1) A bowl is a hemisphere with radius 6 cm Water fills two-fifths of the volume of the bowl. The water is poured into a hollow cone. The depth of the water in the cone is 12 cm​.
the volume of a sphere = 4÷3πr³.
the volume of a cone = 1÷3πr²h.
Solve the radius of the surface of the water in the cone?​

Answer: $505,000

Step-by-step explanation:

The salary difference between a teacher and a cashier is:

$42,630 - $17,380 = $25,250

This means that a teacher earns $25,250 more per year than a cashier.

To find out how much more a teacher would earn over a 20-year career, we need to multiply the salary difference by the number of years:

$25,250 x 20 = $505,000

Therefore, a teacher would earn $505,000 more than a cashier over a 20-year career.

The equation of the line of the best fit is ŷ = 1.05x + 1.70

From the question, we have the following parameters that can be used in our computation:

x 0 1 4 5 6 6 7 8 9 10

Y 1 3 7 6 8 9 9 10 11 12

Using a graphing tool we have the attached graph as the scatter plot and the line of best fit

From the attached graph, the equation of the best fit is

ŷ = 1.05x + 1.70

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Answer: 5/8 as a fraction 0.625 as a decimal

Step-by-step explanation:

Answer:

x = [tex]-\frac{2}{7}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

there is an equation written in the question and one in the figure, to be sure I'll solve them both

Solve the equation.

7x +(4x - 5) = 3 + 2(x − 3)

7x + 4x - 5 = 3 + 2x - 6

7x + 4x - 2x = 3 - 6 + 5

9x = 2

x = 2/9  ( or 0.2repeating)

----------------------------------------------------------------------

7x + 1/2(4x - 5) = 3/2 + 2(x - 3)

7x + 2x - 5/2 = 3/2 + 2x - 6

7x - 5/2 = 3/2 - 6

14x - 5 = -9/2

14x = -9 + 5

14x = -4

x = -2/7 ( or 0.285714 repeating)

Answer:

50

Step-by-step explanation:

P= 2l + 2w Formula for a perimeter

P= 184 given

l= 4x+2 given

w= 5x given

184= 2(4x+2) + 2(5x) substitution

184= 8x+4+ 10x distributive property

184= 18x+4 combine like terms

184 -4 =18x +4 -4 subtract 4 from both sides to get 18x alone

180=18x

180/18= 18x/18 divide both sides by 18 to get x alone

10= x

x=10

Side PS= 5x since it is parallel to RQ which is 5x

5(x)=5(10)=50

According to the solving, the approximate weight of 1 backpack is 7.98 pounds.

1 close to being exact. 2 loose; unrefined; rough. simply a roughly fitting fit. 3 very similar; nearly the same.

We use the kilogram as a unit of weight in everyday life under the assumption that the gravitational field around the globe is fairly constant because there is no practical, straightforward way to quantify mass. Scales must, however, be adjusted locally to account for the minor gravitational field fluctuation in various locations.

To find the approximate weight of one backpack, we can divide the total weight of the 5 backpacks by the number of backpacks. So:

Approximate weight of 1 backpack = Total weight of 5 backpacks / 5

Approximate weight of 1 backpack = 39.9 pounds / 5

Approximate weight of 1 backpack = is 7.98 pounds

Therefore, the approximate weight of 1 backpack is 7.98 pounds.

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The probability of a person being 20 years or younger and preferring strawberry ice cream is: 10 / 50 = 0.2 or 20%, So the answer is 20%.

8 + 10 + 6 + 8 + 6 + 12 = 50

The number of people who are 20 years or younger and prefer strawberry ice cream is 10.

Therefore, the probability of a person being 20 years or younger and preferring strawberry ice cream is:

10 / 50 = 0.2 or 20%

So the answer is 20%.

Among people over 20 years old, chocolate ice cream is the most preferred flavor with a total of 12 votes.

The total number of people who prefer vanilla ice cream is 16 (8 in the 20 years and younger group + 8 in the over 20 years group).

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Cory will owe $21,120 in taxes on the sale of his qualified small business stock.

Tax liability can be defined as the total amount of taxes an individual, corporation, company, etc owes a tax authority or service at a given period of time.

To determine the tax liability on the sale of qualified small business stock, we need to apply the rules for the Section 1202 exclusion.

