A plastic pipe 8 cm long has an outside radius of 6 cm and an inside radius of 5 cm. If the density of the plastic is 0.92 g/cm3, what is the mass of the pipe?

Since, the largest theater has 37 rows, the total seats in this​ theater are 1924

From the question, we have the following parameters:

First row, a = 16

Common difference, d = 2 additional seats

Number of rows, n = 37

The total seats in this​ theater are calculated using the following sum of n terms of an arithmetic sequence

Sn = n/2 * (2a + (n - 1) * d)

So, we have

S37 = 37/2 * (2 * 16 + (37 - 1) * 2)

Evaluate the difference in the above equation

So, we have

S37 = 37/2 * (2 * 16 + 36 * 2)

Evaluate the products in the above equation

So, we have

S37 = 37/2 * (32 + 72)

Evaluate the quotient in the above equation

So, we have

S37 = 18.5 * (32 + 72)

Evaluate the sum in the above equation

So, we have

S37 = 18.5 * 104

Evaluate the products in the above equation

So, we have

S37 = 1924

Hence, the total seats in this​ theater are 1924

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Answer:

2x best represents that 2 pencil was given to each of the x student

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Therefore , as a result Two of a triangle's sides and the included  SAS angle are said to be congruent if they match the corresponding sides and angles of another triangle.

The Side-Angle-Side rule is applied to check the congruence of a set of triangles. The SAS rule states that a triangle is congruent if its two sides and included angles match those of another triangle.

Here,

if the first triangle's two sides and one of its included angles are equal to the second triangle's sides and one of its included angles.

Consequently, the SAS declares two triangles to be congruent. Two triangles are said to be congruent if their matching two sides and their included angles are found in a single triangle, according to the SAS theorem of congruence.

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Answer:

27.50(80) is 2,200

2,200-396-175-264= 1,365

I think this is how u do it correct me if I'm wrong

5 times 5 = 25

5 x 5 = 25

5 + 5 + 5+ 5 +5 = 25

Answer:

answer is going to be 25

Step-by-step explanation:

so pretend you have 5 bags of 5 apples, this should stand for 5(bags of apples) and 5(apples in each bag), if you add the apples all together it will be 25 in total, or just try adding 5 five times: 5+5+5+5+5

The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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\(\textit{internal division of a segment using a fraction}\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-8})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{2})~\hspace{8em} \frac{3}{4}\textit{ of the way from A to B} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_2}{-6}-\stackrel{x_1}{5}~~,~~ \stackrel{y_2}{2}-\stackrel{y_1}{(-8)})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment AB}}}{\left( -11~~,~~ 10 \right)} \\\\[-0.35em] ~\dotfill\)

\(\left( \stackrel{x_1}{5}~~+~~\frac{3}{4}(-11)~~,~~\stackrel{y_1}{-8}~~+~~\frac{3}{4}(10) \right)\implies \left(5-\cfrac{33}{4}~~,~~ -8+\cfrac{15}{2} \right) \\\\\\ \left(\cfrac{20-33}{4}~~,~~\cfrac{-16+15}{2} \right)\implies \left(- \cfrac{13}{4}~~,~~-\cfrac{1}{2} \right)\)

Answer:

The cost of 27 units of electricity will be Rs. 131.10

Step-by-step explanation:

Given that:

Cost of first 20 units = Rs. 80

Cost of per unit after 20 units = Rs. 7.30

Units consumed in a household = 27 units

Bill of first 20 will be Rs. 80 and 7 units will be charged on the rate of 7.30

Cost of 7 units = 7*7.30 = Rs. 51.10

Cost of 27 units = Rs. 80 + 51.10 = Rs. 131.10

Hence,

The cost of 27 units of electricity will be Rs. 131.10

The inputs 4 and 8 have more than one out, the relation is not a function.

A relation is said to be a function if one input is mapped to one output.

that is, each x-value can only have one y-value.

From the table;

Input, output

4 ----- 1

8 ----- 3

4 ------5

8 ----- 4

4  is an input, it has an output of 1.

4 appeared again as input but this time has an output of 5.

This means one input has more than one output.

Also, 8 is an input, it has an output of 3.

8 appeared again as input but this time has an output of 4.

Which also means one input has more than one output.

Therefore, the relation is not a function.

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Answer:

4.0.

Step-by-step explanation:

In sample 1, you do 0.65/1.3 which gets you to 0.5, so then you do the same to the bottom which you also have to divide by 1.3, and 5.2/1.3 is 4.0 or 4.

Answer:

option D.  4.0

Step-by-step explanation:

                    Mass              Volume

Sample 1        0.65                0.5

Sample 2        5.2                   x

\(\frac{0.65}{5.2} = \frac{0.5}{x}\\\\0.65 \times x = 0.5 \times 5.2\\\\0.65x = 2.6\\\\x =\frac{2.6}{0.65} =4\)

Answer:

B) Yes

C) C = 3x + 25

Step-by-step explanation:

Given that:

Yearly charge = $25

Charge per visit = $3

The yearly cost will depend on the number of visits for the year :

B.) Cost can be represented by a linear function, as the graph it yields is a straight line graph having intercept and slope.

