John sent a telegram of 44 words and he was charged shilling 25 for the first ten words and shilling 30 for each extra word .How much did the telegram cost?

Answer:

The answer is between 2 to 3 scoops.

Answer:

The only logical answer would be between 2 and 3 scoops

Answer:

832

Step-by-step explanation:

standard deviation =228 minute

error =13 minute given

confidence level =905% =0.90

α=1-0.90=0.1

[tex]z_\frac{\alpha }{2}=z_\frac{0.1}{2}=1.645[/tex]

we know that sample size should be greater than

[tex]n\geq \left ( z_\frac{\alpha }{2}\times \frac{\sigma }{E} \right )^2[/tex]

[tex]n\geq \left ( 1.645\times \frac{228}{13} \right )^{2}[/tex]

[tex]n\geq 28.850^2[/tex]

[tex]n\geq 832.3668[/tex]

n=832

Answer:

  C.  35

Step-by-step explanation:

Let x represent the largest of the multiples of 7. The sum will be ...

  x + (x -7) + (x -14) = 84

  3x = 105 . . . . . . . . . . . . . add 21 and simplify

  x = 35 . . . . . . . . . . . . . . . divide by 3

The greatest of the numbers of interest is 35.

_____

Two consecutive multiples of 7 will differ by 7. If x is the largest, the next-largest is x-7, and the one before that is x-14.

Answer:

  c)  (-2, 6)

Step-by-step explanation:

Subtracting the second equation from the first gives ...

  (y) -(y) = (x^2 +3x +8) -(2x +10)

  0 = x^2 +x -2 . . . . . simplify

  0 = (x -1)(x +2) . . . . factor

Solutions for x are 1 and -2. The corresponding y-values are ...

  y = 2{1, -2} +10 = {2, -4} +10 = {12, 6}

The solutions are (1, 12) and (-2, 6). The only matching choice is (-2, 6).

Answer:

They can buy 13meals if they buy 100 gallons of gasoline.

Step-by-step explanation:

3.50 PER gallon so 1 gallon is $3.50

if they buy 100 gallons you have to multiply 3.50 by 100 which gives you 350. you subtract 350 from 1000 so 1000-350 and get 650. now, you divide 650 by 50 because each meal is $50. And you get 13 so there you have it.

Final answer:

The family can buy 13 meals.

Explanation:

To find the number of meals the family can buy, we need to calculate the total cost of gasoline and subtract it from the total budget.

The family buys 100 gallons of gasoline at a cost of $3.50 per gallon, so the total cost of gasoline is 100 * $3.50 = $350.

The remaining budget for meals is $1,000 - $350 = $650.

The cost of each meal is $50, so the family can buy $650 / $50 = 13 meals.

Answer:

Part 1) [tex]-17\frac{8}{9}[/tex] -----> [tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]

Part 2) [tex]-15.11[/tex] ------> [tex]-12.48-(-2.99)-5.62[/tex]

Part 3) [tex]-19\frac{8}{9}[/tex] -----> [tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]

Part 4) [tex]-201.65[/tex] -----> [tex]-353.92-(-283.56)-131.29[/tex]

Part 5) [tex]74[/tex] ------> [tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]

Step-by-step explanation:

Part 1) we have

[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]6\frac{4}{9}=\frac{6*9+4}{9}=\frac{58}{9}[/tex]

[tex]3\frac{2}{9}=\frac{3*9+2}{9}=\frac{29}{9}[/tex]

[tex]8\frac{2}{9}=\frac{8*9+2}{9}=\frac{74}{9}[/tex]

substitute

[tex]-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=-\frac{(58+29+74)}{9}=-\frac{161}{9}[/tex]

Convert to mixed number

[tex]-\frac{161}{9}=-(\frac{153}{9}+\frac{8}{9})=-17\frac{8}{9}[/tex]

Part 2) we have

[tex]-12.48-(-2.99)-5.62[/tex]

To calculate the subtraction eliminate the parenthesis first

[tex]-12.48-(-2.99)-5.62=-12.48+2.99-5.62=-15.11[/tex]

