Simplify 12 1/3b + 6 2/3 - 10 2/3b

Answer:

A. The surface area of the cheese is 24·π in.² or 75.40 in.²

B. The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased

Step-by-step explanation:

From the figure attached to a similar question, we have;

Radius, r of cheese = 3 in.

Height, h of the cheese = 1 in.

A. The surface area of the cheese is equal to the area of two circles, one on top and the other underneath added to the surface area of the sides which is equivalent to the surface area of a cylinder given by the relation

Surface area of the cheese = 2×π×r² + 2×π×r×h

∴ Surface area of the cheese = 2×π×3² + 2×π×3×1 = 24·π in.²

Surface area of the cheese = 24·π = 75.398 ≈ 75.40 in.² to the nearest 10th

B. The surface area of the remaining cheese after the wedge is removed is found by first subtracting the cut wedge from the total surface area as follow

Outer surface area of cut wedge = 24·π÷8 = 3·π

New outer surface area = Total surface area - Removed outer surface area

∴ New outer surface area = 24·π - 3·π = 21·π

New total surface area = New outer surface area + Area of newly exposed segment

Area of newly exposed segment = 3 × 1 × 2 = 6 in.²

∴ New total surface area = (21·π + 6) in.² = 71.9734 in.² ≈ 72 in.²

The surface area of the remaining cheese after the wedge is removed is about 72 in.²

2. The surface area decreased.

Answer:

A. The surface area of the cheese is 24·π in.² or 75.4 in.² B. The surface area of the remaining cheese after the wedge is removed is about 72 in.² 2. The surface area decreased

Step-by-step explanation:

It's 75.4 instead of 75.40, thank me please.

Answer:

2.44

Step-by-step explanation:

Given: x³ + 2x² - 5ax - 7      and  x³ + ax² - 12x + 6

Also, R1 + R2 = 6

in order to find the value of a:

Let p(x) = x³ + 2x² - 5ax - 7 and q(x) = x³ + ax² - 12x + 6

Using remainder theorem i.e if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).

Then,

R1 = p( -1 ) = (-1)³ + 2(-1)² - 5a(-1) - 7 = -1 + 2 + 5a - 7 = 5a - 6

R2 = q( 2 ) = 2³ + a(2)² - 12(2) + 6 = 8 + 4a - 24 + 6 = 4a - 10

Now,

R1 + R2 = 6

5a - 6 + 4a - 10 = 6

9a = 22

a=2.44

Therefore, Value of a is 2.44

Answer:

Value of tax liability will be zero

Step-by-step explanation:

Given:

Total estate value = $2,186,000

Estate tax = 40 %

Find:

Heir's tax liability = ?

Computation:

Total taxable estate = Total estate value - Estate Exemption

Note: According to Exhibit 19-6 for Estate Exemption, Estate Exemption  is 11.4 million.

We know that Estate Exemption  is higher than total estate value, therefore will be no tax liability on the successor, so the value of tax liability will be zero.

Answer:3

Step-by-step explanation:

Answer:

34 + 35 + 36 = 105

Step-by-step explanation:

To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 105

3X + 3 = 105

3X + 3 - 3 = 105 - 3

3X = 102

3X/3 = 102/3

X = 34

Which means that the first number is 34, the second number is 34 + 1 and the third number is 34 + 2. Therefore, three consecutive integers that add up to 105 are 34, 35, and 36.

34 + 35 + 36 = 105

We know our answer is correct because 34 + 35 + 36 equals 105 as displayed above.

Answer:

80 units by 16 units

Step-by-step explanation:

4 units : 5 feet

X units : 20 feet

Y units: 100 feet

X/20 = 4/5

X = 20 × 4/5

X = 16

Y/100 = 4/5

Y = 100 × 4/5

Y = 80

Answer:

B. 81 cubic inches

Step-by-step explanation:

Since this is an irregular 3 dimensional object, I will cut it into a 3 by 3 by 3 cube and a 6 by 3 by 3 rectangular prism.

Solving for the cube:

3*3*3=

9*3=

27 units or in this case inches³

Solving for the rectangular prism:

6*3*3=

18*3=

54 units or in this case inches³

To get the total volume, we need to add the cube and rectangular prism's volume together:

54+27=81 inches³

Our answer is B. 81 cubic inches.

