What is the volume of this composite solid

​

Step-by-step explanation:

Per our conceptual understanding, when two parallel lines are cut by a transversal line then their corresponding angles are equal.

So, If PQ and RS are two parallel lines and line L1 as shown is the transversal line then the corresponding angles are equal.

Hence, ∠1 = ∠2Or, c0 = 1800 – c02c = 180c = 90°

Therefore, if we get c = 90° then PQ and RS are parallel else PQ and RS are not parallel,

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

“b = 2a”

Per conceptual understanding, the sum of all the angles of a triangle is 180.

Hence, a + b + c = 180a + 2a + c = 1803a + c = 180

However, from the above equation, we can get many values of a and c.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

“c = 3a”

a + b + c = 180a + b + 3a = 180b + 4a = 180

However, from the above equation, we can get many values of a and b.

Hence, statement 2 is not sufficient to answer the question.Step 5: Combine Both Statements Together (If Needed)

From statement 1:

3a + c = 180

From statement 2:

c = 3a

Combining both the statements:

3a + 3a = 180.

From the above equation, we can find the value of a. Then we can find c.

Since we could find the answer by combining both the statements, option C is the correct answer.

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Answer:

20

Step-by-step explanation:

add 3ft+3ft+11ft+3ft and that's your answer

Answer:

3959

Step-by-step explanation:

Distance from surface to its core is 3,959 miles

Given that;

Diameter of earth = 7,918 miles

Find:

Distance from surface to its core

Computation:

Radius of earth = Distance from surface to its core

Distance from surface to its core = 7,918 / 2

Distance from surface to its core = 3,959 miles

Find out more about 'distance'.

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Answer:

Step-by-step explanation:

Use pythagorean theorem

9^2 +40^2=x^2

81+1600=x^2

1681=x^2

now find the square root of each side

[tex]\sqrt{1681} =\sqrt{x}[/tex]

x=41

Answer:

x=0 y=2 z=5

Step-by-step explanation:

so for z

2z=10

divid both side by 2

z=5

equation one

x+2y+5=9

x+2y=4 ------eqn1

equation two

x-y+ 3(5)=13

x-y+15=13

x-y=-2-----eqn2

now you solve it by elimination

eqn1-eqn2

3y=6

y=2

put y=2 into eqn2

x-2=-2

x=0

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Answer:

it is C.

Step-by-step explanation:

we know,

14+17= 31

so if we subtarct 17 from 31 we get 14

and if we subtract 14 from 31 we get 17

Answer:

x>36

Step-by-step explanation:

Hope this helps and good luck

The interquartile range of Victor's lemonade sale is A = 7

The distance between the upper and lower quartiles is known as the interquartile range. Half of the interquartile range corresponds to the semi-interquartile range. Finding the values of the quartiles in a small data set is straightforward.

The spread of the data, or statistical dispersion, is measured by the interquartile range. The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.

Given data ,

Let the interquartile range of sales of Victor's lemonade be A

Now , the equation will be

Let the 75th percentile data = 29

Let the 25th percentile data be = 22

Now , the IQR is calculated by spread between the data's 75th and 25th percentiles

On simplifying , we get

The IQR = 29 - 22 = 7

Hence , the interquartile range is 7

To learn more about interquartile range click :

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The complete question is :

Victor is selling lemonade to raise money for his school the amount of money he collected from his sales each day is summarized on the box plot below.

What is the interquartile range of the data?

Answer:

Cabral is right

Step-by-step explanation:

Mark me brainleyest plz

Answer:

=4m+8

Step-by-step explanation:

=(4)(m+2)

=(4)(m)+(4)(2)

=4m+8

Answer:

4m +8

Step-by-step explanation:

Take out the parenthesis

Answer:

B.

Step-by-step explanation:

(f-g)(x) = f(x) - g(x) =

= (3x³ + 8x² -7x - 4) - (2x - 6) = 3x³ + 8x² - 7x - 4 - 2x + 6 =

= 3x³ + 8x² - 9x + 2

[tex]\pink{\bigstar}[/tex] Simplified form [tex]\large\leadsto\boxed{\tt\purple{\dfrac{2 \pi}{3}}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf \dfrac{4 \pi \sqrt{5} - 2 \pi \sqrt{5}}{3 \sqrt{5}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf \dfrac{2 \pi \sqrt{5}}{3 \sqrt{5}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf \dfrac{\sqrt{5} (2 \pi)}{\sqrt{5} (3)}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

➪ [tex]\sf \dfrac{\cancel{\sqrt{5}}(2 \pi)}{\cancel{\sqrt{5}} (3)}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ [tex]\bold\red{\dfrac{2 \pi}{3}}[/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, Option A is the correct choice.

option A.