First, we need to determine if the stock meets the requirements for the Section 1202 exclusion. The stock must have been acquired directly from a domestic C corporation that meets the criteria for a qualified small business (QSB). The stock must also have been held for more than five years.

Assuming the stock meets these requirements, we can apply the following formula to determine the taxable gain:

Taxable gain = Sale price - Basis

In this case, the taxable gain is:

Taxable gain = $98,000 - $32,000 = $66,000

Next, we need to determine the amount of the gain that qualifies for the Section 1202 exclusion. The exclusion is equal to the greater of:

In this case, the exclusion is based on the 10 times basis rule since the gain is less than $10 million and there are no prior QSB stock sales. Therefore, the exclusion is:

Exclusion = 10 x $32,000 = $320,000

Since the gain of $66,000 is less than the exclusion of $320,000, the entire gain qualifies for the Section 1202 exclusion.

Finally, we need to determine the tax liability on the remaining taxable income. The marginal tax rate of 32 percent will apply to the taxable gain of $66,000, resulting in a tax liability of:

Tax liability = Taxable gain x Marginal tax rate

Tax liability = $66,000 x 0.32 = $21,120

Therefore, Cory will owe $21,120 in taxes on the sale of his qualified small business stock.

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Answer:

----------------------------------

Volume of a rectangular prism is the product of its three dimensions:

Substitute values of dimensions from the picture into formula:

Answer:

---------------------------

Given equation:

Solve it in below steps:

This equation has one solution.

The correct option is  [tex]r^{-42}[/tex] is not equivalent to [tex](r^{-7} )^{6}[/tex] .

Variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation can all be found in an algebraic statement. In many branches of mathematics, science, engineering, and finance, issues are represented and solved using algebraic expressions.

The expression [tex](r^{-7} )^{6}[/tex] can be simplified using the rule of exponentiation which states that raising a power to another power involves multiplying the exponents. Applying this rule, we get:

[tex](r^{-7} )^{6}[/tex]   = [tex]r^{-42}[/tex]

Therefore, the expression  [tex](r^{-7} )^{6}[/tex]  is equivalent to  [tex]r^{-42}[/tex], which is the first option given.

Option 1:  [tex]r^{-42}[/tex] is not equivalent to [tex](r^{-7} )^{6}[/tex] .

Option 2: 1/ [tex]r^{-42}[/tex] is also not equivalent to [tex](r^{-7} )^{6}[/tex] .

Option 4: [tex]r^{-1}[/tex] is also not equivalent to  [tex](r^{-7} )^{6}[/tex] .

Therefore, the correct option is (a)  [tex]r^{-42}[/tex].

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Answer:

A

Step-by-step explanation:

the function is symmetric about the vertical line [tex]x = 3[/tex]  . This means that the inverse function should also be symmetric about this line. We choose the positive solution for y:This gives us the inverse of H(x). We can write it as[tex]H^(-1)(x) = 3 ± sqrt((x - 4) / 2)[/tex]

To find the inverse of a function, we need to switch the positions of x and y and solve for y.

[tex]Let y = H(x) = 2(x-3)^2+4.[/tex]

We can begin by subtracting 4 from both sides to get:

[tex]y - 4 = 2(x-3)^2[/tex]

Next, we can divide both sides by 2 to get:

[tex](y - 4) / 2 = (x-3)^2[/tex]

Taking the square root of both sides, we obtain:

[tex]±sqrt((y - 4) / 2) = x - 3[/tex]

Adding 3 to both sides gives:

[tex]x = 3 ± sqrt((y - 4) / 2)[/tex]

Therefore, This gives us the inverse of H(x). We can write it as:

[tex]H^(-1)(x) = 3 ± sqrt((x - 4) / 2)[/tex]

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(A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

What is the rate of change?

The rate of change is a mathematical concept that measures how much one quantity changes with respect to a change in another quantity. It is the ratio of the change in the output value of a function to the change in the input value of the function. It describes how fast or slow a variable is changing over time or distance.

A) The initial value is $44,000 and the final value is $15,000. The time elapsed is 2006 - 1992 = 14 years.

Using the formula for an annual rate of change (r):

final value = initial value * [tex](1 - r)^t[/tex]

where t is the number of years and r is the annual rate of change expressed as a decimal.

