The function P(n) = 108 + 10 log(n) gives the
total sound power in decibels when n drill presses are operating in a factory. What is the total sound power, to the nearest decibel, when three drill presses are operating?

Since angle S is 65°, angle Y will also be 65°

Similar shapes are shapes that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Since quadrilateral QRST is similar to quadrilateral WXYZ, then angle Q = angle W , angle R = angle X and angle S = angle Y and angle T = angle Z.

Since angle S is 65° from the diagram shown, angle will be measured as 65°.

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After dilation, the coordinates of image will be (-1,3).

What exactly is dilation?

Dilation is the process of modifying the size of an item or form by reducing or expanding its dimensions according to specific scaling variables. A circle of radius 10 unit, for example, is reduced to a circle with radius 5 unit. This approach is utilised in photography, arts and crafts, and the creation of logos, among other things. There are four primary types of transformations in geometry. They are as follows:

Dilation Properties

Some characteristics of forms that stay constant during dilation changes are:

Now,

As given dilation factor= -3

that means the image will be small and x coordinate will displace from its current value - 3 that is -1.

and y coordinate will be same that is 3

Hence,

          After dilation, the coordinates of image will be (-1,3).

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First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:

[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]

The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].

The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:

[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]

The volume of the cone is about [tex]226.08 in^{3}[/tex].

Subtract 226.08 from 452.16 and you get 226.08.

The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].

Answer:

B

Step-by-step explanation:

given a line parallel to a side of a triangle and intersecting the other 2 sides, then it divides those sides proportionally , that is

[tex]\frac{32}{x}[/tex] = [tex]\frac{20}{30}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2x = 3 × 32 = 96 ( divide both sides by 2 )

x = 48

The number of months it will take to have same number of caregivers is 3 months .And there will be of 17 caregivers of each type.

What is an equation?

An equation is an expression with variables and constant having an equality sign. The degree of equation can be one or more than one.

We are given that initially there are  8 assistant caregivers

and 5 senior caregivers.

And the owner is going to be hiring 3 assistant caregivers per month and

4 senior caregivers per month.

Hence the number of total assistant caregivers after n months will be

3n +8

And the number of senior caregivers after n months will be 4n+ 5

To find n we equate the two

3n + 8 = 4n+5

n =3

Hence after 3 months there will be same number of assistant and senior caregivers

And the total number of assistant and senior caregivers is 3(3)+8 = 17

The number of months it will take to have same number of caregivers is 3 months .And there will be of 17 caregivers of each type.

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The correct statements are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

One leg of an isosceles triangle is 6√2 feet.

As, we know isosceles triangle two of its sides equal in length then the other side can be  6√2 feet.

Now, using Pythagoras theorem

H² = P² + B²

H² = (6√2)² + (6√2)²

H² = 72 + 72

H² = 144

H= 12 units

The statements that applies here are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

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Answer:

The answer is B and D

Step-by-step explanation:

I took the test.

let me know if you would like an explanation down in the comments!

Answer:

31

Step-by-step explanation:

27.9/0.9 = 31

The length of the segment AE is 10 units.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

The two triangles triangle ABE and triangle CDE are similar triangles.

We know that, the ratio of segments of similar triangle are equal thus:

10 / 8 = 2x + 6 / x+ 6

10(x + 6) = 8(2x + 6)

10x + 60 = 16x + 48

60 - 48 = 16x - 10x

12 = 6x

x = 2

Substitute the value of 2 in 2x + 6:

2(2) + 6 = 10 units.

Hence, the length of the segment AE is 10 units.

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Answer: £122.45

Step-by-step explanation: 7.90*15.5

Answer: 109?

Step-by-step explanation:

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'

Here we have

f(x) = - 6x + 14  and g(x) = - 2ˣ + 6  

The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows

=> - 6x + 14 =  - 2ˣ + 6    

=> - 6x + 8 = - 2ˣ    

=> - 6x + 8 = - 2ˣ

=> - 6x + 2ˣ = - 8          

By using the trial and error method

At x = 2

=> - 6(2) + 2² = -8

=> - 12 + 4 = -8

Therefore,

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

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The transformation that maps △UVW to △EFG is (d) (x, y) = (-2x, -2y)

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

The figure

From the figure, we can see that

Triangle EFG is twice the triangle UVW in side lengths

This means that

(x, y) = (2x, 2y)

The orientations are 180 degrees apart

So, we have

(x, y) = (-2x, -2y)

Hence, the transformation is (d) (x, y) = (-2x, -2y)

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]2y+3x=1\implies 2y=-3x+1\implies y=\cfrac{-3x+1}{2} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}}x+\cfrac{1}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3} \implies \cfrac{2}{ 3 }}}[/tex]

so we're really looking for an equation whose slope is 2/3

[tex]{\Large \begin{array}{llll} y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x+\cfrac{5}{2} \end{array}} \qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°The angle of elevation of the road is 5.0°.