Part 3) we have

[tex]-19\frac{2}{9}-4\frac{1}{9}-(-3\frac{4}{9})[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]19\frac{2}{9}=\frac{19*9+2}{9}=\frac{173}{9}[/tex]

[tex]4\frac{1}{9}=\frac{4*9+1}{9}=\frac{37}{9}[/tex]

[tex]3\frac{4}{9}=\frac{3*9+4}{9}=\frac{31}{9}[/tex]

substitute

[tex]-\frac{173}{9}-\frac{37}{9}-(-\frac{31}{9})[/tex]

Eliminate the parenthesis

[tex]-\frac{173}{9}-\frac{37}{9}+\frac{31}{9}=\frac{(-173-37+31)}{9}=-\frac{179}{9}[/tex]

Convert to mixed number

[tex]-\frac{179}{9}=-(\frac{171}{9}+\frac{8}{9})=-19\frac{8}{9}[/tex]

Part 4) we have

[tex]-353.92-(-283.56)-131.29[/tex]

To calculate the subtraction eliminate the parenthesis first

[tex]-353.92+283.56-131.29=-201.65[/tex]

Part 5) we have

[tex]83\frac{1}{5}-108\frac{2}{5}-(-99\frac{1}{5})[/tex]

To calculate the subtraction convert the mixed numbers to an improper fractions

[tex]83\frac{1}{5}=\frac{83*5+1}{5}=\frac{416}{5}[/tex]

[tex]108\frac{2}{5}=\frac{108*5+2}{5}=\frac{542}{5}[/tex]

[tex]99\frac{1}{5}=\frac{99*5+1}{5}=\frac{496}{5}[/tex]

substitute

[tex]\frac{416}{5}-\frac{542}{5}-(-\frac{496}{5})[/tex]

Eliminate the parenthesis

[tex]\frac{416}{5}-\frac{542}{5}+\frac{496}{5}=\frac{(416-542+496)}{5}=\frac{370}{5}=74[/tex]

Answer:

9

Step-by-step explanation:

[tex]\tt distance=\sqrt{(1-1)^2+(-4-5)^2}=\sqrt{0^2+9^{2}}=\sqrt{9^2} =9[/tex]

The formula for distance between two points is:

[tex]\sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}[/tex]

In this case:

[tex]x_{2} =1\\x_{1} =1\\y_{2} =-4\\y_{1} =5[/tex]

^^^Plug these numbers into the formula for distance like so...

[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]

To solve this you must use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

First we have parentheses. Remember that when solving you must go from left to right

[tex]\sqrt{(1-1)^{2} + (-4-5)^{2}}[/tex]

1 - 1 = 0

[tex]\sqrt{(0)^{2} + (-4-5)^{2}}[/tex]

-4 - 5 = -9

[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]

Next solve the exponent. Again, you must do this from left to right

[tex]\sqrt{(0)^{2} + (-9)^{2}}[/tex]

0² = 0

[tex]\sqrt{0 + (-9)^{2}}[/tex]

(-9)² = 81

[tex]\sqrt{(0 + 81)}[/tex]

Now for the addition

[tex]\sqrt{(0 + 81)}[/tex]

81 + 0 = 81

√81

^^^This can be further simplified to...

9

***Remember that the above answers are in terms of units

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

h=2×6/8

x^2=h^2+4

x=5/2

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

[tex](f+g)'=f'+g'[/tex] Sum rule.

[tex](cf)'=cf'[/tex] Constant multiple rule.

[tex](x^n)'=nx^{n-1}[/tex] Power rule.

[tex](x)'=1[/tex] Slope of y=x is 1.

[tex]f(x)=12x^2+8x[/tex]

[tex]f'(x)=(12x^2+8x)'[/tex]

[tex]f'(x)=(12x^2)'+(8x)'[/tex] by sum rule.

[tex]f'(x)=12(x^2)+8(x)'[/tex] by constant multiple rule.

[tex]f'(x)=12(2x)+8(1)[/tex] by power rule.

[tex]f'(x)=24x+8[/tex]

Now we need to find the derivative function evaluated at x=9.

