Amber has been saving quarters and dimes. She opened up the piggy bank and determined that it contained 18 coins worth $2.85. Determine how many dimes and quarters were in the piggy bank.

[tex]\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.

[tex]sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}[/tex]

Then,

[tex]\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10[/tex]

Thank you

Answer:

-10

Step-by-step explanation:

L' Hopital's rule can be used to solve it.

We search for lim (f(x)/g(x))

this is the same as lim (f' (x)/g' (x))

this is the same as lim f'' (x)/g'' (x)

so here we have f(x) =sin(4x)-4sin(x)

g(x)=x^3

g'' (x)= 6x

f'' (x)=-16sin(4x)+4sin(x)

so lim f'' (x) / g ''(x) = -16/6 lim sin(4x)/x + 4/6 lim (sin(x)/x)

= -16*4/6+4/6

=(-64+4)/6=-60/6=-10

Answer:

16p

Direction: positive/upward direction

Step-by-step explanation:

First, the function is f(x,y) = 4ypx

At the point where x=4 and y=1, the maximum rate of change of the function f(x,y) is

4(1)p(4) = 16p

The direction in which it occurs is the positive(upward) direction

Answer:

36.15 miles, 12.05 miles on one gallon

Step-by-step explanation:

4hours=144.6 miles

1 hour= x

Therefore it traveled 36.15 miles per hour.

12 gallon = 144.6 miles.

1 gallon = x

12.05 miles on one gallon

Answer: 4y - x = 8

y = 4x + 7

This equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The slope of this line is 4. Parallel lines have the same slope, thus a line not parallel to this line will not have a slope of 4. Let's check which of these lines does not have a slope of 4.

y - 4x = 9

y = 9 + 4x (add 4x to both sides)

y = 4x + 9 (switch the constant and x-term)

This line has a slope of 4.

4x - y = 8

-y = 8 - 4x (subtract 4x from both sides)

y = -8 + 4x (divide both sides by -1)

y = 4x - 8 (switch the constant and x-term)

This line has a slope of 4.

4y - x = 8

4y = 8 + x (add x to both sides)

y = 8/4 + x/4 (divide both sides by 4)

y = x/4 + 2 (simplify and switch constant and x-term)

This line has a slope of 1/4. It is thus not parallel to the line y = 4x + 7.

Answer: 4y - x = 8

Hoped I helped

Answer:

There are 24 different ways using the letters from "math" can be rearranged.

Hopefully this helps! :)

Answer:

angle ABD=1/2 angle ABC ,Angle CBD =1/2 angleCBD

Step-by-step explanation:

The measure of angles ∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.

We have,

BD bisects the angle ABC makes two  equal halves angle.

So, < ABD= < CBD.

and ∠ABD= (8x + 35)°

∠CBD= (11x + 23)°

Substituting the values of the angles

(8x + 35)° = (11x + 23)°

35-23 = 11x- 8x

3x= 12

x= 4.

Putting x=4 in (i) we have,

∠ABD= 8(4) + 35

∠ABD= 67°

As ∠ABD = ∠CBD,

∠CBD= 67°

Now, ∠ABC= ∠ABD + ∠CBD

∠ABC= 67° + 67°

∠ABC= 134°.

Hence, the measure of m∠ABD= 67°, m∠CBD= 67° and m∠ABC= 134°.

Learn more about Angular bisector here:

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Answer:

C. Integer

Step-by-step explanation: Since the square root of 144 could either be -12 or 12, so it is an integer.

Answer:

it has to be 45.1.

Step-by-step explanation:

The reason why its 45.1 is because I added the equation all together including the negative number. I out that one in parentheses right next to the plus sign of 18.6. then added the last 2 numbers. and get 45.1. I'm not really good with stop by step explanations to be honest.

:(

Answer/Step-by-step explanation:

Given:

m<EFH = (5x + 1)°

m<HFG = 62°

m<EFG = (18x + 11)°

Required:

1. Value of x

2. m<EFH

3. m<EFG

SOLUTION:

1. Value of x

m<EFH + m<HFG = m<EFG (angle addition postulate)

(5x + 1) + 62 = (18x + 11)

Solve for x using this equation

5x + 1 + 62 = 18x + 11

5x + 63 = 18x + 11

Subtract 18x from both sides

5x + 63 - 18x = 18x + 11 - 18x

-13x + 63 = 11

Subtract 63 from both sides

-13x + 63 - 63 = 11 - 63

-13x = -52

Divide both sides by -13

-13x/-13 = -52/-13

x = 4

2. m<EFH = 5x + 1

Plug in the value of x

m<EFH = 5(4) + 1 = 20 + 1 = 21°

3. m<EFG = 18x + 11

m<EFG = 18(4) + 11 = 72 + 11 = 83°

Answer:

  the marked choice is correct

Step-by-step explanation:

It usually works well to follow directions: use technology. The attachment shows the use of the technology I like for short regression problems. For longer problems, a spreadsheet program is a good choice.

_____

In this problem, it is easy to eliminate the nonsensical answers, so no real use of technology is necessary.