Substituting the given values, we get:

$15,000 = $44,000 * (1 - r)¹⁴

Solving for r, we get:

r = 0.0804

So, the annual rate of change between 1992 and 2006 was 0.0804 or approximately 0.0804.

B) To express the rate of change in percentage form, we need to multiply by 100 and add a percent sign:

r = 0.0804 * 100% = 8.04%

C) Assuming the car value continues to drop by the same percentage, we can use the same formula as before to find the value in the year 2009. The time elapsed from 2006 to 2009 is 3 years.

Substituting the known values, we get:

value in 2009 = $15,000 * (1 - 0.0804)³

value in 2009 = $11,628.40

Rounding to the nearest $50, we get:

value in 2009 = $11,650

Hence, (A)  the annual rate of change between 1992 and 2006 was 0.0804

(B) r = 0.0804 * 100% = 8.04%

(C) value in 2009 = $11,650

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According to the solution we have come to find that, The correct value of x in the given equation is 30.

An equation is a mathematical statement that shows the equality between two expressions, usually containing variables and mathematical operations. In an equation, the expressions on both sides of the equals sign have the same value.

For example, the equation 2x + 5 = 11 is an equation that shows the equality between the expressions 2x + 5 and 11. To solve the equation, we need to find the value of the variable x that makes the equation true.

Martina solved the equation x + 14 = 44 as follows:

x + 14 = 44

x = 44 - 14

x = 30

The error that Martina made is that she forgot to subtract 14 from both sides of the equation. The correct solution should be:

x + 14 = 44

x = 44 - 14

x = 30

Therefore, the correct value of x in the given equation is 30.

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Answer:

y = -50x + 500

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (5,250) (7,150)

We see the y decrease by 100, and the x increase by 2, so the slope is

m = -100/2 = -50

Y-intercept is located at (0,500)

So, the equation is y = -50x + 500

Answer:

b

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer: First, we need to find the length of the line segment MN. Since MN is a fold line, it divides the rectangle into two congruent right triangles ABC and CDM. We can use the Pythagorean theorem to find the length of MN:

AC² + CM² = AM²

Since AC = 16 cm and CM = 2 cm (half the width of the rectangle), we have:

16² + 2² = AM²

256 + 4 = AM²

260 = AM²

AM = sqrt(260) = 2sqrt(65) cm

Since MN is the hypotenuse of right triangle ACM, we have:

MN = 2AM = 4sqrt(65) cm

Now, let's draw a line segment from B to MN, perpendicular to MN, and let the intersection point be E. Since triangle ABN is similar to triangle CDM, we have:

BN/DM = AB/CD

BN/2 = 4/16

BN = 1 cm

Since triangle BEN is a right triangle, we can use the Pythagorean theorem to find the length of BE:

BE² + EN² = BN²

BE² + (MN - DM)² = 1²

BE² + (4sqrt(65) - 2)² = 1

BE² + 64*5 - 16sqrt(65) + 4 = 1

BE² = -64*5 + 16sqrt(65) - 3

BE = sqrt(-64*5 + 16sqrt(65) - 3)

Note that BE is an imaginary number, which means that point E is actually below line segment MN. Therefore, the area of pentagon ABNMD' is zero.

Step-by-step explanation:

================================================

Explanation:

Grab some graph paper or use GeoGebra.

Place point A at the origin (0,0). Move 16 units to the right to plot B at (16,0).

Then move 4 units up to get to C(16,4). Then move 16 units left to arrive at D(0,4)

Here are the four points so far:

Next draw a line through A and C.

The equation of line AC is y = 0.25x; I'll skip the steps showing how I got that equation. But let me know if you need to see those steps.

The perpendicular bisector of segment AC is the equation y = -4x+34. Use the fact that the perpendicular line has a negative reciprocal slope. Meaning the slope 0.25 has the negative reciprocal -4. Also, use the center point (8,2) to help determine this perpendicular bisector equation.

Why is the perpendicular bisector so important? It's the mirror line. We'll reflect C over this line to land on A.

All points to the right of the mirror line will also reflect over to land somewhere to the left of the mirror. This will form the pentagon ABNMD where segment NM is the mirror line.

-----------

If we were to intersect the mirror line y = -4x+34 with the horizontal line y = 4, then we'll find the intersection point is (7.5,0) which is the location of point M in the diagram below.