[tex]f'(9)=24(9)+8[/tex]

[tex]f'(9)=216+8[/tex]

[tex]f'(9)=224[/tex]

In case you wanted to use the formal definition of derivative:

[tex]f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}[/tex]

Or the formal definition evaluated at x=a:

[tex]f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}[/tex]

Let's use that a=9.

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]

We need to find f(9+h) and f(9):

[tex]f(9+h)=12(9+h)^2+8(9+h)[/tex]

[tex]f(9+h)=12(9+h)(9+h)+72+8h[/tex]

[tex]f(9+h)=12(81+18h+h^2)+72+8h[/tex]

(used foil or the formula  (x+a)(x+a)=x^2+2ax+a^2)

[tex]f(9+h)=972+216h+12h^2+72+8h[/tex]

Combine like terms:

[tex]f(9+h)=1044+224h+12h^2[/tex]

[tex]f(9)=12(9)^2+8(9)[/tex]

[tex]f(9)=12(81)+72[/tex]

[tex]f(9)=972+72[/tex]

[tex]f(9)=1044[/tex]

Ok now back to our definition:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}[/tex]

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}[/tex]

Simplify by doing 1044-1044:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}[/tex]

Each term has a factor of h so divide top and bottom by h:

[tex]f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}[/tex]

[tex]f'(9)=\lim_{h \rightarrow 0}(224+12h)[/tex]

[tex]f'(9)=224+12(0)[/tex]

[tex]f'(9)=224+0[/tex]

[tex]f'(9)=224[/tex]

Answer:

r = 7

Step-by-step explanation:

let r = x

equation becomes

7x-15= x+27

Let the Left side AND Right side both equal y

y = 7x - 5

y = x + 27

graph these 2 equations. You should get 2 straight lines that intersect at x = 7, y = 34. (see attached)

recall at the start we let r = x, if we replace x with r again, we get r = 7

Answer:

15 miles per hour

Step-by-step explanation:

Average Speed is:

Average Speed = Total Distance/Total Time

Going uphill, she took 12 minuets, that is hours is 12/60 = 0.2 hours

We know D = RT, Distance = Rate(speed) * Time

Thus,

D = 10mph * 0.2 hr = 2 miles

So, total distance (uphill and downhill) = 2 + 2 = 4 miles

Downhill the time she took is

D = RT

2miles = 30mph * T

T = 2/30 = 1/15 hours = 1/15 * 60 = 4 minutes

Hence total time is 12 + 4 = 16 minutes

Note: 16 minutes = 16/60 = 4/15 hours

Now

Average Speed = Total Distance/Total Time

Average Speed = 4 miles/ 4/15 hours = 15 mph

Answer:

The Answer is 15.00000000000000000... miles per hour

Step-by-step explanation: You do tis by doing your work and not checking for answers

Answer:

Part a. t = 7.29 years.

Part b. t = 27.73 years.

Part c. p = $3894.00

Step-by-step explanation:

The formula for continuous compounding is: A = p*e^(rt); where A is the amount after compounding, p is the principle, e is the mathematical constant (2.718281), r is the rate of interest, and t is the time in years.

Part a. It is given that p = $2000, r = 2.5%, and A = $2400. In this part, t is unknown. Therefore: 2400 = 2000*e^(2.5t). This implies 1.2 = e^(0.025t). Taking natural logarithm on both sides yields ln(1.2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(1.2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(1.2)/0.025. This means that t = 7.29 years (rounded to the nearest 2 decimal places)!!!

Part b. It is given that p = $2000, r = 2.5%, and A = $4000. In this part, t is unknown. Therefore: 4000 = 2000*e^(2.5t). This implies 2 = e^(0.025t). Taking natural logarithm on both sides yields ln(2) = ln(e^(0.025t)). A logarithmic property is that the power of the logarithmic expression can be shifted on the left side of the whole expression, thus multiplying it with the expression. Therefore, ln(2) = 0.025t*ln(e). Since ln(e) = 1, and making t the subject gives t = ln(2)/0.025. This means that t = 27.73 years (rounded to the nearest 2 decimal places)!!!

Part c. It is given that A = $5000, r = 2.5%, and t = 10 years. In this part, p is unknown. Therefore 5000 = p*e^(0.025*10). This implies 5000 = p*e^(0.25). Making p the subject gives p = 5000/e^0.25. This means that p = $3894.00(rounded to the nearest 2 decimal places)!!!

