Over the last three evenings, Ann received a total of 70 phone calls at the call center. The first evening, she received 6 more calls than the third evening. The second evening, she received 2 times as many calls as the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening: ​

Linear approximations are used to estimate functions using derivatives

The approximated value of sin(56 degrees) is 0.8429

The trigonometry expression is given as:

[tex]\sin(56^o)[/tex]

Convert 56 degrees to radians

[tex]56^o = \frac{56}{180}\pi[/tex]

To approximate, we make use of 45 degrees.

Where:

[tex]\sin(45^o) = \cos(45^o) = \frac{\sqrt 2}{2}[/tex]

Also, we have:

[tex]45^o= \frac{\pi}{4}[/tex]

And

[tex](\sin\ x)'= \cos\ x[/tex]

So, the approximation of sin(56 degrees) become:

[tex]\sin(56\°) = \sin(45\°) + (\frac{56}{180}\pi - \frac{\pi}{4}) *\cos(45\°)[/tex]

Substitute known values

[tex]\sin(56\°) = \frac{\sqrt 2}{2} + (\frac{56}{180}\pi - \frac{\pi}{4}) *\frac{\sqrt 2}{2}[/tex]

Take LCM

[tex]\sin(56\°) = \frac{\sqrt 2}{2} + \frac{56 - 45}{180}\pi *\frac{\sqrt 2}{2}[/tex]

[tex]\sin(56\°) = \frac{\sqrt 2}{2} + \frac{11}{180}\pi *\frac{\sqrt 2}{2}[/tex]

Solve the expression

[tex]\sin(56^o) = 0.8429[/tex]

Hence, the approximated value of sin(56 degrees) is 0.8429

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Answer:

To get the Least Common Multiple (LCM) of 1820 and 3510 we need to factor each value first and then we choose all the factors which appear in any column and multiply them:

1820: 2 2 5 7 13

3510: 2 3 3 3 5 13

LCM: 2 2 3 3 3 5 7 13

The Least Common Multiple (LCM) is: 2 x 2 x 3 x 3 x 3 x 5 x 7 x 13 = 49140

Answer:

21.748 mph

Step-by-step explanation:

Answer:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

7x−5y=−24−9x+5y=187x-5y=-24-9x+5y=18

Answer:

Assuming this is a system of equations...

Point form > (3, 9)

Equation form > x = 3, y = 9

Step-by-step explanation:

So we need to solve for x in 7x - 5y = -24

Add 5y to both sides

7x = -24 + 5y

-9x + 5y = 18

Divide each term by 7

7x/7 = -24/7 + 4y/7

-9x + 5y = 18

x = -24/7 + 5y/7

-9x + 5y = 18

Now we need to replace all occurences of x with -24/7 + 5y/7

-9(-24/7 + 5y/7) + 5y = 18

x = -24/7 + 5y/7

So lets focus on simplifying -9(-24/7 + 5y/7) + 5y

Apply the distributive property

-9(-24/7) - 9 5y/7 + 5y = 18

Now multiply -9(-24/7)

So -1 by -9

9(24/7) - 9 5y/7 + 5y = 18

Combine 9 and 24/7

9 * 24/7 - 9 5y/7 + 5y = 18

Then Multiply 9 by 24

216/7 - 9 5y/7 + 5y = 18

Now we multiply -9 5y/7

So Combine -9 and 5y/7

216/7 + -9(5y)/7 + 5y = 18

Now Multiply 5 by -9

216/7 + -45y/7 + 5y = 18

Move the negative

216/7 - 45y/7 + 5y = 18

Now we need to multiply by 7/7 to make 5y a fraction with a common denom.

216/7 - 45y/7 + 5y * 7/7 = 18

Combine

216/7 + -45y + 5y * 7/7 = 18

Combine further

216 - 45y + 5y * 7/7 = 18

Multiply

216 - 45y + 35y

Add

216 - 10y/7 = 18

Factor 2 out of the equation

2(108) - 10y/7 = 18

Factor more

2(108) + 2(-5y)/7 = 18

Factor further

2(108 - 5y)/7 = 18

Now we want to solve for y in 2(108 - 5y)/7 = 18

Multiply both sides by 7 then simplify.