Answer:

630

Step-by-step explanation:

Let the number of adult tickets be a.

Let the number of children tickets be c.

For that day's performance, they have sold a total of 1180 tickets. That means that:

a + c = 1180 _____________ (1)

Also, they have sold 80 more adult tickets than children’s tickets.

This means that:

a = c + 80 ______________(2)

Putting (2) in (1):

c + 80 + c = 1180

2c + 80 = 1180

Collecting like terms:

2c = 1180 - 80

2c = 1100

c = 1100 / 2 = 550

From (2):

a = 550 + 80

a = 630

They sold 630 adult tickets.

Final answer:

The theatre has sold 630 adult tickets after solving a system of equations based on the given conditions of total tickets sold and the difference between adult and children's tickets.

Explanation:

The student is presented with a problem where a theatre sells two types of tickets: children's and adult's tickets. For a particular performance, a total of 1180 tickets were sold, and there are 80 more adult tickets sold than children's tickets. We can let 'x' represent the number of children's tickets sold, and thus 'x + 80' will represent the number of adult tickets sold. According to the information given:

x + (x + 80) = 1180

Solving for 'x' we get:

2x + 80 = 1180

2x = 1100

x = 550

Now, to find the number of adult tickets sold, we add 80 to the number of children's tickets.

x + 80 = 550 + 80

x + 80 = 630

Therefore, the theatre has sold 630 adult tickets.

Answer:

b.) 76

Step-by-step explanation:

A triangles angles will always add up to a total of 180°.Since both angles B and C are x, they have the same value. So to find their value, add the choices to 28 twice until you get 180:

[tex]28+76+76=180[/tex]

Or, you can make and equation. 180 on one side of the equation. On the other side, put both x's (2x) plus the value of angle A:

[tex]2x+28=180[/tex]

Solve for x:

[tex]2x+28-28=180-28\\2x=152\\\\\frac{2x}{2}=\frac{152}{2}\\ x=76[/tex]

Finito.

Answer:

1 1/3

Step-by-step explanation:

Solve. Change the division sign into a multiplication, and flip the second fraction:

(8/15)/(2/5) = (8/15) x (5/2)

Multiply across:

(8 x 5)/(15 x 2) = (40)/(30)

Simplify. Divide common factors:

(40/30)/(10/10) = 4/3

4/3 or 1 1/3 is your answer.

~

Answer:

1⅓

Step-by-step explanation:

8/15 ÷ 2/5

8/15 × 5/2

(8×5)/(15×2)

4/3

1⅓

Answer:

Step-by-step explanation:

27m2 units

Answer:

10 ft

Step-by-step explanation:

area of trapezoid = (B + b)h/2

where B and b are the lengths of the bases, and h is the height.

A = (B + b)h/2

115 = (19 + 4)h/2

230 = 23h

23h = 230

h = 10

Answer: 10 ft

The height of the trapezoid with base lengths of 4 and 19 feet and an area of 115 square feet is 10 feet.

A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.

The area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.

[tex]\rm{ Area\ of\ trapezoid = \dfrac{1}{2} \times Height \times(Sum\ of\ parallel\ sides)[/tex]

The area of a trapezoid is given as half the product of the sum of the parallel sides and the height of the trapezoid.

The length of the parallel sides of the trapezoid is 4 and 19 feet, while the area of the trapezoid is 115 square feet. Therefore, the height of the trapezoid is,

115 ft² = 0.5 × (4 ft + 19 ft ) × height

115 ft² = 0.5 × 23 ft × height

height = (115 ft²)/ (0.5 × 23 ft)

height = 10 feet

Hence,  the height of the trapezoid is 10 feet.

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Answer:

515

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

Given Data:

Number of people = 6

Amount of Gold to be shared = 40lbs

Subtract 2/3 from your answer.