Answer:

Given is :

4 different alarm systems were installed in the vault.

Each of the four systems detects theft with a probability of .99 independently of the others.

For solving this question, we have to first find the probability that none works.

It will be given as:

As there is 0.01 probability that all four systems will fail to detect theft. As all are independent, we get probability as: [tex](0.01)^{4}[/tex]

Now, we have to find the probability that at least one system detects the theft, it is given by:  [tex]1 -(0.01)^{4}[/tex]

Answer:

[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex] slope-intercept form

[tex]y+4=\frac{-4}{3}(x-2)[/tex] point-slope form

Step-by-step explanation:

Equation of a line in point-slope form is y-y_1=m(x-x_1) where m is the slope and b is the [tex](x_1,y_1)[/tex] is a point on the line.

So the m, slope, can be found by calculating the rise/run from one to another point on the line.

So let's start at (2,-4) and count to (-4,4).

So the rise is 8 and the run is -6.

The slope is therefore 8/-6=-8/6=-4/3.

Now if you didn't want to count because you can't count all the time.

You could line up the two points and subtract vertically, then put 2nd difference over 1st difference.

Like this:

(  2  ,   -4)

(-4  ,      4)

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

6          -8

So the slope is -8/6=-4/3.

Anyways now using any point on the line as [tex](x_1,y_1)[/tex] along with the slope we found we can finally put into our equation for point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

with [tex](x_1,y_1)=(2,-4)[/tex] and [tex]m=\frac{-4}{3}[/tex].

This gives us:

[tex]y-(-4)=\frac{-4}{3}(x-2)[/tex]

[tex]y+4=\frac{-4}{3}(x-2)[/tex]

We probably want to put into y=mx+b form; not 100% sure so I will give you choices:

y=mx+b is called slope-intercept form because it tells us the slope is m and the y-intercept is b.

[tex]y+4=\frac{-4}{3}(x-2)[/tex]

Distribute the -4/3 to the terms inside the ( ):

[tex]y+4=\frac{-4}{3}x+\frac{8}{3}[/tex]

Subtract 4 on both sides:

[tex]y=\frac{-4}{3}x+\frac{8}{3}-4[/tex]

Simplify the (8/3)-4:

[tex]y=\frac{-4}{3}x+\frac{-4}{3}[/tex]

The equation for this scenario is  6b= 42.

B= 42/6= 7

The value of b that makes the equation true is 7.

Hope this helps!

Answer:

6b = 42

b = 7 for the equation to be true.

Step-by-step explanation:

If Leo has b boxes of pencils with each containing 6 pencils, it means that the total number of pencils Leo has is dependent on the number of boxes given that the number in each box is known.

The product of the number of boxes with the number in each box gives the total number of pencils Leo has. This may be expressed mathematically as

= b × 6

= 6b

Given that Leo has 42 pencils, it means that

6b = 42

Dividing both sides by 6,

b = 42/6 = 7

It means he has 7 boxes.

Answer:

Step-by-step explanation:

Tough question.

Spiritual.

Love (if ever there was a misused word, it is love). I used to ask my classes what this sentence means "I love hunting." Try that one on. I don't know if you are dating someone, but how can you say "I love you." and "I love hunting." and not have something terribly wrong with the definition of the verb. One implies treasuring someone. The other means outfoxing a fox and murder.

Religion. Why are there so many different ones? The claim that there is only one true one makes the definition elusive to say the least. And it has caused a great deal of trouble.

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

Geometry: You have to know what a line segment is before you can say that one segment bears a relationship to another one.

You have to be able to define a point before you can calculate an intersection point of 2 lines or 2 curves or more.

You have to be able to define almost any term in geometry so that you can restrict enough to make it useful.

Answer:

Step-by-step explanation:

The train uses

[tex]\frac{400gallons}{200miles}[/tex]

If you reduce that you get that the train uses

[tex]\frac{2gallons}{1mile}[/tex]

To find the slope of the line, we will use the 2 points on the coordinate plane where the graph goes through:  (0, 0) and (400, 200)

Applying the slope formula:

[tex]m=\frac{200-0}{400-0}=\frac{1}{2}[/tex]

Answer:

6 miles per gallon

slope = 6

Step-by-step explanation:

Answer:

See below in bold.