In order to calculate the angle of elevation of a road, we need to know the vertical distance it has changed and the horizontal distance it has travelled. In this case, we have a vertical distance of 150 feet and a horizontal distance of 0.6 miles. Since there are 5280 feet in a mile, this is equivalent to 3168 feet .Using the formula for angle of elevation, we can calculate the angle of elevation for this road Angle of elevation = tan-1 (vertical distance/horizontal distance)Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°Therefore, the angle of elevation of the road is 5.0°.

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The soy candles cost $12.83 each and the specialty candles cost $10.72 each then the Asunta's Candle Store ordered 293 soy candles and 457 specialty candles.

What is system of linear equations?

Let's use the following variables:

We have two equations based on the information given in the problem:

To solve for x and y, we can use a system of linear equations. One way to do this is to solve for one variable in one equation, and substitute that expression into the other equation. For example, we can solve for x in the first equation:

x + y = 750

x = 750 - y

Then we substitute this expression for x in the second equation:

12.83x + 10.72y = 8660.34

12.83(750 - y) + 10.72y = 8660.34

Simplifying and solving for y:

9622.5 - 2.11y = 8660.34

-2.11y = -962.16

y = 456.5

We can then substitute this value for y in the first equation to find x:

x + y = 750

x + 456.5 = 750

x = 293.5

Therefore, Asunta's Candle Store ordered 293 soy candles and 457 specialty candles.

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The system of equations that correctly represents the situation of Lina and Sarika's ages are:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is called simultaneous equations.

The sum of Lina and Sarika's ages = 31

Lina's age > Sarika's by 5 years

Let Lina's age = L

Let Sarika's age = S

L + S = 31... Equation 1

L - S = 5... Equation 2

2L = 36

L = 18.

Substituting L = 18 into either Equation 1 or 2:

18 + S = 31

S = 31 - 18

S = 13

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The mean absolute deviation, mad, of the given data, 21, 25, 16, 8, 16, 10, is 4.83

From the question, we are to calculate the mean absolute deviation, mad, of the given data

First, we will calculate the mean of the data

21, 25, 16, 8, 16, 10

Mean = (21 + 25 + 16 + 8 + 16 + 10)/6

Mean = 96/6

Mean = 16

Now, we will determine the positive differences of each number from the mean

         Positive differences

21        5

25       10

16        0

8         8

16        0

10        6

Now, we will find the mean of the positive differences

Mean absolute deviation =(5 + 10 + 0 + 8 + 0 + 6)/6

Mean absolute deviation = 29/6

Mean absolute deviation = 4.83

Hence, the mad is 4.83

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Length of the segments are 11 units and 10 units and measures of the angles are 54° and 126°.

Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.

Opposite sides are parallel, and the opposite sides and opposite angles are equal.

Since, CDEF is a parallelogram, opposite angles are equal.

(9y)° = (7y + 28)°

9y - 7y = 28

2y = 28

y = 14

∠C = ∠E = 9y = 126°

Sum of the angles of a quadrilateral is 360°.

∠D = ∠F = (360° - (126°×2)) / 2 = 54°

Opposite sides are also equal for a parallelogram.

2x = x + 5

2x - x = 5

x = 5

CF = DE = 2x = 10 units

CD = FE = 3x - 4 = 11 units

Hence opposite sides are equal with lengths 10 units and 11 units and opposite angles are equal with measures 54° and 126°.

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Answer:

b) octogon

c) irregular pentagon

d) irregular hexagon

Step-by-step explanation:

Answer:

-5/3.

Step-by-step explanation:

To find the slope of a line perpendicular to another line, we need to remember that the slopes of two perpendicular lines are negative reciprocals of each other. To find the slope of the line perpendicular to 3x - 5y = 45, we need to first convert it to slope-intercept form, which is y = mx + b, where m is the slope of the line.

First, isolate the y-term:

3x - 5y = 45

5y = -3x + 45

y = -(3/5)x + 9

So the slope of the original line is -3/5. The slope of the line perpendicular to it would be the negative reciprocal of this slope, which is -5/3.

Therefore, the slope of a line perpendicular to 3x - 5y = 45 is -5/3.