Therefore

If six people are to share 40lbs of gold evenly

= 40lbs / 6

Divide through by 2

= 20lbs / 3

= 20lbs / 3 - 2/3

= 18/3

= 6

Each person would get approximately 6lbs of gold

Answer:

1. Each individual gets [tex]6\frac{2}{3}lb[/tex] of gold

2. After subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5

Step-by-step explanation:

Given

Size of Gold = 40 lbs

Number of people = 6

Required

1. Proportion of each individual

2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion

1. Proportion of each individual

To calculate how many each individuals get (in other words, the proportion of each individual), we simply divide the total size of gold by the number of people

Mathematically,

[tex]Proportion = \frac{Total}{People}[/tex]

[tex]Proportion = \frac{40}{6}[/tex]

Reduce fraction to lowest term by dividing numerator and denominator by 2

[tex]Proportion = \frac{20}{3}[/tex]

Convert to mixed fraction

[tex]Proportion = 6\frac{2}{3}[/tex]

Hence each individual gets [tex]6\frac{2}{3}lb[/tex] of gold

2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion

This is represented by

[tex]6\frac{2}{3} - 1\frac{2}{3}[/tex]

Convert both fractions to improper fractions

= [tex]\frac{20}{3} - \frac{5}{3}[/tex]

Find LCM of both fractions

= [tex]\frac{20 - 5}{3}[/tex]

Subtract

= [tex]\frac{15}{3}[/tex]

= 5

Hence, after subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5

Answer:

3

Step-by-step explanation:

8 x 5 = 40

43 - 40 = 3

The number of students who cannot sit at tables based on the given conditions in a classroom setting are 3.

The number of students who cannot sit at tables can be calculated as follows:

Number of students per table = 8

Total number of students = 43

Total number of students that can be accommodated by tables = 5 tables x 8 students = 40 students

Number of students who cannot sit at tables = Total number of students - Total number accommodated by tables = 43 - 40 = 3 students

Answer:

0.16

Step-by-step explanation:

This probability is the area under the standard normal curve to the right of 82.  Note that 82 is ONE standard deviation above the mean:  75 + 7 = 82.

According to the Empirical Rule, 68% of data lies within one standard deviation of the mean.  In other words, 34% lies between the mean and one standard deviation above the mean.  The remaining area under the standard normal curve is thus (100% - 68%), or 32%.  Half of that is 16%.  

The probability that the temperature is above 82, or above 1 standard deviation above the mean, is 16%, which we can also express as 0.16.

Alternatively, use a calculator with built-in statistical functions.  In this case the desired result is found by executing the following command:

normcdf(82, 10000, 75, 7).  The desired result is 0.1587, or approximately 0.16.

Answer:

[tex]y=18(1.15)^x[/tex]

Step-by-step explanation:

The initial value of the poster =$18

Its value increases by 15% each year.

We can model this using the exponential growth function.

[tex]y(x)=y_0\cdot r^x $ where y_0$ is the initial value and r is the growth factor.[/tex]

Growth Factor, r=1+0.15=1.15

Therefore:

[tex]y(x)=18(1.15)^x[/tex]

After 1 year, when x=1

[tex]y(1)=18(1.15)^1=\$20.70[/tex]

This is true.

Therefore, the model is valid and its value, y after x years will be:

[tex]y=18(1.15)^x[/tex]

Answer:

it is A

Step-by-step explanation:

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Final answer:

The equivalent expression to 16a + 24b is 8(2a + 3b) by factoring out the greatest common factor of 8 from both terms.

Explanation:

The expression equivalent to 16a + 24b is 8(2a + 3b). To find this, we can factor out the greatest common factor from the terms in the original expression. Both 16a and 24b have a common factor of 8, which when factored out leaves us with 2a and 3b, respectively, yielding the expression 8(2a + 3b).

Answer:

r = 3.64 km

Step-by-step explanation:

Given the following information:

=> The area of the town is:

= Total population / population density per square kilometer

[tex]A = \dfrac{20000}{480}[/tex]

[tex]A = 41.667\ km^2[/tex]

As we know, the formula used to find the area of a circle is:

A = π[tex]r^{2}[/tex]

In this situation, we already knew the area of the town

<=> A = π[tex]r^{2}[/tex]  = 41.776

<=> [tex]r^{2}[/tex] = 41.776  / 3.14

<=> r = 3.64 km

So the radius of the town is 3.64 km

Answer:

3.64

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To calculate this, we shall be selecting 2 each from a total of 64

This is a combination question and our required answer is 64C2

Mathematically, if we are to select r from n items , the combination can be computed as follows;

nCr = n!/(n-r)!r!

Thus, we have 64C2 as ; 64!(64-2)!2! = 64!/62!2!

