere can be found as shown below:

Surface Area = 3π*18*18 in²

= 972π in²

We have found the volume and the surface area of the hemisphere. The volume and the surface area of the hemisphere are 3888π in³ and 972π in² respectively.

Therefore, we have found that the volume and the surface area of the hemisphere in terms of π are 3888π in³ and 972π in² respectively. The correct answer is option B.

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Answer: see attachments

Step-by-step explanation:

Use Pythagorean Theorem to find the missing side (x² + y² = h²)

Use the following formulas to find the trig functions:

[tex]sin\theta=\dfrac{y}{h}\qquad \qquad csc\theta=\dfrac{h}{y}\\\\\\cos\theta=\dfrac{x}{h}\qquad \qquad sec\theta=\dfrac{h}{x}\\\\\\tan\theta=\dfrac{y}{x}\qquad \qquad cot\theta=\dfrac{x}{y}[/tex]

The mass of the gasoline in the container is 2657.81grams

The ratio of the mass of an object to its volume is its density. Mathematically;

Density = Mass/Volume

Mass = density * volume

Given the following

Density =  750 kg/m³.

Determine the volume

Volume = πr²h
Volume =3.14(0.75)² * 2

Volume = 3.54375 m³

Determine the mass

Mass = 750 * 3.54375

Mass = 2657.81grams

Hence the mass of the gasoline in the container is 2657.81grams

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Answer:

2649 kg

Step-by-step explanation:

I just took the test

Answer:

Richard, at 2/3, versus Cooper, at 5/8

Step-by-step explanation:                              12 min

Richard's ratio of cardio to resistance is  R = ------------ = 2/3

                                                                            18 min

                            10 min

Cooper's is  C = ------------ = 5/8

                            16 min

The LCD here is 24.  Rewrite 2/3 and 5/8 with denominator 24 for greater ease in comparing the two fractions/ratios:

R = 16/24 and C = 15/24

So it becomes obvious that Richard does a higher ratio of carido to resistance.

Answer:

the net change would be 22.50!

Step-by-step explanation:

add 4.50 5 times!

Answer:

The net change to Ian’s account after the utility company lives up to the agreement will be $22.50.

Step-by-step explanation:

The utility company made a mistake on Ian’s electric bill.

The company has agreed to credit Ian’s account for five transactions, each worth $4.50

This gives [tex]4.50\times5=22.50[/tex] dollars

So, the net change to Ian’s account after the utility company lives up to the agreement will be $22.50.

The expression for the perimeter of a rectangle with length (3x-8) cm and width (2x-7) cm is P = 2 * ((3x - 8) + (2x - 7)). After simplification, the final expression for the perimeter is P = 10x - 30 cm.

The perimeter of a rectangle is given by the formula 2 * (length + width). Here, the length of the rectangle is given as (3x - 8) cm and the width is given as (2x -7) cm. Therefore, substituting these into the formula the expression for the perimeter (P) is P = 2 * ((3x - 8) + (2x - 7)).

To simplify this, we first add up the like terms within the parentheses giving us P = 2 * (5x - 15). Then, apply the distributive property of multiplication over addition to simplify further and we get P = 10x - 30 cm. This is the simplified expression for the perimeter of the rectangle.

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4, 3, 1, -2, -5

Hope this helps.

The following integers from the greatest to least are as follows:

+4, +3, +1, -2, -5

Answer:

5

Step-by-step explanation:

So we want to find the value of x where the area to the left of it is equal to 0.6.

Let's start by finding the area of the first triangle, between x=0 and x=4.

A = 1/2 bh

A = 1/2 (4) (0.2)

A = 0.4

So we know a > 4.  What if we add the area of that rectangle?

A = 0.4 + bh

A = 0.4 + (1) (0.2)

A = 0.6

Aha!  So a = 5.