2(108 - 5y) * 7/7 = 18 * 7

2 * 108 + 2 (-5y) = 18 * 7

Multiply

216 + 2 (-5y) = 18 * 7

Multiply again

216 - 10y = 18 * 7

Reorder 216 and -10y

-10y + 216 = 18 * 7

Simplify the right side

-10y + 216 = 126

Now we need to solve for y

So lets move all terms not containing y to the right side.

-10y = 126 - 216 (Subtract 216 from both sides)

-10y = -90

Divide each term by -10

-10y/-10 = -90/-10

Simplify the left side

-90/10

And the right side

y = 9

x = -24/7 + 5y/7

Now replace y with 9

-24/7 + 5(9)/7

Simplify the right side

-24 + 5(9)/7

Multiply

-24 + 45

Add

21/7

x = 3

Therefore x = 3, y = 9 > (3, 9)

Answer:

8/3

Step-by-step explanation:

To make this function be continuous, we need to make the one-sided limits of the function at x=3 equal.

this means that 3c+8=9c-8

8=6c-8

16=6c

c=16/6 = 8/3

The value of constant c that makes the given function continuous at (-∞ , ∞) is 6.

What do you mean by continuity of a function ?

Continuity of a function meant all the points in the given interval satisfy the function.

We know that the conditions for which a function is continuous at b = x is :

a) f(x) exists

b) [tex]\lim_{ b\to x}[/tex] or f(b) exists.

c) [tex]\lim_{b \to x}[/tex] f(b) = f(x)

We know that for any value of c , for b ∈ ( - ∞ , 3] the function is continuous and for b ∈ ( 3 , ∞) the function is continuous. So , for any value of c, the first two conditions are satisfied.

Now we need to check for the continuity of the function at b = 3.

or

[tex]\lim_{b \to 2}[/tex] f(b) = c × 3 + 8

or

[tex]\lim_{b \to 2}[/tex] f(b) = 3c + 8

Now , check for the continuity of the function for other interval at b = 3.

[tex]\lim_{b \to 2}[/tex] f(b) = c × 9 - 8

or

[tex]\lim_{b \to 2}[/tex] f(b) = 9c - 8

To be continuous both values should be equal.

i.e.,

3c + 8 = 9c - 8

The value of constant c will be :

6c = 18

or

c = 6

Therefore , the value of constant c that makes the given function continuous at (-∞ , ∞) is 6.

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Answer:

a) 2. 4pi (in) , 4pi  

  3. 8pi , 16pi

  4. 16pi, 64pi

  5. 32 pi  ,  256pi

Step-by-step explanation:

b) when radius increase , the areas and circumferences increase to

circumference = 2 pi * radius ; so if you double the radius , circumference will be double

area = pi * radius * radius ; if you double the radius , area will be 2^2 or 4 times

c) circumference will be triple and

area will be 3^2 or 9 times

Answer:

A≈3.14m²

Step-by-step explanation:

Answer:

Area of Circle =

\begin{gathered}\pi {r}^{2} \\ = \pi( {1}^{2} ) \\ = 1\pi \\ = \pi {m}^{2} \end{gathered}

πr

2

=π(1

2

)

=1π

=πm

2

Answer: $29.10

Step-by-step explanation:

Shoes:

10% of 24 is 2.4

The shoes cost 21.60  with the 10% discount and before tax.

Belt:

25% of 10 is 2.5

The belt cost $7.50 with the 25% discount and before tax.

Total:

You still owe 29.10 for the belt and shoes before tax.

You saved $2.4 on the shoes and $2.5 on the belt (total of $4.90)

Answer:

15/2 is the answer to the question

Answer:

15/2

Step-by-step explanation:

Answer:

[tex]y=\displaystyle\frac{2}{3}x[/tex]

Step-by-step explanation:

Hi there!

The given linear equations are organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when x=0)

First, we can determine the slope using the following formula:

[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):

[tex]m=\displaystyle\frac{2-0}{3-0}\\\\m=\displaystyle\frac{2}{3}[/tex]

Therefore, the slope of the line is [tex]\displaystyle\frac{2}{3}[/tex]. Plug this into [tex]y=mx+b[/tex] as m:

[tex]y=\displaystyle\frac{2}{3}x+b[/tex]

We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:

[tex]y=\displaystyle\frac{2}{3}x+0\\\\y=\displaystyle\frac{2}{3}x[/tex]

I hope this helps!