Step-by-step explanation:

we have

[tex] \frac{4\pi \sqrt{5} - 2\pi \sqrt{5} }{3 \sqrt{5} } [/tex]

taking out 2[tex] \pi\sqrt{5}[/tex] common from the numerator

[tex] \frac{2\pi \sqrt{5}(2 - 1) }{3 \sqrt{5} } [/tex]

canceling [tex] \sqrt{5} [/tex] from both numerator and denominator

[tex] \frac{2\pi(1)}{3} [/tex]

hence the answer is option A.

Step-by-step explanation:

To prove - Using the method of proof by contradiction, prove that if

                  a product of two positive real numbers is greater than

                  1,000,000, then at least one of the numbers is greater

                   than 1000.

Proof -

For a proof of contradiction , firstly we have to assume that the statement is not true.

Here given statement is -  A product of two positive real numbers is greater than 1,000,000.

Let if possible, there does not exist 2 +ve integer real number such that at least one of the numbers is greater than 1000.

⇒both the number are in between 0 to 1000

Let a and b are 2 +ve real numbers.

⇒ab < 1000×1000

⇒ab < 1000000

As given,

ab > 1000000

Contradiction.

Hence proved.

If a product of two positive real numbers is greater than 1,000,000, then at least one of the numbers is greater than 1000.

Answer:

y=3x^2 -15x-42

Step-by-step explanation:

Any 3 digit number can be expressed in the form of:

[tex](a*100)+(b*10)+(c*1)[/tex]

Where [tex]a, b, c[/tex] represent any natural number from 0 to 9.

We are told the hundreds number (this means [tex]a*100[/tex] in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means [tex]b>6[/tex] in the expression above.

So, there are multiple numbers the room number could be, namely:

[tex]400+(b*10)+(c*1)\\[/tex]

where [tex]b[/tex] can be 7, 8, or 9; and [tex]c[/tex] can be  0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.

Answer:

18/4 = 4.5

it would take you about 4 hours and 30 minutes  to walk 18 miles

Step-by-step explanation:

Answer:

4 1/2 hours

Step-by-step explanation:

RATIO:

Miles      Hours

4                  1

8                  2

12                 3

16                 4

18               4 1/2

You need to get from 16-18 so you have to get 4-2 and 1 hour to 1/2 hour.

Answer:

w= 1 29/45

isolate the variable by dividing each side by the numbers that don't contain the variable.

Answer:

for 1 student it would equal 11.25

11.25 x 50 = 562.50

ur answer is 50 students hope this helps :)

Answer:

the teacher has 50 students

Step-by-step explanation:

1.75+9.50=11.25

562.50/11.25=50

Answer:

[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]

A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]

Step-by-step explanation:

Given - A tank contains 350 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t.

To find - Find the rate at which the number of grams of salt in the tank is changing at time t.

Find the number A(t) of grams of salt in the tank at time t.

Proof -

Given that,

Total fluid in the tank = 350 litres

Total salt = 40 grams

Rate in flow = 5 L/min

Rate out flow = 5 L/min

Concentration in = 0

Concentration out = (Amount of salt at time t )/ (Solution in tank at time t)

Now,

Total solution in the tank at time t = Total fluid in the tank + (Rate in flow - Rate out flow )t

                                                        = 350 + (5 - 5)t

                                                        = 350

⇒Solution in the tank at time t = 350

⇒Concentration out = [tex]\frac{A(t)}{350}[/tex]

Now,

Rate of change in the tank at time t = [tex]\frac{dA}{dt}[/tex]

                                                           =  (Rate in flow )( Concentration In) - (Rate out flow )( Concentration out)

                                                           = 5(0) - 5([tex]\frac{A(t)}{350}[/tex])

                                                           = 0 - [tex]\frac{A(t)}{70}[/tex]

                                                           = [tex]-\frac{A(t)}{70}[/tex]

⇒[tex]\frac{dA}{dt}[/tex] = [tex]-\frac{A(t)}{70}[/tex]

