The solution set of an equation of a circle is all of he points that lie on the circle.

A. True

B. False

The area of the composite figure is 294 cm square.

The figure above is a composite figure. The figure is formed by combining two trapeziums.

Therefore, the area of the figure is the sum of the whole area of the shape.

Hence,

area of the composite figure = area of the trapezium1 + area of the trapezium2.

area of the trapezium1 = 1  / 2 (a + b)h

hence,

area of the trapezium1 = 1 / 2 (12 + 25)6

area of the trapezium1 = 1 / 2 (37)6

area of the trapezium1 = 111 cm²

area of the trapezium2 = 1 / 2 (24 + 37)6

area of the trapezium2 = 3 × 61

area of the trapezium2 = 183 cm²

Therefore,

area of the composite figure = 111 + 183

area of the composite figure = 294 cm²

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Answer:

24

Step-by-step explanation:

If we convert this problem into "math language", it's basically asking what is 8 divided by 1/3? So, we set this up: [tex]\frac{8}{\frac{1}{3} }[/tex] = 8 * 3 = 24

The height of the electric pole in order to cast a shadow of 10 m in the same condition as to be 14 m.

The flog poce cast a shadow of 5 metre and itself as a height of 7 m.

Now we have to find the height of an electric pole that will cast the shadow of length 10 m under the same conditions.

The word under the same condition means that the angle of elevation will be same in both the cases, so, we can use the tan theta here,

Tan A = perpendicular/base

Tan A will be equal for both.

Tan A = 7/5

Tan A = H/10

H is the height of the electric pole.

7/5 = H/10

H = 14m

The height of the electric pole will be 14 m.

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Step-by-step explanation:

Let the distance between them be y

sin20° =

=> 0.342 =           [  sin20° = 0.342]

=> y =  33/ 0.342

=> y = 96.5 ft

So, the distance between them is 96.5 ft

Answer:

The perimeter of △ABC is 144 cm.

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

Since points C and D are on the perpendicular bisector of AB, we have:

Find the length of AC using Pythagorean:

Find the perimeter of ΔABC:

The angle relationship that will fill the correct angle are given below.

An angle is said to be generated when two or more lines intersect at a point. Thus series of angles which have some common relationship on comparison are formed. Some common angle relationships are; supplementary angles, complementary angles, vertical angles, etc.

The angle relationship to fill the correct angle are:

1. <AXE and <CXD are vertical angles.

2. <AXF and <DXF are supplementary angles.

3. <DXC and <BXC are complementary angles.

4. <CXB and <AXB are adjacent angles.

5. <AXC and <CXD are supplementary angles.

6. <DXE and <AXC are vertical angles.

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It's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.

Statistical inference is the process of drawing conclusions or making predictions about a population based on data from a sample of that population. In other words, statistical inference involves using the principles of probability and statistics to make generalizations about a larger group based on information collected from a smaller group.

For example, a political survey may be conducted to gather opinions from a sample of voters about a particular issue or candidate. The data collected from this sample can be used to make inferences about the opinions of the larger population of voters. Statistical inference allows us to estimate the opinions of the larger population based on the information gathered from the smaller sample.

To illustrate this, suppose a survey is conducted on a random sample of 1000 voters in a city, and 600 of them indicate that they support a particular candidate. Based on this sample, the surveyors can use statistical inference to estimate the proportion of voters in the entire city who support that candidate. A confidence interval could be constructed to provide a range of values within which the true proportion of voters who support the candidate is likely to lie. This estimate can be used to inform political strategy and decision-making.

However, it's important to note that statistical inference is subject to certain assumptions and limitations, and there is always a degree of uncertainty associated with making predictions or generalizations based on a sample. Therefore, it's important to use sound statistical methods and careful analysis to ensure that the inferences drawn are as accurate as possible.