C.) C = mx + b

Where ;

b = intercept = yearly cost

m = slope or gradient = cost per visit

C = total cost

x = number of visits

Hence,

C = 3x + 25

Answer:

0

Step-by-step explanation:

No one is there which satisfies the condition

Answer:

0 or 0/9 of the club members

Step-by-step explanation:

The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.

Answer:

1

Step-by-step explanation:

5(0)+1=1 because 5x0=0 then add the 1

The value of the function f (x) = 5x + 1 at x equal to zero will be 1.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given function is f (x) = 5x + 1. The value of the function at x equal to 0 will be calculated as below:-

f (x) = 5x + 1

f (0) = 5 x 0 + 1

f (0) =  0 + 1

f (0) = 1

Therefore, the value of the function f (x) = 5x + 1 at x equal to zero will be 1.

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Answer:

the answer is 9.4

Step-by-step explanation:

We get that formula is:

d=\(\sqrt{(9-4)^{2} +(7--1)^{2} }=\sqrt{89}=9.4339\)

The quadratic equation is solved and intersect at the points (4, 1) and (-1, 16)

Given data ,

To find the intersection points of the two functions, we can set them equal to each other and solve for x:

x² - 6x + 9 = -x² + 17

Bringing all the terms to one side:

2x² - 6x - 8 = 0

Dividing by 2:

x² - 3x - 4 = 0

We can factor this quadratic equation as:

(x - 4)(x + 1) = 0

So the solutions are:

x = 4 or x = -1

To find the corresponding values of y, we can substitute each value of x into either of the original equations

y = x² - 6x + 9

When x = 4:

y = 4² - 6(4) + 9 = 1

So one intersection point is (4, 1).

When x = -1:

y = (-1)² - 6(-1) + 9 = 16

So the other intersection point is (-1, 16).

Hence , the two functions intersect at the points (4, 1) and (-1, 16)

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Answer:

Step-by-step explanation:

x*y = 490

x + y = 49

x = 49 - y

y*(49 - y ) = 490

49y - y^2 = 490

0 = y^2 - 49y + 490

This does factor (oddly). It doesn't look like it, but it does.

(y - 35) (y - 14) = 0

y - 35 = 0

y = 35

y - 14 = 0

y = 14

x = 49 - y  

Let y = 14

x = 49 - 14

x = 35

x = 49 - y

let y = 35

x = 49 - 35

y = 14

Solutions

(35,14)

(14,35)   Both solutions are valid.

Answer:

a) 4.46 miles

b) 3 miles

Step-by-step explanation:

Law of Sines:

\(\dfrac{\text{a}}{\text{sin(A)}} =\dfrac{\text{b}}{\text{sin(B)}}\)

a) The distance of the plane from point A

The angle of depression corresponds to the congruent angle of elevation therefore, 180 - 28 - 52 = 100°

\(\dfrac{\text{6.7}}{\text{sin(100)}} =\dfrac{\text{b}}{\text{sin(41)}}\)

\(\text{b}=\dfrac{6.7\text{sin}(41)}{\text{sin}(100)}\)

\(\text{b}=4.46 \ \text{miles}\)

b) Elevation of the plane

\(\text{sin}=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

hypotenuse is 4.46 and opposite is the elevation(h) to be found

\(\text{sin}(38)=\dfrac{\text{h}}{4.46}\)

\(\text{h}=\text{sin}(38)4.46\)

\(\text{h}=3\)

Answer: We remove the 16 regular customers and their seats from consideration.

Thus, we consider the 22 - 16 remaining customers = 6 and the 18-16 = 2 seats

overbooking means 3 or more of the 6 remaining passengers; each has a 58% chance remaining.  We can either use the binomial distribution formula P(x) = C(6, x) .58^x .42^(6-x) or use packages that provide the result, including cumulative probabilities.

Overbooking = 1 - P(X <= 2)   In Excel, we use =1 - binom.dist(2,6,.58,1)   ; the 1 is for cumulative.

The solution is 0.7920

Probability of empty seats = P(x <= 1)  = binom.dist(1,6,.58,1) = 0.0510

The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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Answer:

Its D

Step-by-step explanation:

Given, they are supplementry

hence their sum is 180 degree

now, 2x+5+3x-10=180

or, 5x-5=180

or, 5x=185

or, x=185÷5

or, x=37

Then, here we have measures of angle k is

3×37-19

=101

The expression simplifies to |2x| = -2x, when x<0 by definition of absolute value

If x<0, then the expression |2x| simplifies to -2x.

The absolute value of a number is the distance of the number from zero on the number line.