⇒[tex]\frac{dA}{A} = -\frac{1}{70} dt[/tex]

Integrate both sides , we get

ln(A) = [tex]-\frac{1}{70}t + C[/tex]

⇒A(t) = [tex]e^{-\frac{t}{70}+ C}[/tex]

         = [tex]e^{-\frac{t}{70}}*e^{C}[/tex]

         = [tex]C_{1} e^{-\frac{t}{70}}[/tex]

⇒A(t) = [tex]C_{1} e^{-\frac{t}{70}}[/tex]

Now,

Given that,

Initially, the tank has 40 grams of salt

⇒A(0) = 40

⇒C₁ = 40

⇒A(t) = [tex]40 e^{-\frac{t}{70}}[/tex]

Answer:

She can invite 66 people so 66 x 5 = $330 + 120 = $450

Step-by-step explanation:

Answer:

B. [tex] \frac{x}{5} = 8.5 [/tex]; [tex] x = 42.5 ounces [/tex]

Step-by-step explanation:

Total amount of salsa in container = x

Number of bowl the salsa is divided into = 5

Amount contained by each bowl = 8.5 ounces of salsa

Therefore:

[tex] \frac{x}{5} = 8.5 [/tex] ---› equation

Solve for x

Multiply both sides by 5

[tex] \frac{x}{5}*5 = 8.5*5 [/tex]

[tex] x = 42.5 [/tex]

Answer:

The system is of equations is:

[tex]\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.[/tex]

Where g is the amount of general tickets and r is the amount of reserve tickets.

35 general tickets and 25 reserve tickets were sold.

Step-by-step explanation:

Let general tickets be represented by g and reserved tickets be represented by r.

Each general ticket sells for $10 each and reserved tickets $15 each. Dave collected a total of $725. Thus:

[tex]10g+15r=725[/tex]

And a total of 60 tickets were sold. Hence:

[tex]g+r=60[/tex]

Our system of equations is:

[tex]\left\{ \begin{array}{ll} 10g+15r=725 & \quad \\ g+r=60 & \quad \end{array} \right.[/tex]

We can solve by substitution. First, divide both sides of the first equation by 5:

[tex]2g+3r=145[/tex]

Next, we can subtract a variable (r in this case) from the second equation:

[tex]g=60-r[/tex]

Substitute:

[tex]2(60-r)+3r=145[/tex]

Distribute:

[tex]120-2r+3r=145[/tex]

Simplify:

[tex]120+r=145[/tex]

Subtract:

[tex]r=25[/tex]

Using the previous equation:

[tex]g=60-r[/tex]

Substitute and evaluate:

[tex]g=60-(25)=35[/tex]

So, 35 general tickets and 25 reserve tickets were sold.

Answer:

Sorry If I'm wrong but I'm pretty sure you would use theoretical

Step-by-step explanation:

Because Theoretical is used to make predictions and when doing this you would have to make lots of predictions on what you would get.

(Hope It's Right!)

Step-by-step explanation:

1. Is a table which is contained in the attachment

2. The crude ratio measure

= 4000x3000+20*5800/7000*6000+200*3980

= 12000000+116000/42000000+796000

= 12116000/42796000

= 0.283

3. Stratum specific for high lipid

= 12000000/42000000

= 0.285

= 0.29

Stratum specific for chf

= 116000/796000

= 0.145

= 0.15

4. High lipid has higher risk than chd from the solution here

Answer:

The answer would be D

Step-by-step explanation:

Why? because as the temperature increases the amount of lemonade sold increases by 2

This is represented in 2(x) if that makes sense

For every 1-degree increase in high temp of the day, sales decrease by 2 glasses of lemonade. Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The function is given below.

f(x) = 2(x – 65) + 12

f(x) = 2x – 130 + 12

f(x) = 2x – 118

For every 1-degree increase in high temp of the day, sales increase by 2 glasses of lemonade. Then the correct option is D.

More about the linear equation link is given below.

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The missing options are given below.

a) for every 65-degree decrease in high temp of the day, lemonade sales increase by 1 glass of lemonade

b) for every 1-degree increase in high temp of the day, sales increase by 2 glasses of lemonade

c) for every 65-degree decrease in high temp of the day, sales decrease by 1 glass

d) for every 1-degree increase in high temp of the day, sales decrease by 2 glasses of lemonade