Intersect y = 0 (aka the x axis) with y = -4x+34 to find the location of point N(8.5, 0)

So we should have

M = (7.5, 0)

N = (8.5, 0)

-----------

Pentagon ABNMD is composed of the following triangles

But notice carefully that triangle NPQ has folded over mirror line MN to land exactly on top of triangle ABN. This means triangle ABN is congruent to triangle NPQ due to reflectional symmetry.

Also due to the symmetry of the fold, triangle ADM = triangle NPQ

Because of symmetry we have:

Apply the transitive property to find triangle ADM = triangle ABN

-----------

area of triangle ADM = 0.5*base*height

area of triangle ADM = 0.5*MD*AD

area of triangle ADM = 0.5*7.5*4

area of triangle ADM = 15

Therefore, triangle ABN is also 15 square cm as well.

area of triangle MNA = 0.5*base*height

area of triangle MNA = 0.5*AN*4

area of triangle MNA = 0.5*8.5*4

area of triangle MNA = 17

-----------

Summary of the triangle areas:

Therefore,

pentagon ABNMD = (triangle ADM)+(triangle MNA)+(triangle ABN)

pentagon ABNMD = (15)+(17)+(15)

pentagon ABNMD = 47 square cm is the final answer.

The diagram is shown below. I used GeoGebra to make it. The diagram is to scale.

Notes:

The missing values in the figure is solved using Inscribed Angle Theorem to get

x = 7

arc KL = 92 degrees

arc KLJ = 225 degrees

The arc length KL is solved with the knowledge that sum of arc length in a circle is 360 degrees

135 + 133 + KL = 360

KL = 360 - 135 - 133

KL = 92

Solving for x

inscribed angle = 0.5 * intercepted arc

5x + 11 = 0.5 * 92

5x + 11 = 46

5x = 46 - 11

5x = 35

x = 7

Arc KLJ

= 92 + 133

= 225

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If I eat too much, then I will get sick." The reverse of this statement would be "If I get sick, then I ate too much." However, this is not always true, as getting sick can have multiple causes and not just be Attributed to eating too much

An if-then statement is a type of logical statement that relates two propositions, where the second proposition is the consequence of the first. An example of an if-then statement is "If it rains, then the ground will be wet." The reverse of this statement would be "If the ground is wet, then it rained."

Using everyday knowledge, an example of an if-then statement whose reverse is not correct is "If I eat too much, then I will get sick." The reverse of this statement would be "If I get sick, then I ate too much." However, this is not always true, as getting sick can have multiple causes and not just be attributed to eating too much.

Another example could be "If I study hard, then I will pass the test." The reverse of this statement would be "If I pass the test, then I studied hard." This may not always be true, as there could be other factors that contributed to passing the test. Therefore, it is important to be mindful of the validity of if-then statements and their reverses.

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Answer:

angle 3 is 127 and angle 4 is 31

Step-by-step explanation:

If you see the base of the triangle looks like an angle measurer of 180 degrees. so if 2 is 53 then subtract 180-53 to get 127. Once you have 3 just subtract 180 - 22 and 127 to get 31  

:D

The sector has a central angle of 270° and the radius is 9m. So, the area of the sector is:

A_sector = (270/360) * π * (9m)^2 = 57.15m²

To find the area of the triangle, we need to find the height of the triangle. We can use the Pythagorean theorem to find the height:

h = √[(9m)^2 - (4.5m)^2] = √(81m^2 - 20.25m^2) = √60.75m^2 = 7.8m

The base of the triangle is 4.5m (half of the diameter), so the area of the triangle is:

A_triangle = (1/2) * 4.5m * 7.8m = 17.55m²

Therefore, the area of the shaded segment is:

A_shaded segment = A_sector - A_triangle = 57.15m² - 17.55m² = 39.6m²

Rounded to the nearest tenth, the area of the shaded segment is 39.6m².