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The M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

The general equation is -

y{t} = A sin(ωt + Ф)

Given is a body describes an M.A.S according to the function -

{x} = 2 cos{(π/2)T+ π)r

Now -

For {T} = 2, we can write -

{x} = 2 cos{(π/2) x 2+ π)r

{x} = 2 cos{2π}r

{x} = 2 x 1 x r

{x} = 2r

For {T} = 2/3, we can write -

{x} = 2 cos{(π/2) x 2/3+ π)r

{x} = 2 cos{π/3}r

{x} = 2 x -0.33 x r

{x} = - 0.66r

Therefore, the M.A.S motion for two different time periods {T} = 2s and

{T} = 2/3s is calculated above.

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{Question in english -

a body describes an M.A.S according to what is specified.

x= 2 cos (π/2 T+π) r

Find its elements in:

T= 2

T= 2/3 sec

K=f/x}

Answer:

-0.061 dollars per day.

Step-by-step explanation:

(R(t + h) - R(t)) / h

We can use this formula to find the average rate of change of R(t) over various time intervals h, starting with t = 3:

For h = 1 day:

R(3 + 1) = 30(3 + 1) - 3(3 + 1)^2 = 27 - 6 = 21

Average rate of change = (21 - 30(3) + 3(3)^2) / 1 = (21 - 27) / 1 = -6

For h = 0.1 day:

R(3 + 0.1) = 30(3 + 0.1) - 3(3 + 0.1)^2 = 29.7 - 8.91 = 20.79

Average rate of change = (20.79 - 30(3) + 3(3)^2) / 0.1 = (20.79 - 27) / 0.1 = -0.61

For h = 0.01 day:

R(3 + 0.01) = 30(3 + 0.01) - 3(3 + 0.01)^2 = 29.93 - 8.9699 = 20.9601

Average rate of change = (20.9601 - 30(3) + 3(3)^2) / 0.01 = (20.9601 - 27) / 0.01 = -0.061

As we can see, as the value of h decreases, the average rate of change approaches a more accurate value. The average rate of change of R(t) at t = 3 days is approximately -0.061 dollars per day.

The solution to the equation is (b) x = -18

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

X

= 6

-3

Represent the equation properly

So, we have the following representation

x/-3 = 6

Cross multiply the equation

This gives

x = -3 * 6

Evaluate the products

x = -18

Hence, the solution is (b) x = -18

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Answer:

x = 72

Step-by-step explanation:

x : 4 = 54 : 3

express the ratios in fractional form

[tex]\frac{x}{4}[/tex] = [tex]\frac{54}{3}[/tex] = 18 ( multiply both sides by 4 to clear the fraction )

x = 4 × 18 = 72

Answer:

(x+y)(8a - 1)

Step-by-step explanation:

For the first expression:

(a-7) - y(a-7)

We can factor out (a-7) from both terms:

(a-7)(1 - y)

So, the factored expression is:

(a-7)(1 - y)

For the second expression:

8a(x+y) - (x+y)

We can factor out (x+y) from both terms:

(x+y)(8a - 1)

So, the factored expression is:

(x+y)(8a - 1)

Answer: (1-y)(a-7) and (8a-1)(x+y)

Step-by-step explanation:

When the values in the parentheses are the same twice, they reappear only once after grouping. In the first problem, the coefficients are 1 and -y, therefore, the answer becomes (1-y)(a-7).

Hope this helps

MM

If we have four variables, then four equations will we have in our system of linear equations.

A linear equation is a mathematical equation that represents a straight line on a graph. It is an equation that can be written in the form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point where the line intersects the y-axis.

Linear equations can be used to model a wide range of real-world phenomena, from simple physics problems such as calculating the speed of a moving object, to economic models that describe the relationship between price and demand. They are also widely used in fields such as engineering, finance, and statistics.

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Answer:

uhhhh

Step-by-step explanation:

The length of the segment NT is  4.5  units

What is isosceles triangle?

An isosceles triangle is one that has two sides of equal length.

The angles opposite to equal sides are equal.

Let RM=x, then  MS=RN=NT=x  ( because RS = RT )

RS=RT =2x

RST and RMN are two similar triangles

So, we have

ST/MN = RT/NT

=>  ST/3.5 = 2x/x

=> ST/3.5 = 2

=> ST = 2*3.5 = 7

Given , perimeter = 25

=> RS+ST+RT = 25

=> 2x+ST+ 2x = 25

=>  4x + 7 = 25

=> 4x= 25-7 = 18

=> x=18/4 = 4.5

NT=x= 4.5  units

The length of the segment NT is  4.5  units

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The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.