Step-by-step explanation:

Ship's vector:

Horizontal component = 30 cos 30  = 25.98.

Vertical component = 30 sin(-30) = -15.

So it is <25.98, -15).

The current's vector:

Horizontal component =  5 sin 20 = 1.71.

Vertical component = 5 cos 20 = 4.7.

So it is <1.71, 4.7>.

The ship's vector representing its actual motion is 30.73 mph east of north.

To solve this problem, we can break down the velocities of the ship and the water current into their horizontal and vertical components. The ship's vector can be represented as:

Ship's Vector: 30 mph at an angle of 30° south of east

Breaking this down into horizontal and vertical components:

Horizontal Component = 30 mph * cos(30°) = 25.98 mph east

Vertical Component = 30 mph * sin(30°) = 15 mph south

The water current's vector can be represented as:

Water Current's Vector: 5 mph at an angle of 20° east of north

Breaking this down into horizontal and vertical components:

Horizontal Component = 5 mph * cos(20°) = 4.75 mph north

Vertical Component = 5 mph * sin(20°) = 1.71 mph east

To find the ship's actual motion, we can add the horizontal and vertical components together:

Horizontal Component = 25.98 mph east + 4.75 mph north = 30.73 mph east of north

Vertical Component = 15 mph south + 1.71 mph east = 16.71 mph south of east

Therefore, the ship's vector representing its actual motion is 30.73 mph east of north.

Answer:

-44 4/9

Step-by-step explanation:

-36 4/9-(-10 2/9)-(18 2/9)

-36 4/9+10 2/9 = 26 6/9

26 6/9 - (18 2/9)= -44 4/9

The correct answer to the given fraction after simplification is equal to [tex]-44\frac{4}{9}[/tex] .

" Simplification is defined as the reduce the given expression, fraction or problem into the easiest form."

Convert mixed fraction to proper fraction

[tex]p\frac{q}{r} = \frac{(r\times p)+q}{r}[/tex]

According to the question,

Given fraction,

[tex]-36\frac{4}{9}- (-10\frac{2}{9})-(18\frac{2}{9})[/tex]

Simplify the given fraction using conversion mixed fraction to proper fraction we get,

[tex]\frac{-328}{9}+ \frac{92}{9}- \frac{164}{9}\\\\= \frac{-328+92-164}{9}\\ \\= \frac{-400}{9}\\ \\= -44\frac{4}{9}[/tex]

Hence, Option(A) is the correct answer.

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Final answer:

To find the probability of selecting 5 non-defective widgets from 25 produced, we consider the independent probabilities of selecting a non-defective widget for each selection and multiply them together.Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.

Explanation:

To find the probability of selecting 5 widgets where none are defective, we need to consider the probability of selecting a non-defective widget for each of the 5 selections.

The probability of selecting a non-defective widget from the 25 produced is (25-5)/25 = 20/25 = 4/5.

Since the selections are independent, we can multiply the probabilities. So the probability of selecting 5 non-defective widgets is (4/5)⁵ = 1024/3125.

Therefore, the probability of selecting 5 widgets where none are defective is 1024/3125 or approximately 0.327.

Since the number of cats has to be less than 28, a statement could be "the shelter can house no more than 28 cats.

Answer:

Possible values of c are

[tex]c=0,1,2,3,4,...,26,27[/tex]

For example: The shelter can house 17 cats because 17 < 28.

Step-by-step explanation:

Let c be the number of cats.

The given inequality is

[tex]c<28[/tex]

We need to find the possible number of cats that a shelter can house.

The number number of cats can not be

1. A fraction value

2. A Decimal value

3. A negative value

Since c<28, therefore the number of cats must be greater that or equal to 0 and less that 28.

[tex]0\leq c<28[/tex]

The possible values of c are

[tex]c=0,1,2,3,4,...,26,27[/tex]

For example: The shelter can house 17 cats because 17 < 28.