Answer:

60 divided by 2 = 30

We half it because Angle E halfs Angle D

Step-by-step explanation:

As with all quadrilaterals, the sum of the interior angles of a rhombus is 360 degrees; as with a parallelogram, the angles of opposite pairs of vertices are equal, and the sum of the angles of two adjacent vertices is 180 degrees.

Answer:

60 in²

Step-by-step explanation:

Area of parallelogram = base x height

= 10 in x 6 in

= 60 in²

The area of the parallelogram is 60in².

Proportions are corresponding assuming they address a similar relationship. One method for checking whether two proportions are corresponding is to keep in touch with them as divisions and afterward decrease them. Assuming the decreased divisions are something similar, your proportions are relative.

Answer:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

Step-by-step explanation:

Answer:

16 minutes

Step-by-step explanation:

multiply 20 by 80% (20 times .80)

Answer:

1/12

Step-by-step explanation:

Since these are dependent events, the fractions will vary on the second trial.

First trial 3 green marbles out of a total of 9 marbles. That's a 3/9 chances of the marble being green.

Second trial if you already pulled out a green. 2 green marbles are left with 6 other colors. That makes it a 2/8 odds.

Multiply the fractions and you get 6/72, which simplifies to 1/12.

Answer:

3/9

Step-by-step explanation:

Simply add up the marbles the total being 9 and the 3 green marbles.  

Answer:

What are you referring to?

Step-by-step explanation:

Speed is the rate of change of distance over time

It takes Rohit 2 hours to cover the same distance

Represent Rajeev with A, and Rohit with B

Speed is calculated as:

[tex]Speed = \frac{Distance}{Time}[/tex]

Rohit covers 1/6 of the distance between point AB

So, we have:

[tex]S_B = \frac{AB/6}{T_B}[/tex]

Make T the subject

[tex]T_B = \frac{AB/6}{S_B}[/tex]

[tex]T_B = \frac{AB}{6S_B}[/tex]

Rajeev's speed is twice that of Rohit.

So, we have:

[tex]S_A = 2 * S_B[/tex]

[tex]S_A = \frac{AB}{T_A}[/tex]

So, the time taken by Rajiv to cover 1/6 of the distance is:

[tex]T_A = \frac{AB}{12S_B}[/tex]

The difference between the time is given as 1.

So, we have:

[tex]\frac{AB}{6S_B} - \frac{AB}{12S_B} = 1[/tex]

Multiply through by 12SB

[tex]2AB - AB = 12S_B[/tex]

[tex]AB = 12S_B[/tex]

Recall that:

[tex]T_B = \frac{AB}{6S_B}[/tex]

So, we have:

[tex]T_B =\frac{12S_B}{6S_B}[/tex]

[tex]T_B = 2[/tex]

Hence, it takes Rohit 2 hours to cover the same distance

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Answer:

7x - 10 is the simplify of the expression

If you was asking about the simplify of the expression it is 7x - 10

Answer:

Robert should put $32 in his wallet.

Step-by-step explanation:

18 + x > 50

-18      -18

x > 32

Hope this helps!

Answer:

3.75 pounds of carrots

Step-by-step explanation:

Multiply 0.75 by 5 and get 3.75

Answer:

3.75 lbs of carrots

Step-by-step explanation:

10/2=5

.75*5=3.75

You basically just need to multiply your serving by 5

Answer:

a) -0.6

b) 8.1

c) -6.5

d) 5.2¯9. The little line on top of the 9 is "bar notation".

Step-by-step explanation:

Hope this helps =)

Answer: m < 1 or m > 7

The correct answer is m < 1 or m > 7.

Step-by-step explanation:

Hope this helps =)

Answer:

26%×N=78

Reduce the fraction 26/100 to lowest terms by extracting and cancelling out 2.

13

– N=78

50

multiply both sides by 15/30 the reciprocal of 13/50

N=78× (50/13)

Express 78×(50/13) as a single fraction

N=78×50

———

13

multiply 78 and 50 to get 3900.

N=3900

———

13

Divide 3900 by 13 to get 300.