Subtract 2 from both sides:

y - 2 - 2 = -43(x + 6) - 2

y - 4 = -43(x + 6)

Divide both sides by -43:

(-1/43) * (y - 4) = x + 6

(-1/43)y - (-4/43) = x + 6

x = (-1/43)y + (-38/43)

Add 6 to both sides:

x + 6 = (-1/43)y + (-32/43)

Subtract (-1/43)y from both sides:

x + 6 - (-1/43)y = (-32/43) - (-1/43)y

x + 6 + (1/43)y = (-32/43)

Multiply both sides by -43:

(-43)(x + 6 + (1/43)y) = (-43)(-32/43)

-43x - 250 = -32

Add 250 to both sides:

-43x - 250 + 250 = -32 + 250

-43x = 218

Divide both sides by -43:

x = (-218)/(-43)

x = 5

The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.

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Answer:

180 most likely

Applying the Two Tangents Exterior Angle Theorem, the value of x is: 12.

m(BD) = 120°

If you draw two tangents from a point outside a circle, the size of the angle they form is equal to half of the difference between the sizes of the two arcs they intercept inside the circle, based on the Two Tangents Exterior Angle Theorem.

Therefore, we have:

6x - 12 = 1/2[(-12 + 21x) - (12x - 24)] (according to the Two Tangents Exterior Angle Theorem)

Solve for x:

6x - 12 = 1/2[(-12 + 21x - 12x + 24)

2(6x - 12) = -12 + 21x - 12x + 24

12x - 24 = 9x + 12

12x - 9x = 24 + 12

3x = 36

x = 36/3

x = 12

m(BD) = 12x - 24 = 12(12) - 24

m(BD) = 120°

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The required probability of removing a white marble followed by a blue marble is 2/33.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
There are 12 marbles in the bag in total, so the probability of selecting a white marble on the first draw is 4/12 or 1/3.

After the first marble is put aside, there are now 11 marbles in the bag, with 2 of them being blue. Therefore, the probability of selecting a blue marble on the second draw is 2/11.

To find the probability of selecting a white marble followed by a blue marble, we need to multiply the probability of the first event (selecting a white marble) by the probability of the second event (selecting a blue marble):

P(white, then blue) = P(white) x P(blue|white)

P(white, then blue) = (1/3) x (2/11)

Simplifying:

P(white, then blue) = 2/33

Therefore, the probability of removing a white marble followed by a blue marble is 2/33.

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The function represented by the graph is:

f(x) = |x – 1| + 3

This function takes the absolute value of the difference between x and 1, and then adds 3 to the result. The graph of this function will have a "V" shape centered at x = 1 with the vertex at (1, 3). The left side of the vertex will have a slope of -1, and the right side of the vertex will have a slope of +1. The y-intercept will be 3 units above the x-axis.

Answer:  B

Step-by-step explanation: YES

Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

A solution to an equation is a number that can be substituted for the variable to provide a true number statement.

Let's call the number of hours Camden works babysitting "x".

We know that x + 9 (hours of lifeguarding) cannot be more than 14 and that his total earnings must be at least $180. So we can write two equations based on these conditions:

x + 9 ≤ 14 (hours worked can't exceed 14)

10x + 18 × 9 ≥ 180 (earnings must be at least $180)

Now we can substitute the first equation into the second:

10x + 18 × 9 ≥ 180

10x + 162 ≥ 180

10x ≥ 18

x ≥ 1.8

Since x has to be a whole number of hours, we round up to find that Camden must work at least 2 hours babysitting.

So, Camden must work a minimum of 2 hours babysitting and 9 hours of lifeguarding to meet the requirements.

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A total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.