Answer:

  see below

Step-by-step explanation:

The Law of Cosines tells you ...

  a² = b² + c² -2bc·cos(A)

Substituting the given values gives you ...

  a² = 4² +7² -2(4)(7)cos(52°)

Answer:

∠R = 36.06°, ∠Q = 90.81°

Step-by-step explanation:

I used the Law of Cosines to find angle R first.  If you use the Law of Sines, the main angle is the same, but it differs in the decimal value.  Since you started the process with the Law of Cosines, I used it again.  Setting up to find angle R:

[tex]36^2=48^2+60^2-2(48)(60)cosR[/tex] and

1296 = 2304 + 3600 - 5760cosR so

-4608 = -5700cosR and

.8084210526 = cosR

Taking the inverse cosine to find the angle,

R = 36.06

That means that Q = 180 - 36.06 - 53.13 so

Q = 90.81

Answer:

x = 28,000

Step-by-step explanation:

"What" is our unknown, x; "is" is an equals sign; 70% expressed as a decimal is .70; "of" means to muliply.

Our equation, then, is

x = .70(40,000) so

x = 28,000

Answer:

28000

Step-by-step explanation:

70% of 40,000 is 28000.

28,000/40,000 = 70%

40000=100%

x=70%

40000/x=100%/70%

Answer:

Pool will be filled in 280 hours

Step-by-step explanation:

Inlet pipe fills in  40 hours = 1 pool

Inlet pipe fills in 1 hours = [tex]\frac{1}{40}[/tex]

Drain pipe empty in 42 hours = 1 pool

Drain pipe empty in 1 hour =  [tex]\frac{1}{42}[/tex]

If both pipes are opened together

 then in pool fills in 1 hour =  [tex]\frac{1}{40}[/tex] -  [tex]\frac{1}{42}[/tex]

      on simplifying the right side ,we get  [tex]\frac{42-40}{(40)(42)}[/tex]

                                                                 =      [tex]\frac{2}{(40)(42)}[/tex]

                                                                 =     [tex]\frac{1}{840}[/tex]

      [tex]\frac{1}{840}[/tex]  pool fills in 1 hour

                       1 pool will be filled in 840 hours

    [tex]\frac{2}{3}[/tex]     pool is filled

empty pool =  1 - [tex]\frac{2}{3}[/tex] =  [tex]\frac{1}{3}[/tex]

therfore  [tex]\frac{1}{3}[/tex] pool will be filled in     [tex]\frac{1}{3}[/tex]X 840 =

                                                                                           = 280 hours

The  calculations indicate that 280 hours is the  time required to fill 2/3 of the pool with both pipes open.

Inlet Pipe Rate:

The inlet pipe can fill the pool in 40 hours.

Therefore, the rate of the inlet pipe is 1/40 pool per hour.

Drain Pipe Rate:

The drain pipe can empty the pool in 42 hours.

Therefore, the rate of the drain pipe is 1/42 pool per hour.

Combined Rate when both pipes are open:

The net rate when both pipes are open is the difference between their individual rates:

Net rate = (1/40) - (1/42)

Simplify the Net Rate:

Find a common denominator for 40 and 42, which is 840:

Net rate = (42 - 40) / 840 = 2/840 = 1/420

Time to Fill 2/3 of the Pool:

Set up the equation: Net rate * Time = 2/3

Substitute the net rate: (1/420) * Time = 2/3

Cross-multiply to solve for time: Time = (2/3) * (420/1) = 280

Therefore, it takes 280 hours to fill 2/3 of the pool when both the inlet and drain pipes are open.

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Final answer:

To find the height of the building, we use the tangent function with the angle of depression and the horizontal distance from the point to the building's base, resulting in a building height of 22 meters when rounded to the nearest meter.

Explanation:

To calculate the height of the building when the angle of depression from the top of the building to a point P on the ground is 23.6 degrees and the distance from P to the foot of the building is 50 meters, we can use trigonometry.

Specifically, we use the tangent function which relates the angle of a right triangle to the ratio of the opposite side (height of the building in this case) over the adjacent side (distance from P to the foot of the building).