N=300

So the answer is N=300

Step-by-step explanation:

#Carry on learning

Step-by-step explanation:

let x represent the monthly budget.

13 % of x = $ 2600

(13/100) * x = $2600

13/100 = $2600/x

thus, the answer is D.

hope this helps you!

-s.

Answer:

0.003*10=0.03

0.3*10=3

30x10=300

300x10=3000

Step-by-step explanation:

Multiply each by 10

Answer:

0.03 , 3, 300, 3,000

Step-by-step explanation:

every time you multiply a decimal by 10 you move the decimal to the right once , on a whole number you just add another zero

Answer:

c. 18%

e. 46%

Step-by-step explanation:

c. Since the time given is 5.9, it is easiest to just calculate for every 0.1 second. So, there are 50 0.1 seconds in 5 seconds. If you divide 100/50 you get 2. So that is your percentage for each 0.1 seconds. It says less than 5.9 so theres 10 0.1 seconds. If you multiply 9x2 you get 18%.

e. based on 2% for every 0.1 seconds, there are 5 0.1 seconds between 5 and 5.5 and 18 0.1 seconds between 7.2 ad 10. 23x2= 46%

I would like to note that this question is incorrectly asked as it says less than which means the time given wouldnt count. It would have made much more sense to say 5.9 minutes or less.

Im pretty sure this is the right answer but it could be c. 20% and e. 50%

Hope this helps!

Suppose the time it takes Lizzie to eat an apple is uniformly distributed:

a. The distribution of X is Uniform, denoted as X ~ U(5, 10).

b. To find the probability that it takes Lizzie more than 11 minutes to finish the next apple, find the area of the distribution curve to the right of 11. Since the distribution is uniform, the probability is the ratio of the length of the interval [11, 10] to the total length of the interval [5, 10].

Probability (X > 11) = (10 - 11) / (10 - 5) = -1 / 5 = 0 (rounded to 4 decimal places)

c. Probability (X < 5.9) = (5.9 - 5) / (10 - 5) = 0.18

d. Probability (5.5 < X < 7.2) = (7.2 - 5.5) / (10 - 5) = 0.34

e. To find the probability that it takes Lizzie fewer than 5.5 minutes or more than 7.2 minutes to finish the next apple, find the sum of the probabilities of these two disjoint events:

Probability (X < 5.5 or X > 7.2) = Probability (X < 5.5) + Probability (X > 7.2)

= (5.5 - 5) / (10 - 5) + (10 - 7.2) / (10 - 5)

= 0.1 + 0.36

= 0.46

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Answer:

one answer ( y=0 )

Step-by-step explanation:

solve for y

-3y + 21 = 3y + 15 + 6

-3y +21 = 3y +21

(-6y = 0)/-6

y=0

Answer:

A. The equation has one solution, y = 0.

Explanation:

3(-y + 7) = 3(y + 5) + 6

-3y + 21 = 3y + 15 + 6

-3y -3y = 21 - 21

-6y = 0

y = 0

Answer: See below

Step-by-step explanation:

Event 1:

When the aces and twos (8 cards in total) are removed:
52 - 8 = 44 total cards

Since 2 cards (an ace and a two) were removed there are a total of 11 hearts

Probability: 11/44

P = 1/4 or 25%

Event 2:

Since 4 cards (2 aces and 2 two's) were removed there are a total of 22 blacks

Probability: 22/44

P = 1/2 or 50%

Event 3:

There are 12 face cards in the deck

Probability: 12/44

P = 3/11 or 27.27%

Event 4:

Probability of a heart + Probability of not a heart = 1 --> 100%

P(not a heart) = 1 - P(heart)

P = 1 - 1/4

P = 3/4 or 75%

Answer:

214,921,200 ways

Step-by-step explanation:

[tex]first \: price \: to \: one \: of \: the \: 600 \: \\ participant \\ so \: 600 \: choices \\ 2nd \: 599 \: choices \\ 3rd \: 598 \: choices \\ simplify \: 600 \times 599 \times 598 = \\ = 214,921,200[/tex]

Answer:

214,921,200 ways

Step-by-step explanation:

First = 600

Second = 599

Third = 598

Hence,

600 × 599 × 598

359400 × 598

214,921,200

Hence, in 214,921,200 different ways.

~Lenvy~