Answer:

3/5

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

[tex]-8(v+1)=2(1-4v)-9\\-8v-8=2-8v-9\\8=-7\\8\neq-7[/tex]

Hence, there are no solutions to make both sides of the equation true.

Answer:

1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

1. identify the constant you will need to multiply each equation by to eliminate x

2. multiply all terms by -3 in equation 1

3. multiply all tems by 5 in equation 2

4. add the sum of the equation together to eliminate x

We can say that  by equation 12 metres below the ocean's surface, a fish may be found. 28 metres above the ocean's surface, a sea bird may be seen and distance between them is 40 meters.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

We require knowledge about an object's elevation to tackle such issues.

12 metres below the ocean's surface, a fish may be found.

28 metres above the ocean's surface, a sea bird may be seen.

A fish is 12 metres below the ocean's surface.

The fish's elevation is negative since it is below sea level. Consequently, the fish's elevation is -12 metres.

B.) A marine bird flies 28 metres above the water's surface.

given that the seabird is above the water. The sea bird is 28 metres above sea level.

If the bird soars straight over the fish, (C),

If the fish and the bird are immediately above one another,

Distance between fish and bird = |(elevation of the fish)| + |(elevation of the sea bird)|

= |-12| + |28|

= 12 + 28

= 40 meters

distance between them is 40 meters.

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Answer: MHT = 125; AHM = 55

Step-by-step explanation:

(2x + 11) + (6x - 7) = 180 since they are supplementary angles

8x + 4 = 180 ---- subtract 4 on both sides

8x = 176 ---- divide by 8 on both sides

x = 22

MHT = 6x - 7

6(22) - 7 = 132 - 7 = 125

AHM = 2x + 11

2(22) + 11 = 44 + 11 = 55

Answer:

ABCD forms a rhombus

Step-by-step explanation:

When you graph it out on a graph, the points make a rhombus

Answer:

As 1000g=1 kg ⟹1g=

1000

1

​

 kg.

26 kg 50 g.

=26 kg+50 g

=26 kg+50(

1000

1

​

)kg.

=26+0.05 kg.

=26.05 kg.

Answer: 26kg, 0.045kg

Step-by-step explanation:

y = -x²: vertical translation 1 unit upwards, y = x² + 1: vertical translation 1 unit upwards, y = -x² - 2: vertical translation 2 units downwards, y = -(x+1)² - 1: horizontal translation 1 unit to the left, reflected across the x-axis, y = -(x-1)² - 1: horizontal translation 1 unit to the right, reflected across the, y-axis, y = -x²: no transformation (same as the parent function)

The parent function is y = -x² - 1.

The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.

The function y = x² + 1 is obtained by adding a constant term "1" to the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = x² + 1 is the same as the parent function, except that it shifts upwards by 1 unit.

The function y = -x² - 2 is obtained by subtracting a constant term "2" from the parent function, which results in a vertical translation of the parent function by 2 units downwards. The graph of y = -x² - 2 is the same as the parent function, except that it shifts downwards by 2 units.

The function y = -(x+1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the left, and then it is reflected across the x-axis. The graph of y = -(x+1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the left and reflected across the x-axis.

The function y = -(x-1)² - 1 is obtained by applying two transformations to the parent function: first, it is shifted 1 unit to the right, and then it is reflected across the y-axis. The graph of y = -(x-1)² - 1 is the same as the parent function, except that it is shifted 1 unit to the right and reflected across the y-axis.

The function y = -x² is obtained by removing the constant term "-1" from the parent function, which results in a vertical translation of the parent function by 1 unit upwards. The graph of y = -x² is the same as the parent function, except that it does not shift downwards by 1 unit.

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Complete question provided in the image attached

The expected student population of the school will be N(t) = 15000*(1+3%)6=17910.78.

The term "population" refers to all citizens who are either permanently residing in a country or who are just passing through.  Growth rates are the population changes that occur each year as a result of births, deaths, and net migration. The world population clock maintained by the US Census Bureau indicated that there were 7,922,312,800 people on the planet as of September 2022, and that number would rise to 8 billion by mid-November. China and India will have the two largest populations in the world in 2022, followed by the United States, the European Union, Indonesia, and Pakistan.

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The correct statement regarding the probabilities is given as follows:

d. The experimental probability is closer to the theoretical probability for group X than group Y.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

For the theoretical probability, a coin is equally as likely to be heads or tails, hence for each group they are given as follows:

p = 1/2 = 0.5 = 50%.

The experimental probabilities for obtaining heads in each group are given as follows:

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