Answer:

what trapezoid? please provide the trapezoid so I can help you

Answer:

To find the surface area of the three-dimensional figure, we need to first determine the shape of the figure. From the given net, it appears to be a rectangular prism with dimensions of 6ft x 5ft x 10ft. The surface area of a rectangular prism can be calculated by adding up the areas of all six faces. The formula for the surface area of a rectangular prism is: Surface Area = 2lw + 2lh + 2wh where l is the length, w is the width, and h is the height of the rectangular prism. Using the given dimensions, we can plug them into the formula and get: Surface Area = 2(6 x 5) + 2(6 x 10) + 2(5 x 10) Surface Area = 60 + 120 + 100 Surface Area = 280 square feet

The exact value of the inverse-trigonometric expression arccos( [tex]cos\frac{\pi }{2}[/tex] ) is found to be  [tex]\frac{\pi }{2}[/tex].

These are also called as arc functions. These trigonometric functions are inverse operations of given trigonometric functions. The cosine of the angle indicates the ratio of base of right triangle and hypotenuse of the same triangle and the inverse of the cosine is the ratio of base and hypotenuse will give the respective angle. Inverse functions can be used to unknown angles, angle of elevation or depression in any right triangle.

The given expression is arccos( [tex]cos\frac{\pi }{2}[/tex] )

we know that arc cosine or inverse cosine= [tex]cos^{-1}(-x)[/tex] = [tex]\pi - cos^{-1} - (x)[/tex]

also we know that cos(-x)=cosx

arccos( [tex]cos\frac{\pi }{2}[/tex] ) = arccos( [tex]-cos\frac{\pi }{2}[/tex] )

                    = [tex]\pi - cos^{-1} (cos \frac{\pi }{2})[/tex]

                    = [tex]\pi - \frac{\pi }{2}[/tex]

                   = [tex]\frac{\pi }{2}[/tex]

∴ The value of arccos( [tex]cos\frac{\pi }{2}[/tex] ) is  [tex]\frac{\pi }{2}[/tex].

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The experimental probability of landing on a number greater than 5 is 8/60, which simplifies to 2/15.

Experimental probability is the probability of an event based on the results of an experiment or observation.

It is calculated by dividing the number of times the event occurs by the total number of trials or observations.

It is also called empirical probability or observed probability.

Experimental probability can be used to estimate the theoretical probability of an event, which is the probability of the event based on mathematical reasoning or modeling.

As the number of trials or observations increases, experimental probabilities tend to approach theoretical probabilities. 

The experimental probability of landing on a number greater than 5 is the number of times a number greater than 5 (i.e., 6) is obtained divided by the total number of tosses.

From the table, we see that 6 is obtained 8 times out of 60 tosses.

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Answer:

Expanded Form of 2.327:

2.327 = (2 * 100) + (3 * 1/101) + (2 * 1/102) + (7 * 1/103)

2.327 = (2 * 1) + (3 * 1/10) + (2 * 1/100) + (7 * 1/1,000)

2.327 = 2 + 3/10 + 2/100 + 7/1,000

2.327 = 2 + 0.3 + 0.02 + 0.007

The range for the skull size of Welsh Corgis is given by the compound inequality 54.8 ≤ D ≤ 59.7.

We can solve the given inequality 25 ≤ 1.05D – 32.7 ≤ 30 for D by adding 32.7 to all three parts of the inequality:

25 + 32.7 ≤ 1.05D – 32.7 + 32.7 ≤ 30 + 32.7

57.7 ≤ 1.05D ≤ 62.7

Then, we can divide all three parts of the inequality by 1.05:

57.7/1.05 ≤ D ≤ 62.7/1.05

54.76 ≤ D ≤ 59.71

Mathematical statements that compare two quantities are known as inequality. They represent the relationship between the quantities with symbols like, >,, and. An inequality may have one or more variables, and based on the values of those variables, the inequality may be true or false. The collection of all values for the variables necessary to make an inequality true is the answer to the inequality. In real-world applications, inequalities are frequently used to indicate limitations, limits, or ranges of values.

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Therefore , the solution of the given problem of function comes out to be 3x – 6 as a result.

The questions on the midterm exam will cover every topic, including created and actual places and also algebraic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

We can easily add the two functions to obtain f(x) + g(x):

=> F(x) = (x² + 6x - 5) + (-x² - 3x - 1) + G(x)

By condensing similar words, we can say:

=>  x² + 6x - 5 - x² - 3x - 1 = f(x) plus g(x).

=>  (x² - x²) + (6x - 3x) + f(x) + g(x) (-5 - 1)

=>  f(x) + g(x) = 3x - 6

=>  F(x) + G(x) = 3x – 6 as a result.

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