= (64 * 63 * 62!)/62!2! = (64 * 63)/2 = 32 * 63 = 2,016 pairings

Answer:

4 sqrt(5)

8.94427191

Step-by-step explanation:

We want to find the length  ( or distance) between the two points

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (8-0)^2 + (1 - -3)^2)

  = sqrt( (8)^2 + (4^2)

  = sqrt( 64+16)

 sqrt( 80)

sqrt(16) sqrt(5)

4 sqrt(5)

8.94427191

Answer:

4sqrt(5)

Step-by-step explanation:

Length² = (-3-1)² + (0-8)²

Length² = 16 + 64

Length² = 80

Length = 4sqrt(5)

sqrt: square root

Answer:

b

Step-by-step explanation:

y= -3x+7

Answer:

The answer is option 2.

Step-by-step explanation:

It is given that the slope of the line is -3 so you just have to substitute it into the slope-form equation, y = mx+b where m is gradient and b is y-intecept. In order to find b value, you have to put in the coordinates :

[tex]y = mx + b[/tex]

Let m = -3,

[tex]y = - 3x + b[/tex]

At (1,4),

[tex]4 = - 3(1) + b[/tex]

[tex]4 = - 3 + b[/tex]

[tex]b = 4 + 3[/tex]

[tex]b = 7[/tex]

[tex]y = - 3x + 7[/tex]

Answer:

61°

Step-by-step explanation:

∠SPQ is a straight line, so it equals to 180°.

∠SPR is 119° and since we're looking for ∠QPR, we subtract 119° from 180°.

180° - 119° = 61°, so ∠QPR = 61°

Answer:

61 degrees

Step-by-step explanation:

Because SPQ is said to be a straight line, we know that a straight line in this kind of equation is equal to 180 degress.

Since we already know the measure to one angle (119), we would need to find the difference between 180 and 119, meaning we'd have to subtract.

(180-119)

Then we would just get the sum, which in this case, is 61 degrees.

Answer:

r = 0.9 in.

Step-by-step explanation:

the volume equation of a cone is πr^2h/3 in this case you have the volume and the height measurements but youre missing the radius, so you have to divide the volume by the rest of the equation and backtrack and when you do, you get a radius value of 0.9

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Answer:

The answer on edge. is f(x) =  9,974.73  ( 1.05 )x

Step-by-step explanation

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The value that complete the regression equation is f(x) =  9,974.73  ( 1.05)^x.

How to solve for the value

We have the exponential equation as

[tex]y=ab^{x}[/tex]

a is the initial rate

b is the rate

x is 0

y = 10000

When substituted the rate is given as

f(x) =  9,974.73  ( 1.05 )x

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Answer:

(5, -2)

Step-by-step explanation:

(6+4)/2 , (1-5)/×

10/2 , -4/2

5 , -2

Answer:

Step-by-step explanation:

The fidelity investment mutual funds is $10.92 per share.

The fund charges 2.5%.

So, if 2.5% is charged,

Then, 2.5% of the share is

2.5% of $10.92 = 2.5 / 100 × $10.92

2.5% of $10.92 = $0.273

Then, total offer price is 0.273 + 10.92

Therefore, total offer is $11.193

Final answer:

The offer price of the real estate income mutual fund from Fidelity Investments is $11.2135 per share.

Explanation:

The offer price of the real estate income mutual fund from Fidelity Investments can be calculated by adding the load to the selling price per share. In this case, the load is 2.5% of $10.94 per share. To find the load amount, multiply 2.5% by $10.94, which is equal to $0.2735. Then, add the load amount to the selling price per share: $10.94 + $0.2735 = $11.2135.

Answer:

i think the answer is 3.3

Step-by-step explanation:

Final answer:

Quita paid $6.60 in sales tax for an $88 jacket.

Explanation:

To calculate the sales tax Quita had to pay for her jacket, we need to follow a simple two-step process.

First, we will calculate the amount of tax by converting the percentage to a decimal and then multiplying it by the price of the jacket.

Since the tax rate is 7.5%, we convert this to a decimal which gives us 0.075.

Then, we multiply this decimal by the price of the jacket:

Amount of sales tax = price × rate of sales tax

$88.00 × 0.075 = $6.60

So, the sales tax on the jacket priced at $88 is $6.60.