Let's denote the height of the building as H. Thus, we have:

tan(23.6°) = H / 50

From this, we can solve for H:

H = 50 × tan(23.6°)

Rounding to the nearest meter, the height of the building is 22 meters.

[tex]b[/tex] - the side of a square

[tex]a=b\sqrt2\\b=\dfrac{a}{\sqrt2}\\\\b=\dfrac{a\sqrt2}{2}[/tex]

Answer:

a√2 / 2.

Step-by-step explanation:

Using the Pythagoras Theorem;

a^2 = s^2 + s^2 where s is the length of each side of the square.

2s^2 = a^2

s^2 = a^2 / 2

s =  √(a^2 / 2)

= a / √2

= a√2 / 2 .

Answer:

Step-by-step explanation:

You must use a combination:

[tex]_nC_k=\dfrac{n!}{k!(n-k)!}[/tex]

We have n = 16, k = 3.

Substitute:

[tex]_{16}C_3=\dfrac{16!}{3!(16-3)!}=\dfrac{13!\cdot14\cdot15\cdot16}{2\cdot3\cdot13!}\qquad\text{cancel}\ 13!\\\\=\dfrac{14\cdot15\cdot16}{2\cdot3}=\dfrac{7\cdot5\cdot16}{1}=560[/tex]

The number of possible selections is 560.

The library is to be given 3 books as a gift. The books will be selected from a list of 16 titles.

Here we used the combination

[tex]= nC_n\\\\= 16C_3\\\\= \frac{16!}{3!(16-3)!}\\\\ = \frac{16!}{3!13!}\\\\ = \frac{16\times 15\times 14\times 13!}{13!3!}\\\\ = \frac{16\times 15\times 14}{3\times 2\times 1}\\[/tex]

= 560

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Answer:

15, 18, 21, 24, 27

Step-by-step explanation:

Five multiples of 3 means we have 5 terms we are adding together to = 105.

For the sake of having something to base each one of these terms on, let's say that the first term is 3.  It's not, but 3 is a multiple of 3 and we have to start somewhere.  These terms go up by the next number that is divisible by 3.  After 3, the next number that is divisible by 3 is 6.  The next one is 9, the next is 12, the last would be 15.

Let's then say that 3 is the first term, and we are going to say that is x.

To get from 3 to 6, we add 3.  Therefore, the second term is x + 3.

To get from 3 to 9, we add 6.  Therefore, the third term is x + 6.

To get from 3 to 12, we add 9.  Therefore, the fourth term is x + 9.

To get from 3 to 15, the last term, we add 12.  Therefore, the last term is x + 12.

The sum of these terms will then be set to equal 105:

x + (x + 3) + ( x + 6) + ( x + 9) + ( x + 12) = 105

We don't need the parenthesis to simplify so we add like terms to get

5x + 30 = 105.  Subtract 30 from both sides to get

5x = 75 so

x = 15

That means that 15 is the first multiple of 3.  

The next one is found by adding 3 to the first:  so 18

The next one is found by adding 6 to the first:  so 21

The next one is found by adding 9 to the first:  so 24

The last one is found by adding 12 to the first:  so 27

15 + 18 + 21 + 24 + 27 = 105

Notice that all the numbers are, in fact, consecutive multiples of 3 as the instructions stated.

The five consecutive multiples of 3 that sum up to 105 are 15, 18, 21, 24, and 27.

The question posed is regarding five consecutive multiples of 3. The sum of these multiples equals 7x15 (or 105). Let's call the first multiple of 3 as '3x'. Therefore, the five consecutive multiples can be represented as 3x, 3x+3, 3x+6, 3x+9, 3x+12.

The sum of the five consecutive multiples then is 15x + 30 (comprising 5 times 'x', plus 30 from the sum of 3, 6, 9, and 12). We know that this sum equals 105, so we can set up the following equation:
15x + 30 = 105.

Solving this equation for 'x' gives:
x = 5. This means the first multiple is 3x, or 3x5 = 15. The next multiples are therefore 15+3 (18), 18+3 (21), 21+3 (24) and 24+3 (27).

So, the five multiples of 3 that yield a sum of 105 are 15, 18, 21, 24, and 27.

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