Since x is negative in this case, 2x will be negative as well.

Taking the absolute value of -2x will give us the opposite of -2x, which is 2x.

However, since we know that x<0, this means that -2x will always be a positive number.

Hence, the expression simplifies to |2x| = -2x, when x<0.

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Complete question

Simplify the expression |2x|  when x is less than 0, x<0

Answer:

-8/15 is less than 10/18 so <

Step-by-step explanation:

Answer:

M

Step-by-step explanation:

2,462 rounded is 2,500

2.5 × 10^3= 2,500

The answer is 2.5 × 10³ Because its = 2500

Answer:

the probability that the two committees have at least one member in common is approximately 0.3622.

Step-by-step explanation:

To find the probability that two committees have at least one member in common, we can use the complement rule, which states that the probability of an event happening is 1 minus the probability of the event not happening.

Let A be the event that the two committees have no members in common. To calculate the probability of A, we can first find the number of ways to choose three people out of 20 without any overlap, and then use this to find the total number of ways to choose two committees of three people each without any overlap:

Number of ways to choose 3 people out of 20 without overlap:

C(20,3) = (201918)/(321) = 1140

Number of ways to choose 3 people out of 20 with overlap:

C(20,3) - C(2,1)C(17,2) = 1140 - 2(2*136) = 680

The first term is the total number of ways to choose 3 people out of 20, and the second term is the number of ways to choose 3 people out of 20 such that one particular person is included. We multiply by 2 because there are two committees.

The total number of ways to choose two committees of three people each without any overlap is:

C(20,3) * C(17,3) = (1140*680) = 775200

Therefore, the probability that the two committees have no members in common is:

P(A) = 775200 / (C(20,3)*C(17,3)) = 0.6378

So the probability that the two committees have at least one member in common is:

P(at least one member in common) = 1 - P(A) = 1 - 0.6378 = 0.3622

Therefore, the probability that the two committees have at least one member in common is approximately 0.3622.

Answer:

Step-by-step explanation:

P = J - 15

       P + J = 55

(J - 15) + J = 55

           2J = 40

             J = 20 years

Answer:

232−202+17+18

Given statement solution is :- a) The area of one semi-circle at one end is  58.09 square feet.

b) The area of the garden is 274.42 square feet.

c) The area in square metres is approximately 58.09 square feet.

The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.

Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.

Now we can calculate the area of the semi-circle:

A = (π * 4.3²) / 2

A ≈ 58.09 square feet

b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.

Area of the rectangular portion = length * width

Area of the rectangular portion = 18.4 feet * 8.6 feet

Area of the rectangular portion ≈ 158.24 square feet

Area of the two semi-circles = 2 * (area of one semi-circle)

Area of the two semi-circles ≈ 2 * 58.09 square feet

Area of the two semi-circles ≈ 116.18 square feet

Total area of the garden = area of the rectangular portion + area of the two semi-circles

Total area of the garden ≈ 158.24 square feet + 116.18 square feet

Total area of the garden ≈ 274.42 square feet

c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.

Area in square meters = Total area of the garden * (0.3048)²

Area in square meters ≈ 274.42 square feet * 0.3048²

Area in square meters ≈ 25.49 square meters

Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.

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The only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

What is a valid triangle?

A valid triangle is a three-sided polygon that satisfies the following conditions:

The sum of the lengths of any two sides of the triangle is greater than the length of the third side.

The lengths of all three sides of the triangle are greater than zero.

Adam should use the dimensions 40 in., 44 in., 58 in. for a triangular frame to form a right triangle.

To determine if a right triangle can be formed, we need to check if the Pythagorean theorem is satisfied, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the length of the longest side (the hypotenuse).

Let's check each set of dimensions:

For 25 in., 60 in., 65 in.:

25^2 + 60^2 = 625 + 3600 = 4225

65^2 = 4225

The Pythagorean theorem is satisfied, so a right triangle can be formed. However, this triangle is not a valid option for Adam because the lengths are too short for building walls.

For 40 in., 44 in., 58 in.:

40^2 + 44^2 = 1600 + 1936 = 3536

58^2 = 3364

The Pythagorean theorem is not satisfied, so a right triangle cannot be formed using these dimensions.

For 50 in., 110 in., 130 in.:

50^2 + 110^2 = 2500 + 12100 = 14600

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

For 130 in., 50 in., 60 in.:

50^2 + 60^2 = 2500 + 3600 = 6100

130^2 = 16900

The Pythagorean theorem is satisfied, so a right triangle can be formed.

Out of the options given, only the dimensions 50 in., 110 in., 130 in. and 130 in., 50 in., 60 in. satisfy the Pythagorean theorem, but both are too large for building walls.

Therefore, the only valid option for Adam is to use different dimensions that form a right triangle. The dimensions 40 in., 44 in., 58 in. are the closest valid set of dimensions.

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