First of all, the y-value for x=0 needs to be near 48, eliminating the last two choices.

Second, the minimum of the function corresponds to a positive x-value, so the coefficient of the x-term must have opposite sign from the coefficient of the x^2 term. This eliminates the second choice, leaving the marked choice as the only viable one.

Answer:

3

Step-by-step explanation:

(20a - 1) ÷ b

a = 2

b = 13

(20(2) - 1) ÷ 13

(40-1)÷13

39÷ 13

= 3

answer: 32a^{13}b

your welcome

Answer: y=-8/5x+2

Step-by-step explanation:

The equation for slope-intercept form is y=mx+b. We know that m is the slope and b is the y-intercept. We can determine that b=2 because the y-intercept passes through the y-axis. This line passes through the y-axis at y=2. Now, all we have to do is find the slope. We can do that by using any two points on the graph. Let's use (-5,10) and (5,-6). The formula for slope is [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

[tex]m=\frac{-6-10}{5-(-5)} =\frac{-16}{10} =-\frac{8}{5}[/tex]

With our slope, we can piece together the slope-intercept form equation.

y=-8/5x+2

Answer:

5 Green earrings

Step-by-step explanation:

Given that:

Total amount held = $51

Cost per pair of green earrings = $9

One time shipping fee = $6

How many pairs of green earrings did grace purchase?

Let the number of green earrings purchased = g

Then,

$9*g + $6 = $51

$9g + $6 = $51

$9g = $51 - $6

$9g = $45

g = $45 / $9

g = 5

Hence, the number of green earrings purchased = 5

Answer: x=15, y=10

*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.

Step-by-step explanation:

For this problem, we can use system of equations. Let's use x for one number and y for the other.

First Equation:

x+y=25

We get this equation because it states that the sum of the two numbers is 25.

Second Equation:

y=x-5

We get this equation because it says one number (y) is 5 less than the other (x).

Since we have two equations, we can use substitution method to solve.

[tex]x+(x-5)=25[/tex]                                  [distribute 1 to (x-5)]

[tex]x+x-5=25[/tex]                                     [combine like terms]

[tex]2x-5=25[/tex]                                         [add both sides by 5]

[tex]2x=30[/tex]                                                [divide both sides by 2]

[tex]x=15[/tex]

Now that we have x, we can plug it into any of the equations to find y.

[tex]x+y=25[/tex]                                          [plug in x=15]

[tex]15+y=25[/tex]                                         [subtract both sides by 15]

[tex]y=10[/tex]

Finally, we have our answer, x=15 and y=10.

Answer:25,-5

Step-by-step explanation:

Answer:

10 c

Step-by-step explanation:

4 c = 2 qt

8c + 2c = 10c

Answer:

i think the answer is b by far

Answer:B

Step-by-step explanation : DEF will be reflected across a line such that all of vertices of triangle D’E’F are in there own quadrant ways. The line of reflection is used to form triangle D’E’F’.

The line of reflection is  (B. x = 0 )

Answer:

5

Step-by-step explanation:

Given the following :

Number of workers - - TVs produced

0 - - - - - - - - - - - - - - - - - 0

1 - - - - - - - - - - - - - - - - - - 35

2 - - - - - - - - - - - - - - - - - 68

3 - - - - - - - - - - - - - - - - - - 99

4 - - - - - - - - - - - - - - - - - - 128

5 - - - - - - - - - - - - - - - - - - 155

We need to calculate the marginal product :

Workers - - - marginal product - - - value of m/p

0 - - - - - - - - - - - ____ - - - - - - - - - - - - - - __

1 - - - - - - - - - - - 35 (35 - 0) - - - - - - 35000

2 - - - - - - - - - - - - 33 (68 - 35) - - - - 33000

3 - - - - - - - - - - - - 31 (99 - 68) - - - - - 31000

4 - - - - - - - - - - - - 29 (128 - 99) - - - - - 29000

5 - - - - - - - - - - - - 27 (155 - 128) - - - 27000

The marginal product shows the change in output due to one additional unit of a certain input of production, in this case, number of workers. If the going wage of workers is $16,000, the company can afford to hire up to 5 workers and still make profit.

Answer:

Step-by-step explanation:

Let A,B, and C be the respective events that the first, second, and third drawn orange is good.

Therefore, probability that first drawn orange is good, P(A)=

15

12

​

The oranges are not replaced.

Therefore, probability of getting second orange good, P(B)=

14

11

​

Similarly, probability of getting third orange good, P(C)=

13

10

​

The box is approved for sale if all the three oranges are good.

Thus, probability of getting all the oranges good =

15

12

​

×

14

11

​

×

13

10

​

=

91

44

​

=0.48

Therefore, the probability that the box is approved for sale is 0.48

Answer:i

i) 7/15

ii) 7/15

Step-by-step explanation:

total: 10

good: 7

bad: 3

i) both are good

p(both good) = 7/10 * 6/9 = 42/90 = 7/15

ii) one good & one bad

p(first good & second bad) = 7/10 * 3/9 = 21/90 = 7/30

p(first bad & second good) = 3/10 * 7/9 = 21/90 = 7/30

p(one good & one bad) = 7/30 + 7/30 = 14/30 = 7/15

Answer:

Median is 78

Step-by-step explanation:

The median is the number where 50% of the other numbers are lower and 50% of the other numbers are higher, the middle, so in this case 78 is the middle number.