Let the three-digit number be written as abc, where a, b, and c are the hundreds, tens, and ones digits, respectively. We want b to be the absolute value of half the difference between a and c. In other words, we want b = [tex]\left|\frac{a-c}{2}\right|.[/tex]

Since a, b, and c are digits, we know that [tex]0 \leq a, b, c \leq 9.[/tex] Since b is the absolute value of a number, we know that b is non-negative.

Case 1: [tex]a \geq c[/tex]

If [tex]a \geq c[/tex], then[tex]b = \frac{a-c}{2}[/tex]. Since b must be non-negative, we have two

subcases to consider:

Subcase 1: a=c

In this subcase, b=0, which means that the number abc is of the form a00, where [tex]0 \leq a \leq 9[/tex]. There are 10 such numbers.

Subcase 2: a>c

In this subcase, [tex]b = \frac{a-c}{2}[/tex] is a positive integer. Since a and c must have the same parity (i.e., they are either both even or both odd), we have two

sub-subcases to consider:

Sub-subcase 1: a and c are both even

In this sub-subcase, a and c are both integers between 0 and 8 inclusive (since they are even and cannot be equal to 0 or 9). There are 4 such pairs of values for a and c: (2,0), (4,2), (6,4), and (8,6). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Sub-subcase 2: a and c are both odd

In this sub-subcase, a and c are both integers between 1 and 9 inclusive (since they are odd and cannot be equal to 0 or 8). There are 4 such pairs of values for a and c: (9,7), (7,5) , (5,3), and (3,1). For each pair, the value of b is uniquely determined, so there are 4 corresponding numbers abc.

Case 2: a < c

If a < c, then[tex]b = \frac{c-a}{2}[/tex]. Since b must be non-negative, we have only one

subcase to consider:

Subcase: c- a is even

In this subcase, c-a is an even integer between 2 and 8 inclusive (since it cannot be equal to 0 or 9). There are 4 such even integers: 2, 4, 6, and 8. For each even integer, the values of a and c that satisfy c-a are uniquely determined, and the value of b is then uniquely determined. So there are 4 corresponding numbers abc.

Putting everything together, we have a total of [tex]10 + 4 + 4 = \boxed{18}[/tex] three-digit numbers that satisfy the given property.

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Answer: A

Step-by-step explanation:

: 4x+25, 3x+15. x=10

The volume of the given 3 - D figure is 156.36 cubic inches.

A volume is a collection of a three dimensional coordinate points enclosed by a two dimensional coordinate points.

Given is the 3 - D figure as shown in the image.

We can write the volume as -

V = πr²h/3 + lbh

V = (3.14 x 3 x 3 x 8)/3 + (9 x 9 x 1)

V = 156.36 cubic inches

Therefore, the volume of the given 3 - D figure is 156.36 cubic inches.

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The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is 5/52

probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations.

Given that, if each coded item in a catalog begins with 4 distinct letters followed by 4 distinct nonzero digits

Like the 4 distinct letters be A,B,C,D

4 distinct nonzero digits are 2,3,4,5

The probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to the 10/104 = 5/52

Here the probability is an occurence of a particular events. This particular problem can be solved using permutations and combinations and the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even is approximately equals to 5/52

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The compound interest rate charged is given as follows:

13% per year.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 12000, A(t) = 22109.22, n = 1, t = 5.

Hence the interest rate is obtained as follows:

22109.22 = 12000(1 + r)^5

(1 + r)^5 = 22109.22/12000

1 + r = (22109.22/12000)^(1/5)

1 + r = 1.13

r = 1.13 - 1

r = 0.13.

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Answer:

5.6lbs

Step-by-step explanation:

multiply 180 by .08

8%=14.4

14.4-180=165.6

165.6-160= 5.6

The percent of sales tax that has been applied to the item is 5%.

A sales tax is a consumption tax imposed on the sale of items. It is often applied to the selling price of an item.

Here, the original cost is $90 and the final cost is $94.5.

Let, the sales tax rate is r%.

Calculate the percentage of sales tax.

Final price after sales tax = Selling Price×(1 + Rate of sales tax/100)

94.5 = 90(1+r/100)

94.5 = 90 + 0.9r

0.9r = 4.5

r = 5

Therefore, the obtained answer is 5%.

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