The median of the data sets 67, 98, 78, 75, 83, 44, and 98 will be 78.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The data is given below.

67, 98, 78, 75, 83, 44, 98

Arrange the data set in ascending order, then the data set is given as,

44, 67, 75, 78, 83, 98, 98

The number of terms in the data set will be 7.

Then the median of the data set will be 78.

More about the median link is given below.

https://brainly.com/question/300591

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Answer:

plz ask question correctly

Answer:

The  correct option is  B

Step-by-step explanation:

From the question we are told that

  The null hypothesis is  [tex]H_o : p = 0.10[/tex]

   The alternative hypothesis is  [tex]H_a : p > 0.10[/tex]

   The  p-value  is  [tex]p-value = 0.09[/tex]

   The  level of  significance is  [tex]\alpha = 0.025[/tex]

From the given values [tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis

So there is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

Answer:

yes

Step-by-step explanation:

yes because they are in the same line

Complete Question

Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10.

(a) What is the probability that professor will arrive at place B?

(b) If Professor Jin arrives at place B, what is the probability that she chooses road IV?

Answer:

a

  [tex]P(B) = 0.36[/tex]

b

  [tex]P(4 /B) = 0.62[/tex]

Step-by-step explanation:

From the question we are told that

  The number of ways from A to B is  n =  4

   The  probability if road 1 is selected is  [tex]P(1) = \frac{1}{8}[/tex]

   The  probability if road 2 is selected is  [tex]P(2) = \frac{1}{6}[/tex]

    The  probability if road 3 is selected is [tex]P(3) = \frac{1}{4}[/tex]

    he  probability if road 4 is selected is [tex]P(4) = \frac{9}{10}[/tex]

The probability that professor will arrive at place B is mathematically represented as

      [tex]P(B) = \frac{1}{n} * P(1) + \frac{1}{n} * P(2) + \frac{1}{n} * P(3)+ \frac{1}{n} * P(4)[/tex]

      [tex]P(B) = \frac{1}{4} * \frac{1}{8} + \frac{1}{4} * \frac{1}{6} + \frac{1}{4} * \frac{1}{4} + \frac{1}{4} * \frac{9}{10}[/tex]

      [tex]P(B) = 0.36[/tex]

If Professor Jin arrives at place B, what is the probability that she chooses road IV is mathematically represented as

      [tex]P(4 /B) = \frac{ \frac{1}{n} * P(4)}{P(B)}[/tex]

=>     [tex]P(4 /B) = \frac{ \frac{1}{4} * \frac{9}{10} }{0.36}[/tex]

=>      [tex]P(4 /B) = 0.62[/tex]

Answer:

(x - 5)(x - 3)

Step-by-step explanation:

Step 1: Write out expression

x² - 8x + 15

Step 2: Factor

(x - 5)(x - 3)

Answer:

2C - 58

Step-by-step explanation:

Chrissy = C

=> 2C - 58

I wrote 2C - 58 because 58 is decreased from 2 times C

=> 2 times C = 2C

=> 58 decreased = -58

=> 2C - 58

Answer:

The answer is B, don't listen to the dude that said is A... A is wrong

Step-by-step explanation:

De nada :)

There are 4 coordinates which means we can make 4 points on the graph.

4 points is the correct answer.

Given,

Kelsey is going to graph the ordered pairs that are represented by this table on a coordinate plane.

______________

|x| – 6 | –4   |  3  | 5|

|y| –4  | –6   | –6 | 0|

We need to find how many points should appear in Kelsey’s graph.

Coordinates are the points in a given plane.

The plane can be a two-dimensional plane or a three-dimensional plane.

In a two-dimensional plane the coordinates are represented as:

(x, y).

In a three-dimensional plane the coordinates are represented as:

(x, y, z).

Find the coordinates from the given table.

We have,

There are four x values and four y values.

So,

(x, y) = { (-6, -4), (-4, -6), (3, -6), (5, 0) }

We see that we can make 4 coordinates in the coordinate plane.

Thus there are 4 coordinates which means we can make 4 points on the graph.

Learn more about matching the coordinates with the points on the coordinate plane here:

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Answer:

Step-by-step explanation:

Let the initial point of of the sea level be 0. If the whale was initially 460 feet below sea level, then its distance from the surface of sea level to the 460ft below the sea level will be 460 - 0 = 460ft.

Also, if the whale rises up and breaches out of water to a height of 27 feet above sea level, then its distance from the surface of sea level to the 27ft above the sea level will be 0 - 27 = 27ft.

The vertical distance that the whale travels = distance from the sea level to 460ft below the sea level + distance from the sea level to 27ft above the sea level

The vertical distance that the whale travels  = 460ft + 27ft

The vertical distance that the whale travels  = 487ft